Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 1

1. The geometric mean of two numbers is 16 then their product is a.4

b. 256

c. -4

d. None of these.

2. npn =5040 then 'n' is a.6

b. 7

c. 8

d. 9

3. Two coins are tossed simultaneously the probability of getting both heads on the top is 𝟏

a.𝟐

b. 2

c. 4

𝟏

d.𝟒

4. The marks scored by a student is 75, x, 80, 82, 90, 65 & the average marks is 80. Then the value of x is a.40

b. 80

c. 98

d. 76

5. If g[X]= x2- 4x + 4 then the factor of g[X] is a. [x-1]

b. [x+2]

c. [x-2]

d. [x-4]

𝟐𝟎

6. Given cot Ɵ=𝟐𝟏 then tan Ɵ is 𝟐𝟎

𝟏𝟏

a.𝟐𝟏

𝟐𝟏

b.𝟏𝟎

c.𝟐𝟎

𝟏𝟎

d. 𝟏

7. The slope of the line whose inclination is 450 is a.

𝟏

b. √𝟑

√𝟑

c.1

d. 0

8. The distance between the points [2,3] & [6,6] is a. 10 units

b. 5 units

c. 6 units

d. 17 units.

II. Ansswer the following:

6x1=6

9. Express 3825 as product of prime factors 10.If A=[a,b,c,d,e] B=[a,c,e,f] then represent A-B in venn diagram. 11.Find the F[-1] if F[x] = 2x3+3x2-11x+6 12.State converse of basic proportionality theorem. 13.In the figure BC is a tangent to 2 circle with Centre O, AP is a diameter &∟QPC = 300 find ∟PAQ? 14.Find the surface area of sphere of radius 14 cm. 15.Find the smallest number that when divided by 5, 56 & 91 leaves remainder of 7 is each case. 16.In a group of passengers, 100 know kannada, 50 know English & 25 know both if Passengers know either kannada or English. How many passengers are in the group? 17.State Fundamental principal of counting. 18.How many diagonals can be drawn in a hexagon? 19.Two dice are thrown together. Find the probability that a sum greater 10 turn up?

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Model Maths Papers To Get Success 20.Rationalize

3√𝟓 √𝟔 - √𝟑 𝟑

21.Find the product of √𝟐 and √𝟒 22.The polynomials (ax3+3x2-13) & (2x3-4x+a) are divided by (x-3) if the reminder in each case is the same, find the value of 'a'. (OR) Find the quotient& reminder using synthetic division method (3x3-2x2+7x-5) ÷ (x+3) 23. Solve x2-7x+12=0 by formula method. 24. In 𝜟ABC, calculate “x" for which DE will be parallel to AE. 25.Show that (1-sin2Ɵ) sec2 Ɵ =1 26.Find the distance between the points (2,3) and (6,6) 27.The CSA of a cone is 308 cm2 and slant height is 14 cm find the diameter of the base of the cone.

OR

The diameter of a garden roler is 1.4cm & 2m long how much area will it cover is 5 revolutions? 28. Draw a circle of radius 3.5cm & construc t a pair of tangents such that the angle between them is 400 29. The slant height of a frustrum of a cone is 4cm and the Metre to D 150 100

perimeter of its circular base are 18cm and 6cm respectively. 70 to C

To E 80 80

Find the curved surface area of the frustrum. 30. Draw a plan from the recordings given below (scale

30

40 to B

20m=1cm)

From A

III

Answer the following:

6x3=18

31.The third term of an A.P is 8 and 9th term of the A.P xceeds three times the third term by 2. Find the sum of its first 19 terms. 32. Calculate Standard Deviation of the given data C.I

0-10

10-20

20-30

30-40

40-50

F

7

10

15

8

10

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Model Maths Papers To Get Success 33.If one root of equation x2+PX+q=0 is 3 times other P.t 3p2=16q. (OR) The sum of two natural number is 8 determine the number if sum of their Reciprocal is 8/15 34.Prove that area of similar triangle have the same ratio as thesquare of the corresponding attitudes.

OR

In trapezium ABCD, AB||CD and ΔAED III ΔBEC. Prove that AD=BC 35.If∟A=600 and ∟B=300 prove that, tan (A-B) = tan A-tanB 1+tanAtanB OR A tall building casts a shadow of 300m.Long when the sun's attitude (elevation) is 30 0 find the height of the tower. 36.If two circles touch each other externally the centres and a point of contact are collinear prove.

OR

Prove that the tangents draw from an external point to a circle. a. Are equal.b. Subtend equal angles at the centre. c. Are equally inclined to the line joining the centre and the external point. 𝟏

𝟏

37.In a H.P T5=𝟏𝟐 and T11=𝟏𝟓 find T25.

OR

Find the G.P of S10:S5 = 33:32 and T5 = 64. 38.Draw the graph of y=x2+x-6 and find the Roots. 39.Draw two direct common tangents to two circles of radii 5 cm. And 3cm having their centres 11cm apart measure the length of D.C.T and verify. 40. State and prove Pythagoras theorem.

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Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS Set - 2

1.The AM between 10 and 30 is .................................. a. 10

b. 15

c. 20

d. 25

2.The HCF of 28 and 72 is ................................ a.2

b. 4

c. 1

d. 6

3.Three coins are tossed simultaneously the probability of getting all the three heads up is ................................. 𝟑

a. 𝟖

𝟏

𝟖

b. 𝟖

𝟏

c. 𝟑

d. 𝟑

4.The maximum number of diagonals that can be drawn in a polygon is 9. Then the number of sides is ........................................ a.5

b. 6

c. 7

d. 8

5.The arithmetic mean of a set of scores is 70 and C.V is 6, then S.D is ............................... a.4

b. 4.2

c. 0.42

d. 0.4

6. If f(x)=2x3+3x2-11x+6, then f (-1)= ------------------a.1

b. 22

c. 0

d. 6

7.If sinx=3/5, then cosec x = -------------a.

𝟑 𝟓

b.

−𝟑

c.

𝟓

𝟓 𝟑

8. The slope of a line whose inclination is a. 1 II

𝟏

b.𝟔

c.

d. 600

𝟏 √𝟑

−𝟓 𝟑

is -----------------d. √𝟑

Answer the following:

1x6=6

9.Express 1440 as a product of prime factors. 10.Draw the venn diagram representing AU[B∩C]. 11.Find the degree of the polynomial √𝟑x2+19x+14. 12.How many transverse common tangents can be drawn for two externally touching circles. 13.In the A ABC, DE || BC, AD = 2cm, DB = 3cm, AE = 6cm Find EC. 14.Find C.S.A of a cone given radius of the base 7 cm and slant height 10 cm. III

Answer the following question.

2x16=32

15.Prove that 3+ √𝟓 is an irrational number. 16.In a group of 50 people. 30 like tea, 25 like coffee and 16 like both. Find, a.The number of people who like only tea or coffee. b.The number of people who like neither tea nor coffee.

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Model Maths Papers To Get Success 17.How many 3digit numbers can be formed by using the digits 1,2,3,4,5 & 7 without repeating any digit. 18.If 6Pr=360 & 6Cr=15. Then find the value of 'r'. 19.Simplify by rationalizing the denominator.

√𝟔 - √𝟑 √𝟔 + √𝟑

𝟑

20.Find the product of √𝟐x √𝟑 21.Find the zeroes of the polynomial x2-2x-15 and verify.

OR

If x=1 is a zero of the polynomial f(x)= x3-2x2+4x+k, then find the valur of k. 22.Solve by the method of completing the square 2x2+5x-3=0. 23.Find the value of

; tan2 600+2tan2 450.

To E (in mts)

24.Find the slope of the line joining the points (3,-2) and (4,5). 25.In a circle of radius 5cm draw two radii such that the angle between them is 600. Construct tangents at the ends of the radii. 26.Draw a plan from the recordings given below.

350 To D 100 300 To C 75 250 150

27.A sphere of radius 18 cm is melted and recasted into a wire of radius 0.4cm. Find the length of the wire .

OR

150 to F

100 to G

To B 50 50 From A

Find the volume of a cone formed by the rotation of a right angled triangle whose sides containing the right angle are 6.3 cm and 10 cm.

28. . Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm. 29.In the AABC, XY||BC, XY=3cm, AY=2cm, AC=6cm. Find BC. 30.A card is drawn from a pack of 52 cards. What is the probability of getting (a) A queen (b) A Red King. IV

Answer the following:

3x6=18

31.Find the sum of all natural nos between 200 & 300 which are divisible by 6. 32.Calculate the standard deviation.

C.I

10-20

20-30

30-40

40-50

50-60

60-80

F

2

5

12

19

9

4

33.Difference between the squares of two numbers is 80. The square of the smaller number is 8 times bigger than the bigger number. Find the two numbers

OR

The diagonal of a rectangle is 60 mt greater than the longer side and longer side is 30 mt greater than the smaller side. Find the measure of the sides.

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Model Maths Papers To Get Success 34.In the figure DE||BC and CD||EF. Prove that AD2 = AF x AB. 35.Show that SinƟ 1+cos Ɵ

+

1+cos Ɵ = 2 cosec Ɵ SinƟ

OR

The angle of elevation of the top of a Flagpost from a point on a horizontal ground is found to be 300 on walking 6mt towards the post, the elevation increased by 150. Find the height of the flag post. 36.Prove that when two circles touch each other externally then the centres of the two circles and the point of contact are collinear.

OR

Prove that the tangents drawn to a circle from an external point. a.Are equal.

b.Subtend equal angles at the centre.

c.Are equally inclined to the line joining the external point and the centre. V

Answer the following.

4x4=16

37.A T.V manufacturering company manufacture 600 T.V sets in the 3 rd year and 700 T.V sets in the 7th year. If the production increases in A.P. Find (a) The no. of T.V sets produced in the first year. (b) Total no. of T.V sets produced in 7 years.

OR

Find 3 terms in GP whose sum and products are respectively 31 and 125. 38.Solve graphically x2-8x+7=0. 39.State and prove Pythagoras theorem. 40.Construst D.C.T to two circles of radii 5 cm and 2.5 cm whose centres are 10 cm apart

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Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers MATHEMATICS

Set - 3

𝟖

1.The H.M between two terms is 𝟑, If one term is 2, then the other term is -----a.4

b.2.3

c. 2

d. 1

c. 4

d. 5

2.If nc2 =10, then the value of 'n' is ---------a.2

b.4 3

3.A die is rotted, the probability of getting the number 5 is------𝟏

a.`𝟏𝟐

𝟏

b.𝟑𝟔

c.

𝟏 𝟔

𝟏

d. 𝟓

4.If mean score [x]=30 and the co-efficient of variation is 0.2, then the standard deviation is ----------a.0.06

b.6

c.0.6

d. 60

5.If x=1 Ts a zero of the polynomial f(x]=x2-2x2+4x+k, then the value of Kis ----a.-2

b.2

c.-3

d. 3 𝟏

6.The value of Sin 300 is ---------------a.0_______

b. 𝟐

c.2

d.

𝟏 √𝟐

7.The angle of inclination of straight line whose slope is “O” is -------------a.00

b.300

c. 600

d. 900

8.The slope of the line passing through the points P[7,3] and Q (0,-4).Then the slope of the line parallel to PQ is----- a.0 II

b.2

c.1

d. 3

Answer the following:

1x6=6

9.State the Euclids division lemma. 10.I U={1,2,3,4,5,6,7,8}. A={1,2,3} B={2,3,5} find (AUB)1. 11.Give an example for quadratic polynomial. 12.In a right angled triangle ΔABC, B=900, Ac=17 cms and AB=8cms. Find BC. 13.In the adjoining figure, what is the measure of ∟ACB. [AB is diameter]. 14.Find the TSA of a hemisphere of radius 7 cm. III

Answer the following:

2X16 =32

15.Prove that 3+ √𝟓 is an irrational number. 16.In a committee, 60 people speak Kannada, 25 people speak English and 10 speak both kannada & English. How many people speak atleast one of these two languages. 17.How many words [with (or) without dictionary meanings] can be made from the letters in the word. “LASER” all letters are used at a time assuming that no letter is repeated it. 18.How many diagonals can be drawn in a dodecagon. 7 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 19.A coin is tossed repeatedly twice. Find the probability of getting (a) Atleast one head 20.Rationalise the denominator & Simplify.

(b) No head. 3√𝟓 √𝟔-√𝟑

𝟑

𝟒

21.Find the product of √𝟐 and √𝟑 22.Find quotient and remainder using “synthetic division” method. (6x4-29x3+40x2-12)÷ (x- 2) OR What must be substracted from (x3+5x2+5x+8), so that the resulting polynomial is exactly divisible by (x2+3x-2). 23.Find the value of “m” so that the equation x2+4x+[2m+ 1/2] =0 has one root equal to zero. 24.In the adjoining figure ∟ABC=900 and ∟AMP=900, then prove that CA/PA = BC/MP. 25.Find the angle of elevation if an object is at a height of 50m on the tower and the distance between the observer and the foot of the tower is 50m. 27.Find the distance between the pairs of points are (-4,5) and (12,3). 28.Draw a circle of radius 3.5 cms and construct a chord of length 6cms in it. 29.The curved surface area of cylindrical pipe is 550 cm2. If the height of the pipe is 25 cms. Find the diameter of the base. 30.Draw a plan of a level ground using the information given below. IVAnswer the following:

3x6=18

Meter to 'C' To D 120 220

31.Verify Eulers formula for the following Polyhedra.

210

32.The sum of six (6) terms which forms an AP is 345. The difference

120 To E 80 80

between the first and last terms is 55. Find the terms.

From A

33.Find the standard deviation for the given data. Class Intervals 1-5 6-10 11-15 16-20 Frequency (f) 2 3

4

1

34.Anirudh bought some books for 60 and had bought 5 more books for the same amount. Each book would have cost him one rupee less. Find the number of books bought by Anirudh and price of the each book

OR

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200 to B

Model Maths Papers To Get Success A dealer sells an article for 24 and gains as much percent as the cost price of the article. Find the cost price of the article. 35. InΔABC, ABC=900, BD ┴ AC, If AB='C' units, BC='a' units, BD='P' units, CA='b' units. Prove that l/a2+1/c2=1/p2.

OR

In an equilateral ΔABC, the side BC is produce to 'D'.Such that BC=CD. Prove that AD2=3AB2. 36.Prove that Sin Ɵ + 1+cos Ɵ

1+cos Ɵ = 2 cosec Ɵ Sin Ɵ

OR

Prove that 1+ Sin Ɵ = [Sec Ɵ +tan Ɵ ]2 1- Sin Ɵ 37.Prove that “If two circles touch each other extremely the centres and the point of contact are collinear”.

OR

Prove that “The tangents drawn from an external point to a circle are equally inclined to the line joining the centre and the external point. ”

V

Answer the following questions:

4X4 = 16

38.Find the three terms of GP whose sum is 7 and the product of their reciprocal is 1/8. OR 𝟏

Find the GP the ratio of 5th term and 10th term is 32:1 and T7 = 𝟑𝟐. 39.Solve graphically: x2+x-6=0. 40. Prove that “If a straight line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally”.

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Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 4

1.The sum to infinity of the GP 2+ 2/3 + 2/9 + ----- is a.4

b. 9

c. 3

d. 8

2. If 9P5 + 5.9P4 = 10Pr , then the value of r is , a. 4

b. 5

c. 9

d. 10

3.A letter is chosen at random from the letters of the word MATHEMATICS, let the event be E, the probability that the chosen letter is M then P(E) = -----------𝟑

𝟒

a. 𝟏𝟏 4.

𝟏

b. 𝟏𝟏

𝟐

c. 𝟏𝟏

d. 𝟏𝟏

The value of variance is 6.25, then the standard deviation is , a. 0.25

b. 0.025

c. 25

d. 2.5

5. If Sin x=3/5, then cosec x is_ 𝟑

𝟓

a. 𝟓

𝟒

b.𝟑

𝟓

c. 𝟓

d. 𝟒.

6.The equation of straight line is 3x+2y=0, then its slope is equal to ----------𝟑

𝟐

a. 𝟐

b. 𝟑

c.

−𝟑

d.

𝟐

−𝟐 𝟑

.

7.If the m2-n2 and 2mn are the two sides of the right angled traiangle, then the hypotenuse is ----a. m2-n2 8.If A=

√𝟑 2 a 𝟒 𝟑

a. 𝟏𝟏 II

b. m4+n4

c. m2 + n2

d. m4-n4

and if A = 16√ 3 , then the value of a = -----------b. 16

c. 8

Answer the following:

𝟑

d. 𝟏𝟏 6X1 =6

9.Use Euclid's division algorithm to find the H.C.F of 237 and 81. 10.State De Morgan's I and II Law. 11.In ΔABC, ∟ABC=900, BD ┴ AC, If AB='C' units, BC='a' units, BD='P' units, CA='b' units. Prove that l/a2+1/c2=1/p2. 12. In the figure ∟QOR = 1000, then find ∟QPR. 13. Find the volume of a sphere whose radius is 10.5cm. 14.Find the rationalizing factor of 5√𝒂 + 𝒃 III

Answer the following:

16X2 =32

15.Prove that 3 -√𝟓 is an irrational number. 16.Everybody in a function shakes hand with everybody else. The total number of handshekar is 45. Find the number of persons in the function. 17.In how many ways can 6 women draw water from 6 wells ? 10 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 18.Rationalise the denominator and simplify.

4√𝟑+√𝟐 √𝟑 + √𝟐

𝟏

19.Simplify 4 √𝟐 –

𝟏 𝟐

√𝟖

20.What must be added to the polynomial [7x3+4x2-x-10] so that the resulting polynomial is exactly divisible by [2x2+3x-2]

OR

Divide p[x] = 2x4 - 5x2 + 15x - 6 by g[x] = x-2 and verify division algorithm. 21.Solve √𝟐x2+7x+5√𝟐 = 0 22.Show that [1+tan2Ɵ] [1-sinƟ ] (1+sinƟ ] = 1. 23.The distance between the points [3,1) and [0, x) is 5 units. Find x. 24.Construct two chords of length 6cm and 8cm on the same side of the centre of a circle of radius 4.5 cm. Measure the distance between centre and the chords. 25. Plan out and find the ares of the field from the data given from the surveypr's field book. 26.A solid cylinder has a T.S.A of 462 cm2. Its CSA is

Metre to E

one third of its TSA. Find the volume of the cylinder. OR A right circular metallic cone of height 20cm and base radius 5 cm is melted and recast into a sphere. Find

350 To D 100

300

To C 75

250

150to F

150

the radius of the sphere.

100 to G

50

27. The inner radius of a hollow sphere is 10 cm. Find

From A

its volume.. 28.In the given figure, AE || DB, BC=7cm BD=5cm, DC=4cm. If CE=12cm find AE and AC. 29.Three cards are drawn at random from a pack of 52 cards. What is the probability that all the three cards are king. 30.The sum of 6 terms which form an AP is 345. The difference between first and last term is 55. Find the terms. 31. In rhombus ABCD, the diagonals AC and BD intersect at E. If AE=x, BE = x+7 andAB=x+8, Find the lengths of the diagonals AC and BD. 32.In a study of diabetic patients in a village, the following onservation

Age in years

10-20

20-30

30-40

40-50

50-60

60-70

No. of patients

2

5

12

19

9

4

were noted. Calculate the mean and standard deviation. Also interpret the results. 33.Prove that if the area of two similar triangles are equal then they are congruent. 11 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 34.From the top of a building 16 mt high, the angular elevation of the top of a hill is 60 0 and the angular depression of the foot of the hill is 300. Find the height of the hill.

OR

SinƟ + 1+cosƟ = 2 cosecƟ 1+cosƟ

SinƟ

35.Prove that the tangents drawn from the external point to a circle.aAre equal.b.Subtend equal angles at the centre.

OR

In the figure two circles touch each other externally at p. AB is a direct common tangent to these circles. Prove that (a) tangent at p bisects AB at Q (b) ∟APB=900. 36.A person saved every year half as much he saved the previous year. If he totally saved Rs. 19,375 in 5 years. How much did he save the first year? OR If 'a' be the arithmetic mean between b and c and 'b' the geometric mean between a and c, then prove that 'c' will be the harmonic mean between a and b. 37.Solve graphically x2 + x - 6=0. 38.In a right angled triangle the square on the hypotenuse is equal to the sumof the square on the other two sides prove it. 39.Construct a direct common tangent to two circles of radii 4cm and 2cm whose centres are 8cm apart. Measure and verify the length of the tangent. 40. In an AP whose first term is 2, the sum of first five terms is one fourth the sum of the next five terms. Show that T20 = –112. Find S20 .

OR

The third term of an A.P is 8 and the ninth term of the A.P exceeds three times thethird term by 2. Find the sum of its first 19 terms.

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Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 5

1.The angle of inclination of straight line whose slope is “1” is -------------a.00

b.300

c. 600

d. 450

2. The first term and the common ratio of a GP are a and r respectively, then the GP is -----------------b. a, ar, ar2

a. a, a+r, a+2r

c. a.r2, ar3

d. r2 r3 r4

3.nc8 = nc12 then the value of n is ----------------a.4

b. 12

c. 8

d. 20

4.Probabilty of an event A is given by -----------a. n(A)/n(S)

b. na.ns

c. n(S)/n(A)

d. na+ns.

5.Formula used to calculate the harmonic mean is ----------------a. a+b/a+b

b. a+b/2ab

c. 2ab/a+b

d. √𝒂𝒃

6.If f(x) = x2+7x-10, then the value of f(x) is -------------------a.8

b. 16

c. 25

d.

18

7. tan2 60+ 2 tan2 45 = -----------------a.8

b. 9

c.12

d. 5

8.The formula used to calculate co-efficient of variation is------------------𝝈

a.𝑿X100.

𝑿

b. 𝝈X100

c.

𝝈𝑿 𝑿 𝟏𝟎𝟎

𝟏𝟎𝟎

d. 𝝈 𝑿 𝑿

9. The slope of the line whose inclination 600 is ----------------a.√𝟑

b.

√𝟑 𝟐

c. 1

d. 0

10. Express 6762 as a product of prime factors. 11. If U={1,2,3,4,5} and A={2,4} then find A1. 12. Find the degree of the polynomial 2x+4+6x2. 13. In the triangle ΔABC, DE||BC AD/DB = 2/3, AE = 3.7, then find EC. 14.Write the formula used to calculate the T.C.T. 15.Find the surface area of a sphere of radius 21 cms. II Answer the following

2x16=32

16.Prove that 2 + √5 is irrational number. 17.In a class 50 students offered maths 42 offered biology 24 offered both the subjects. Find the number of students who offer,a. Mathematics only b. Biology only.And also find the total number of students in the class. 18.nPr = 840, ncr = 35, find n. 13 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 19.A committee of 5 is to formed out of 6 men and 4 ladies. In how many ways can this be done. When at least 2 ladies are included. 20.Show that (x+2) is a factor of polynomial x3 - 4x2 - 2x + 20. OR Find the quotient and remainder of (x3+x2-3x +5) ÷ (x-1). 21.If one root of the equation x2+px+q=0 is 3 times the other. P.T 3p2=16q. 𝟑

𝟓

22.Find the product of √𝟐 and √𝟑 23.Simplify

√10 √5 + √3

24.Draw the plan for a recordings from the Survey's field work book given below (Scale 20 mts = 1 cms).

Metres D

80

120

60C

100

40 to B

50 From A

25.Construct tangents to a circle of radius 4cm from a point whose distance from the centre equal to, to the diameter of the circle. 26.Prove that (1+tan2Ɵ) cos2 Ɵ =1. 27.A clown's cap is in the form of a right circular cone of base radius 7 cm and height 24cm. Find the area of the sheet required to make 10 such caps. 28.Verify Euler's formula for the given netweork. 29.The distance between the points (3,1) and (0,x) is 5 units. Find x. 30.There are 30 boys and 25 girls in a class. A student is chosen at radam. Find the probability that the chosen students in a (a) Boy(b) Girl. 31.At a certain time of the day a tree costs its shadow 12.5 feet long. If the height of the tree is 5 feet. Find the height of another tree that costs it's the height of another tree that costs its shadow 20 feet long at the same time.

OR

In the trapezium ABCD AB||CD, AB=2CD and area of ΔAOB =84cm2. Find the area of ΔCOD.

14 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 32.Find the four numbers in AP such that the sum of 2nd and 3rd terms is 22 and the product of 1st and 4th terms is 85. 33.The distribution of the ages in years of 20 persons in a locality are recorded as follows. Find the standard deviation. Ages

30-34

35-39

40-44

45-49

50-54

No. of persons

2

5

6

5

2

34.Anirudh bought some books for 60 and had bought 5 more books for the same amount. Each book would have cost him one rupee less. Find the number of books bought by Anirudh and price of the each book. 35.Prove that

Sin Ɵ 1+cos Ɵ

+ 1+cos Ɵ = 2 cosec Ɵ Sin Ɵ OR

From the top of a building 50√𝟑 m heigh the angle of depression of an object on the ground is observed to be 450. Find the distance of the object from the building. 36. If two circles touch each other, the centres and the point of contact are collinear. OR The tangents drawn from an external point to a circle. a.Are equal.b.Subtend equal angles at the centre. c.Are equally inclined to the line joining the centre end the external point. IV Answer the following :

4x4=16

37.Find 3 terms in GP whose sum and product is 21 and 216. OR The sum of 4th and 8th term of an AP is 24 and the sum of 6th and 10th terms of the same AP is 44. Find the first three terms. 38. y= 2x2 and find the value of √𝟕. 39.Prove that in a right angle triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. 40.Construct a transverse common tangent of two circles of radii 3cms and 2cm with their centres 9 cms a part measure the length of the tangent and verify

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Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS Set - 6

1.If in a geometric progression, T7:T4= 8:1, then the common ratio is -------------b. ±23

a. ±2

c.+2

d. -2

c.7

d. -7

2.If np4=20np2 then the value of n ------------------a.+2

b.-2

3.The sum of oneincident and its alternate incident ----------------a.0

b.1 c.

0 or 1

d. 2

4.The variation co-efficient of a term is 12 and its average score is 50, then the standard deviation is -----------------a.60

b.6

c.600

d. 0.6

5.In equation kx2+3x+k the factor is -------------a. -6/5

b. -5/2

c. -5/6

d. 6/5

6If tanx = 7/24, then cotx = -----------a.7

b.24

c.7/24

d.24/7

7.The equation of a line is 3x-4y=5. Find its slope and y intercept are --------------. a. 3/4 , -5/4

b. -3/4 , 5/4

c.3/4 , 5/4

d. -3/4 , -5/4

8.The distance between the points P (4, -3) -----------------a.3cm

b. 1cm

c. 5cm

II. Answer the following:

d.

6cm. 6x1=6

9.Prove that 2 -√𝟑is a irrational number. 10.If U={0,1,2,3,4} and A={2,3,4}, B={0,2,3} then find A1∩B1. 11.If p(x] = x3-4x2+3x+1 is a polynomial when it is divided by [x-1]. Find the remainder. 12.Write the formula for finding the length of direct common tangent. 13.If the area of a sphere is 616 sq. cm, find its radius. 14.In the figure ∟PTO = 300 and PT is a tangent find ∟POT. IIIAnswer the following:

16x2=32

15.Find the smallest number that, when divided by 35, 36 and 91 leaves remainders of 7 in each case. 16.In a group of 25 people, 8 people drink only tea, 7 people drink only coffee and 4 people drink both tea and coffee. Find out the number of people who take neither tea nor coffee. Verify using venn diagram.

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Model Maths Papers To Get Success 17.Write the formula to find our the diagonals of a polygon. How many diagonals can be drawn in a octagon? 18.In a programme each one shake their hands with another. If the total number of shaking hands are 45, then find the number of persons who participated in the programme. 19.Two dice 1-6 are throwntogether. Find he probability of getting a sum equalto8 20, Rationalise the denominator and simplify. √5 + √3 √5 - √3 𝟏

21. If x = 2√𝟔 + 5 then find the value of x + 𝒙

22. Find the quotient and remainder on dividing. 23.Three numbers are in the ratio 1/3 : 1/5 : 1/6. If the sum of their squares is 644. Find the numbers. 24. If the polynomials (ax3+4x2+3x+4) and (x3+x2+4x+a) when divided by (x-3) then the remainder is equal then find the value of 'a'. 25. Prove tan100 tan150 tan 750 tan 800 = 1. 26. Draw a paln of the field using the following data. To D (in mts) 450 3000 to E 100

300 to C

250 100

50 to B

From A 27.In a circle of radius 3.5cm, draw two radii such that the angle between them is 400. Draw two tangents. 28. Find the TSA of a hemisphere of radius 5 cm.. 29.Prove that the verticles A[1,3], B[-3,0] and C[4,1] are equilateral triangle. 30.A right circular cone of height is 81cm and radius of base 16cm is melted and recast into a right circular cylinder of height 48cm. Find the radius of the base of the cylinder. IV

Answer the following:

6x3=18

31.If S10 : S5 = 33:32 and T5 = 64, then find G.P.

17 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 32.Find the standard deviation for the following data. C.I

10-19

20-29

30-39

40-49

f

14

9

20

7

33.The sum of two numbers is 8. Determine the numbers, if the sum of their reciprocal is 8/15. OR Sowmya takes 6 days less than the number of days taken by Bhagya to complete a piece of work. If both sowmya and Bhagya together can complete the same work in 4 days. In how many days will Bhhagya alone complete the work? 34.In ΔABC x and y are midpoint of AB and AC. Prove that the area of ΔABC is fourth of area of ΔAXY.

OR

If in a trapezium ABCD AB || CD and ΔAED ||| ΔBEC, then prove AD =BC. 35.Prove that the tangents drawn from an external point to a circle. a.Are equal.b.Subtend equal angles at the centre. c.Are equally inclined to the line joining the centre and the external point. OR If two circles touch each other, the centres and the point of contact are collinear. 36.Prove:

1 - tan2A = 1-2 Sin2A. 1 + tan2A

OR

Two observes are 1 km a part in the same vertical plane as a balloon, but on opposite sides of it, found the angles of elevation to be 600 and 450. How high is the balloon above the ground? V

Answer the following:

4x4=16

37.A dealer buys steel vessel in an installment scheme. He returns money in 12 months. In first month 1800rs, in the second month 1750rs and in the third month 1700rs like wise. If the total price of the vessel is 15000rs, then find, a)The amount paid in 12 months.b)The excess amount he paid.

OR

A Spiral is made up of successive semicircles, with centres alternatively at A and B , starting with centres at A, of radie 0.5cm . 1cm , 1.5cm , 2cm ……as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles ? 38.Draw the graph of x2-2x-3=0 39.State and prove Pythogorus theorem . 40. Two circles of a diameter 8cm and 4cm are at a distance of 11cm. Draw the direct common tangent. Measure its length.

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Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 7

1. If 3, x, 4 is in H.P, then the value of x ---------a. 24/7

b. 5

c. 21

d. 7/24

2. If npr = 336 and ncr = 56, then the value of (n+r) -------a. 8

b. 11

c. 24

d. 13

3. Two coins are tossed together what is the probability of getting exactly one head. a.1/4

b. ¾

c.1/2

d.2/3

4.If ΣD2 = 1044, N= 10 then standard deviation is ------------a.

1.044

b. 10.44

c. 10.2

d. 104.4

5. If f(x) = x2+7x-10, then f(2) = a. 3

b. 5

c. 8

d. 10

c. Cos2A

d. Cosec2A

6. 1 + cot2 A = -------------a. tan2A

b. Sin2A

7. The co-ordinates of the midpoint of line joining the points (2,3) and (4,7).is ----a. (3,5)

b. (7,3)

c. (3,4)

d. (8,3)

8. The slope of a straight line passing through the points (x1,y1) and (x2,y2) 𝒙 −𝒙

a.𝒚𝟐 − 𝒚𝟏 𝟐

𝟏

𝒙 −𝒙

b. 𝒚𝟏 − 𝒚𝟐 𝟏

𝟐

𝒚 −𝒚

𝒙 .𝒙

c. 𝒙𝟐 − 𝒙𝟏 𝟐

d. 𝒚𝟐 .𝒚𝟏

𝟏

II. Answer the following

𝟐

𝟏

6x1=6

9. Find the prime factor of 120. 10.Draw venn diagram of AIUBI. 11.Write relation between p(x), g(x), q(x) and r(x) 12.In the figure, the chord AB = chord CD. If OP=x then what is the length of OQ ? 14.If the radis of 2 spheres are in the ratio 4:5, then what is the ratio of their volume? 15.If in the figure AB = 8cm, CE = 2cm and BD = 16cm, then find the length of CD. III

Answer the following:

16x2=32

16.In a school of the strength in 8th, 9th and 10th standards are respectively 48, 42 and 60. Find the least number of books required to be distributed equally among the students of 8 th, 9th and 10th standards.

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Model Maths Papers To Get Success 17.In a medical examination of 150 people, it was found that 90 had eye problem, 50 had heart problem 30 had both complaints, what percentage of people had either eye trouble or heart trouble. 18.What is fundamental principal of counting? How many 3 digit even numbers can be formed using the digit 3, 5, 7, 8, 9 if the digits are not repeated? 19.A Polygon has 44 diagonals, find the number of sides. 20.If A is an event of a random experiment such that p[A] : p[A]1 = 6:15, then find (a) p[A] (b) p(A)1 𝟑

𝟒

21.Find the product of √𝟐 x √𝟐. 22.Find the product of following surds:[ √𝟕𝟓 - √𝟒𝟓] [√𝟐𝟎 +√𝟏𝟐] 23.Find the quotient and remainder using synthetic division. 4x 3-16x2-9x-36 ÷ x+2. OR What must be added x3-2x2-12x-9, so that is exactly divisible by x2+x-6 24.Form a quadratic can whose roots are a/b & b/a, if a & b are roots of x2 – 3 = -2. 25In the figure PQ || BC & AP = 3cm, AR = 4cm, AQ = 6cm & AB = 5 cm. Then find the length of AB. 26.If 13 SinƟ = 5, then find the value of

5 SinƟ - 2 Cos Ɵ tanƟ

27.Construct a pair of tangents to a circle if radius 3 cm from a point 5cm. 28. Find the volume of a sphere whose surface area is 154 cm2 . 29.Draw a plan of the field using the following data. To D in mts 140 100 E 140

80C

40 100

60B

From A

30.Prove that a line passing through the points (4,5) and (0, -2) is perpendicular to the line joining (2, -3) & (-5, 1).

20 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 31.The diameter of a metallic sphere is 18cm. It is melted & drawn into a wire having diameter of cross section 0.4cm. Find the length of the wire . IV

Answer the following:

6x3=18.

32.Find the three no's in A.P whose sum & products are 21 & 231 33.Find the std deviation for the following data. x

3

8

13

18

23

f

7

10

15

10

8

34.Nandana takes 6 days less than the no. of days taken by Shobha to complete a piece of work. If both Nandana and shobha together can complete the same work in 4 days, in how many days will Shobha alone complete the work? OR The ages of Kavya and Karthik are 11 years and 14 years. In how many years time will the product of their ages be 304. 35.In a ABCD trapezium if AB || CD & ΔAED III ΔBEC, then prove AB = BC.

OR

Prove that tangents drawn from an external point to a circle a.Are equal.b.Subtend equal angles at the centre. c.Are equally inclined to the line joining the centre and the external point. OR If two circles touch each other, the centres and the point of contact are collinear. 36. SinƟ 1+cosƟ

+

1+cosƟ = 2 cosecƟ

OR

SinƟ

From a point 50 m above the ground the angle of elevation of a cloud is 30° and the angle of depression of its reflection in water is 60°. Find the height of the cloud above the ground.

V

Answer the following:

4X4 =16

37.A sum 700rs is given to the students of a school based on the managing sources as 7 prize. Each of the prize rate varies.

OR

A person saved every year half as much he saved the previous year. If he totally saved 19,375 in 5 years, how much did he save the first year? 38.Solve with the help of graph. x2+x-12 = 0. 30.State & prove phthagores problem. 40.Two circles of radius 3cm & 1.5cm are at a distance of 12cm. Draw transverse common tangents & measure its length. 21 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 8

1)IfthethirdtermofaGeometicProgressionis2,thentheProductofitsfirstfive termsis,( A)52

(B)25

(C)10

(D)15

2) If nc8 = nc12 then the value of n is -------------A) 10

B) 20

C) 25

D) 30

C)10

D)100

3) Probability of an Impossible event is -------------A) 0

B)1

4) IfMeanscoreX=20andthecoefficientofvariationis0.1,thentheStandard deviationis, (A)2

(B)0.2

(C)20

(D)0.02

(C)8

(D)10

5) If f(x) =x2+7x-10thenthevalueoff(2)is, (A)3

B)5 𝟕

6) If tanx = 𝟐𝟒 then COtx is --------------A)7

B) 24

𝟕

C)𝟐𝟒

D)

𝟐𝟒 𝟕

7) Thecordinates ofthemidpoint oftheline segmentsjoiningthepoints(2,3)and(4,7)is, (A)(3,5) 8)

(B)(7,3)

(C)(3,4)

(D)(8,3)

Theslope oftheline joiningthepoints(3,-2)and(4,5)is, (A)3

(B)5

(C)7

(D)8

II. Answer the following 9)

(1x6=6)

Express 6762 as a Product of Prime factors.

10) If Universal Set U={1,2,3,4,5,6,7,8} and sub set A= {1,2,3} findA1 11) Findthezero ofthePolynomialx2+2x+1 12) In ΔABC,∟ABC=900,BD ┴AC. If BD=8cm and AD=4cm find CD. 13) In the figure ‘O’isthe centre of the circle, PT is a tangent and if ∟PTQ=300,find ∟POT 14) FindtheSurfaceAreaofasphereofradius7cm III. Answer the following 15) Prove that 5- √𝟑

is an Irrational number.

16) In a college,60students enrolled in Chemistry,40 in Physics, 30 in Biology and 15in Chemistry and Physics, 10inPhysics and Biology,5in Biology and Chemistry.No one enrolled in all the three subjects.Findhowmanyareenrolledinatleastoneofthesubjects. 22 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 17) Classifythefollowing intoPermutationsandCombinations. a) Fivedifferentsubject bookstobearrangedonashelf . b) Thereare8chairsand8peopletooccupythem. c) Inacommitteeof7persons,achair person,asecretary andatreasurerareto bechosen. d)Fivekeysaretobe arrangedinacircularkeyring. 18) Acommitteeof5istobeformedoutof6menand4ladies. Inhowmayways canthisbedonewhenatleast2ladiesareincluded. 19) Rationalisethedenominator andsimplify :

𝟓√𝟐 − √𝟑 𝟑√𝟐 − √𝟓

𝟏

𝟏

𝟐

𝟐

20) Simplify: 8√ −

√𝟖

21) Whatmustbe addedto2x3+3x2-22x+12sothattheresultis exactly divisible by 2x2+5x-14? or Divide P(x)= x2+ 4x+4 by g(x) = x+2 andverify division algorithm 22) Threenumbers areintheratio

𝟏 𝟏 𝟏

: :

Ifthesumoftheirsquaresis644,find the numbers.

𝟑 𝟓 𝟔

23) Show that, tanƟ.sinƟ + cosƟ = secƟ 24) Findthe valueofx,suchthatthe distancebetween the points(2,5) & (x,7) is 13units. 25) Drawacircleofradius3.5cmandconstructachordoflength6cminit.Measure the shortestdistancebetween thecentreandthe chord. To D in mts

26) Drawa plan for the recordings from the surveyor’s field work

410

book given below. (Scale20meters=1cm)

120

27)A solid cylinde rhas aT.S.A.of 462square cm.Its C.S.A.i s one third of theT.S.A. Find the radius of the cylinder.

80 to E 100

or

Arightcircularmetallicconeofheight20cmandbaseradius5cmismelte dand recast intoasphere. Findtheradiusofthesphere

50 From A

28) The diameter of a metallic sphere is 18 cm. It is melted and drawn into a wire having diameter of cross section 0.4 cm. Find the length of the wire. 29) InΔABC, PQIIBC. AP=3cm,AR=4.5 cm, AQ=6cm,AB=5cmandAC=10cm. Find the length of AD. 30) ABagcontains27balls,ofwhichsomeareWhite others are red balls. A red ball is choosen random . The probability of getting red ball is

60 to C

𝟐 𝟑

. Find the

number of white balls.

23 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

40 to B

Model Maths Papers To Get Success IV

Answer the following:

6X3 =18

31)The third term of an Arithmetic Progression is 8 and the ninth term of the Arithmetic Progression exceeds threet imes the third term by 2. Find the sum of its first 19 terms.

C.I 0-10 10-20 20-30 30-40 40-50

32) Calculate theStandardDeviation

f

7

10

15

8

10

of the given data 33)TheagesofKavyaandKarthikare11yearsand14years.

Inhowmanyyears

willtheproductoftheiragesbe304. or Amotorboat whosespeedis15km/hr instillwatergoes30kmdownstream and comesbackinatotal ofa4hours 30minutes. Determine thespeedofthe stream. 34) ThroughthemidpointMofthesidesofa Parallelogram ABCD, thelineBMisdrawn intersectingAC atLandAD ProducedatE. Provethat EL=2BL.

OR

Provethatanytwomediansofatriangledivideeachotherintheratio2:1. 35) Theangleofelevationofthetopofatowerofheight h”metersfromtwopointsatadistanceof“a”and“b” meters fromthebase,andinthesamestraightline withitare complementary.Prove thatthe height of the toweris √abmeters. 36) If twocirclestoucheachotherexternallythe centresandthe pointofcontactare collinear. or Prove that the equiangular triagles are similar triangles. V

Answer the following:

4X4=16

37) The sumofaninfinitegeometricprogressionis15andthe sumof the squaresof thesetermsis45. Findtheseries.

OR

ThecommondifferencebetweenanytwoconsecutiveinterioranglesofaPolygon is50. Ifthesmallestangleis1200. FindthenumberofsidesofthePolygon? 38) SolveGraphically:x2-x-2=0. 39) “Ifthe squareonthelongestsideofatriangleis equal tothe sumofthe squares ontheothertwosides,thenthosetwosidescontainarightangle”Prove. 40) Drawtwodirectcommontangentstotwocirclesofradii5cmand3cmhaving theircentre11cmapart. Measurethelength ofD.C.T.andverify.

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Model Maths Papers To Get Success S.S.L.C

Examination Model Question Papers

MATHEMATICS

Set – 9

1. The third term of a G.P is 4 and fifth term is 16,then the forth term is............ A) 64

B) 16

C) 8

D) 2

2. If np3 = np2 then the value of n is............. A) 1

B) 2

C) 3

D) 4

3) The probability of getting at least one head when a coin tossed twice is....... 𝟏

A)𝟒

B)

3 4

C) 3

D) 4

4) The mean of three scores is 4 ,the sum of the first two scores is 6, then the value of third score is.......... A) 0.5

B) 1

C) 4

D) 6

5) If f(x)= x2-10 then the value of f(-1) is............ A) -9

B) 9

C) -11

D) 11

C) cos θ

D) cosec θ

6) sin θ X cotθ = …....... A) tan θ

B) cot θ

7) The slope of the line passing through the points P(7,3) and Q(0,-4) is-----A) 0

B) 1

C) -1

D) 3

𝟏

8) The equation of a line having slope 𝟐.and y-intercept -3is.......... A) Y=x+2

B) Y=x- 2

C) Y=2-x

D) y=x-1

II Answer the following

(1X6=6)

9) Express 3825 a product of prime factors. 10) If A= {1,2,3,5} and B={4,5,6,7} then find A\B. 11) Find the zero of the polynomial x2 + 9x -36. 12) In the figure if DE || AB and CD : AC = 1:2 find the ratio of the areas of ΔACB and ΔDCE 13) find the surface area of a sphere of radius 14 cm. 14) In fig. If PR is tangent to the circle at point at P and Ois the centerof the circle and ∠QRP=600, find ∠POQ. III. Answer the following 15) prove that 2+ √𝟑 is an irrational number. 16) In a class of 60 students every student should select volleyball, football or both. If 40 students select volleyball,35 students select football, how many students do select only football?

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Model Maths Papers To Get Success 17) There are 7 badminton players. Amar is one of them. In how many ways 5 players be selected including Amar ? 18) There are 12 points in a plane of which 4 are collinear. Find the number of straight lines can be drawn from these points ? 19) Rationalize the denominator and simplify :

𝟐√𝟑+ √𝟐 𝟑√𝟐 + √𝟓

20)√𝟒 ಮತ್ತು √𝟐 multiply. 𝟑

𝟓

21) What must be subtracted from x3-6x2-5x+80 so that the result is exactly divisible by x2+x-12 ?

or Divide p(x)= 4x4 -10x2+12x-3 by g(x)=x+1 and verify division algorithm. 22) Draw a plan for the recordings from the surveyor's field work book

meters To D

given below.

200

23)A point P(2,-1) is equidistant from the points (a,7) and (-3,a) Find

120

“a” 24) Draw a circle of radius 3.5 cm Draw two tangents to it such that

To E80

the angle between tangents is 700 . 25) If the

12th

80 50

term of an A.P exceeds the

3rd term

by 36 and

16th

term

To C 70

To B 100

From A

is 64, find the first term? 26) prove that sin2θ(1+ cot2θ) =1 27) the height of water level in the cylindrical well is 7mts and its diameter is 10 mts calculate the volume of water stored in the well in liters.

or A steel sphere of volume 38808 cm3 is melted to form a steel rod of radius 3cm, find the length of the rod? 28) The diameter of a metallic sphere is 4.2cm. it is melted and recast into a right circular cone of height 8.4cm. find the radius of the base of the cone. 29) In ∆ABC , PQ II BC , AP= 3cm AR=4.5cm AQ=6cm AB= 5cm and

AC=10cm Find the length

of AD. 30) In simultaneous throw of two dice,what is the probability of getting a total of 7 IV. Answer the following

( 3X6=18)

31) Find the sum of all two digit numerals which are divisible by 3.

26 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 32) calculate the standard Deviation of the given data.

C.I

33) the age of a man is twice the square of the age of his

f

30-34 2

35-39 40-44 45-49 50-54 5

6

5

son. Eight years hence,the age of the man will be 4 years more than three times the age of his son. Find the present age?

or

Find three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. 34) In ∆ABC DE II BC and CD II EF , prove that AD2=AF x AB.

or If the diagonals of quadrilateral divide each other proportionally then prove that the quadrilateral is a trapezium. 35)From the top of a building 16mt high,The angular elevation of the top of the hill is 600 and angular depression of the foot

OR

of the hill is 300. find the hight of the hill

From the top of a building 16 m high, the angular elevation of the top of a hill is 60° and the angular depression of the foot of the hill is 30°. Find the height of the hill. 36) If two circles touch each other externally the centers and the point of contact are collinear. Prove. OR In the given figure , M is the mid point of AB. Semicircles are drawn on AB with AM and MB as diameters. A circle with centre 'O' touches all three semicircles as shown. Prove that the radius of this circle is 1/6AB V. Answer the following

(4x4=16)

37) solve Graphically: x2+x-6=0 38) State and prove Pythagoras theorem. 39) Draw two direct common tangents to two circles of radii 4cm and 2.5cm having their center 10cm apart. Measure the length of DCT. 40) The 3rd and 7th terms of H.P are respectively

𝟔 𝟏𝟗

and

𝟐

find 10th term.

𝟗

or Three numbers are in A.P have their sum 24. If the 1st number is decreased by 1 and the 2nd number is decreased by 2 then the three new numbers are in G.P. find the numbers .

27 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

2

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 10

1.Which one of the following is a correct relationship? (a)nPr = nCr x r

(b) nCr = nPr x r!

(c) nPr = nCr÷ r!

(d) nCr = nPr ÷ r!

2.Probability of getting 3 heads or 3 tails in tossing a coin 3 times is, (a)1/8

(b)3/8

(c) 1/2

(d) 1/4

3.The sides of two similar triangle are in the ratio 2 : 3. Then their areas are in the ratio (a)9 : 4

(b) 4 : 9

(c)2 : 3

(d) 3 : 2

(b) B/A

(c) B

(d) A

4.If AB then, A ∩B is (a) A/B

5.Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of variation is, (a) 48

(c) 15

(b)42

(d)25

6.If ax2 + bx + c = 0 has equal roots. Then c is equal to a)b2/4a

b)b2/2a

(c)b2/a

d) - b2/4a

7.In the adjoining figure, D and E are the mid points of AB and AC respectively. If DE = 4 cm, then BC is equal to (a) 4 cm

(b) 6 cm

(c) 8 cm

(d) 12 cm

(c) 16

(b) 2

(d) 4

8.(l + tan2 60°)2 is equal to (a) 1 II

1 mark x 6 = 6

9.Express 6762 as the product of prime factors. 10.Find the zeroes of the polynomial 4a2 - 49. 11.For the equation 143 = x2 -1, find the value of x. 12.Form the quadratic equation whose roots are 3 and 5. 13. In ΔABC. ∟ABC = 90° and BD┴ AC. If BD = 8 cm and AD = 4 cm, find CD. 14.O is the centre of the circle. P is external point. If AP = 8 cm, AP = BP and ∟APB = 60° then find the length of the chord AB. Ill 15.

2 x16 = 32 In a school, the strength of 8th, 9th and 10th standards are

respectively 48, 42 and 60. Find the least number of books required to be distributed equally among the students of 8th, 9th and 10th standard. 28 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 16.In a town 85% of the people speak English, 40% speak Kannada and 20% speak Hindi. Also 42% speak English and Kannada, 23% speak Kannada and Hindi and 10% speak English and Hindi. Find the percentage of people who can speak all the three languages. 17.Find the sum of all natural numbers between 1 and 201 which are divisible by 5. 18.The 10th term of a G.P. is 320 and 6th term is 20. Find the progression. 19.It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible? 20.How many maximum diagonals that can be drawn in a octagon? OR Everybody in a function shakes hand with everybody else. The total number of handshakes is 45. Find the number of persons in the function. 21.There are 2 red and 2 yellow flowers in a basket. A child picks up at random three flowers. What is the probability of picking up both the yellow flowers? 22.Rationalise the denominator and simplify: 𝟑

𝟒√𝟑+ √𝟐 √𝟑+ √𝟐

𝟓

23.Multiply: √𝟒 𝑿 √𝟐 24.Solve by using formula: 15m2 - 11m + 2 = 0.

OR

If one root of the equation .x2 + px + q = 0 is 3 times the other, then prove that 3 p2 = 16q. 25.

Find the value of

𝐬𝐢𝐧 𝟑𝟎° + 𝐭𝐚𝐧 𝟒𝟓°− 𝐜𝐨𝐬𝐞𝐜 𝟔𝟎° 𝐬𝐞𝐜𝟑𝟎° + 𝐜𝐨𝐬𝟔𝟎° + 𝐜𝐨𝐭𝟒𝟓°

26.Find the slope of the line perpendicular to the line joining the points (1, 7) and (-4, 3). 27.A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a. 28.Draw a circle of radius 4 cm and construct a pair of tangents such

To D meters

that angle between them is 50°.

300

29. A right angled triangle of which the sides containing the right angle are 6.3 cm and 10 cm in length, is made to turn around on the longer side. Find the volume of thesolid thus generated.

to E 50

200

100 to C

150

75 to B

100

30.Draw a plan for the recordings from the surveyor’s field work book given below: (Scale 25 m = 1 cm)

From A

29 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success IV

3marks x 6 = 18

31. Draw Pie chart to represent the following data: 32.Find the divisor g(x), when the polynomial P(x) = 4x3 + 2x2 -10x + 2 is dividedby g(x) and the quotient and remainder obtained are (2x2 + 4x

+1)

and 5 respectively.

OR

If the quotient obtained on dividing (8x4 - 2x2 + 6x - 7) by (2x +1) is (4x3 + px2 - qx + 3) then find the value ofp, q and also the remainder. 33.If two circles touch each other internally their centres and the

Name of the Number of sport

students

Foot ball

35

Tennis

14

Volley ball

16

Hockey

7

point of contact are collinear. Prove. 34. In the trapezium ABCD, ABII DC and ΔAED ||| ΔBEC. The prove that AD = BC.

OR

D, E and F are the mid-points of sides of ΔABC. P, Q, R are the mid points of sides DEF.This process of marking the mid-points and forming a new triangle is continued. How are the areas of these triangles related? 35.Show that :

𝟏− 𝒕𝒂𝒏 𝟐 𝜽 𝐜𝐨𝐭𝟐Ѳ −𝟏

= tan2Ѳ

OR

Show that secA(1 - sin A)(sec A + tan A) = 1.

36.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the capsule is 14 mm and the width is 5 mm. Find the surface area. OR 36. The diameter of the internal and external surfaces of a hollow hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of diameter 14 cm. Find the height of the cone. V

4 marks x 4= 16 37.In an A.P. whose first term is 2 the sum of first five terms is one fourth the sum of the next five terms. Show that T20 = -112 and also find S20 .

OR

Sum of three terms in a G.P. is 31 and their product is 125. Find the numbers. 38.A man travels a distance of 196 km by train and returns in a car which travels at a speed of 21 km/hour more than the train. If the total journey takes 11 hours, find the average speed of the train and the car respectively. 39.In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Prove. 40.

Construct a transverse common tangent to two circles of radii 4 cm and 2 cm having their

centre 10 cm apart. Measure the length of the TCT and verify by calculation. 30 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 11

1.(1 + cosѲ)(1 - cosѲ) is equal to (a)sin2 Ѳ

(b) tan2 Ѳ

(c) 1

(d) 0

2.If P = {2, 3, 4} and Q = {3, 5, 7} then P/Q is equal to (a){3, 7}

(b) {2, 4}

(c) {3}

(d) {2, 4, 3, 7}

(c) 20

(d) 10

3.If nP2 = 90 then n is equal to (a)90

(b) 45

4.If X = 1 is a zero of the polynomial f (x) = x3 - 2x2 + 4x + K then the value of Kis (a)-3

(b) 3

(c) 4

(d) -4

5.sin A. cos A.tan A + cos A. sin A. cot A is equal to (a)sin 2A - cos 2A

(b)tan2A + cot2A

(c) sin2 A + cos 2A

(d) sin2A + tan2A

6.In the given figure, APB is tangent to the circle at the point P on the circle. PQis a chord. If ∟BPQ - 62°then ∟PRQ = (a) 28°

(b) 118°

7.If 1 + 2 + 3 + ------------(a) 13

(c)124°

(d) 62°

n = 78 then the value of n is,

(b) 12

(c) 11

d ) 16

𝟑

8.The product of √𝟐 and√𝟐is 𝟔

a) √𝟕𝟐 II

𝟔

(b) √𝟒

𝟔

(c)√𝟐𝟒

𝟔

(d)√𝟏𝟔

Answer the following:

6X1 =6

9.Using Euclid’s division algorithm, find the HCF of 65 and 117. 10.A die is rolled. Find the probability of getting a square number. 11.Using Euler’s formula verify:N = 6, R = 6, A = 10. 12.Verify Euler’s formula for a Hexahedron. 13.The height of a right circular cylinder is 14 cm, and the radius of its base is 2 cm. Find its curved surface area. 14.Find sinѲ and cos Ѳ using the following figure, if AB = 24 units, AC = 25 units and BC = 7 units. IIIAnswer the following:

16X2 =32

15.Prove that √3 + √ 2 is an irrational number. 16.If U = {4, 8, 12, 16, 2Ѳ, 24, 28}, A = {8, 16, 24}, and B = {4, 16, 20, 28} verify that (A UB)1 = A1 n B1.

31 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 17.The arithmetic mean of two numbers is 17 and their geometric mean is 15. Find the numbers. 18.The first term of a G.P. is 50 and the fourth term is 1350. Find its fifth term. 19.How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 without repeating any digit? How many of these are even numbers. 20. If nPr = 336 and nCr = 56 find n and r. 21.There are 6 red, 7 white and 7 black balls in a basket. Two balls are drawn at random. Find the probability that the balls are red or both the balls are black. 22.Performance of two players is given below:

Player Mean SD

Who is more consistent in performance?

Arun

23.Draw a pie chart for the following data: Particulars

Hostel fee

College fee

Miscellaneous

Amount (Rs.)

360

120

60

70

4.2

Bharath 60

3.0

24.Find the value of p so that the equation 4x2 - 8px + 9 = 0 has roots whose difference is 4. 25.In ΔABC. XYII BC and XYdivides the triangle into two parts of equal area. Find BX: AB. [Hint: AABC = 2AAXY] 26.

In the given figure Prove that AB2 +CD2 = BD2 +AC2

27.ABCD is a square. F is the midpoint of AB. BE is one third of BC. If the area of AFBE is 108 cm2. Find the length of AC. 28.The line passing through the points (2, 7) and (3, 6) and parallel to a line joining (9, a) and (11, 3). Find a. 29.Find the co-ordinates of the midpoint of the line joining the points (-3, 10) and (6, -8). 30.Construct a pair of tangents to a circle of radius 3.5 cm fTom a point 3.5 cm away from the circle. Measure the length of the tangent. IV

Answer the following

3x 6= 18

31.The third term of an A.P. is 8 and the ninth term exceeds three times the third term by 2. Find the sum of its first 19 terms.

OR

In a H.P. T4 = ¼ and T14 = 3/23 find T19 32. If (X3 + ax2 - bx +10) is divisible by x2 - 3x + 2 find the values of a and b. OR 32 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success Using the remainder theorem find the remainder when P (x) = x3 + 3x2 - 5x + 8 is divided by g(x) = x - 3. Verify the result by actual division. 33.The age of a man is twice the square of the age of his son. Eight year hence the age of the man will be 4 years more than three times the age of his son. Find their present age. OR Solve by completing the square 2 x2 + 5x - 3 = 0. 34.Prove that

√𝟏 + 𝐬𝐢𝐧Ѳ + √𝟏− 𝐬𝐢𝐧Ѳ = 2secѲ √𝟏− 𝐬𝐢𝐧Ѳ + √𝟏∓𝐬𝐢𝐧Ѳ

OR 𝟏

𝟏

Prove that sin230° cos2 45° + 4tan230° + 𝟐sin290° + 𝟖cot2 60° = 2 35. Simplify:

𝟕√𝟑 √𝟏𝟎− √𝟑

-

𝟐√𝟓 √𝟔+𝟐

36.The tangents drawn from an external point to a circle (i) are equal, (ii) subtend equal angles at the centre. V 37.

Answer the following:

4x 4 = 16

From the top of a cone of base radius 24 cm and height 45 cm, a cone of slant height 17

cm is cutoff. What is the volume of the remaining frusturn of the cone? OR (a)The radii of two right circular cylinders are in the ratio 2 : 3 and the ratio of their curved surface area is 5 : 6. Find the ratio of their heights. (b)A right circular cone is of height 3.6 cm and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base 1.2 cm. Find the height of the cone so formed. 38.State and prove basic proportionality theorem. 39.Solve graphically x2 - 3x -10 = 0. 40.Construct a transverse common tangent to two circles of radii 3 cm and 2 cm with their centres 9 cm apart. Measure the length of the tangent and verify.

33 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers MATHEMATICS

Set - 12

1.A = {1, 2, 3}, B = {4, 5, 6} then A / (BnC) is, (a) {1, 2, 3}

(b){4, 5,6}

2.15th term of the A.P. x - 7, x - 2, x + 3 --------(a) x + 73

(b) x + 63

(c){1, 3, 5}

(d){2, 4,6}

is, (c) x + 83

(d) x + 53

𝟑

3.The rationalising factor of 2 √𝒙 is (a) √𝒙

(b) 𝟒√𝒙

c)√𝒙𝟐

𝟑

d) √𝒙

(c) 1

(d) 0

𝟑

4.If f (x) = 2x3 + 3x2 - 11x + 6 then f(1) is -------(a) 6

(b) 2

5.One root of the equation x2 - 5x + K = 0 is 2. Then K is, (a) -6

(b) 6

(c) 5

(d) 2

6.In ΔABC, DE II BC. If AD = 3 cm, BD = 2 cm and AE = 2.7 cm then AC is equal to (a)6.5 cm 7.If

(b)4.5 cm

(c)3.5 cm

(d)5.5 cm

(b) 1

(d) 0

𝟑

1 - cos 2 Ѳ = 𝟒, then sinѲ is (a)

√𝟑 𝟐

(c) ½

8.The distance between the origin and the point (12, -5) is, (a) -5 units II

(b)12 units

(c) 7 units

(d) 13 units

nswer the following:

6X1 =6

9.Find the harmonic mean between 1 and 4. 10.Two coins are tossed together. What is the probability of getting exactly one head. 11. Subtract5√xfrom 9√xand express the result in the index form. 12.In the polynomial, g(x) = x - 2, q(x) = x2 - x +1 and r (x) = 4 find P(x). 13.

Find the equation of the line whose angle of inclination 0 = 60° and y intercept is -2.

14.

In the given figure AX, AY and AZ are the tangents to the circles. If

AX = 8 cm find AY and AZ.

III

II Answer the following:

2 x 16 = 32

15.Find geometric progression if T3:T6= 1:8 and T5 = 64. 16.

Shekar is one member of a group of 5 persons. If 3 out of these 5 persons is to be chosen

for a committee, find the probability of Shekar being in the committee. 17.Find the variance for the following data:40, 36, 64, 48, 52. 34 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 18.Rationalise the denominator and simplify:

𝟑+ √𝟔 √𝟑 + 𝟔

19. Divide P (x) = x2 + 4 x + 4 by g (x) = (x + 2) and verify division algorithm. OR Find the quotient and remainder using synthetic division ( 3x3 -2x2 + 7x-5 ) ÷(x + 3). 20.Find the value of q so that the equation 2x2 - 3qx + 5q = 0 has one root which is twice the other. 21.In ΔABC, ∟ABC = 90°, BM┴AC, AM = 8x2, MC = 2x2, find BM and AB. 22.In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)? 23. The radius of a cone is 7cm and area of curved surface is 176 cm. Find its slantheight. 24.Set A and set B are the subsets of the universal set U. n ( A) = 285, n (B) = 195, n (U) = 500 and n (A U B) = 410 find n (A1U B1). 25.If nPr = 840 and nCr = 35 find the value of n. 26.Find two numbers whose sum is 18 and sum of their squares is 290. 27.If 3tanѲ = 1 find sinѲ and cosѲ .

OR 4sin260°- cos2 45°

Find the value of

tan2 30° + sin200

28.In the given figure, PQ, PR and BC are the tangents to the circle. BC touches the circle at x. If PQ = 7 cm then find the perimeter of APBC. 29.The curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and the total surface area of the cone.

OR

A solid hemisphere of wax of radius 12 cm is melted and made into a cone of base radius 6 cm. Calculate the height of the cone. 30.In a circulating library the number of different books circulated daily are given below:Draw a Pie chart to represent the data. Types of books Daily Circulated

Kannada Novels 40

Magazines 50

Science

English

Books

Novels

25

05

35 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success IV

3 x 6= 18

31.A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girls; (ii) at least one boy and one girl. OR From 8 gentlemen and 5 ladies a committee of 6 is to be formed. In how many ways can this be done so that the committee contains at least 3 ladies. 32.If a straight line divides two sides of a triangle proportionally, then the straight lines is parallel to third side. (Converse of Thales theorem) Prove.

OR

In a trapezium ABCD, AB II DC and ΔAED ||| ΔBEC then prove that AD = BC. 33.A rectangular hall is 18 m 72 cm long and 13 m 20 cm broad. It can be paved with square tiles of the same size. Find the least possible number of such tiles. 34.A straight drawn through the point of contact of two circles with centres A and B intersect the circles at P and Q respectively. Show that AP and BQ are parallel. OR Tangents AP and AQ are drawn to circle with centre O, ^om an external point A. Prove that ∟PAQ = 2∟OPQ. 𝑪𝒐𝒔𝑨

35.Show that: 𝟏−𝒕𝒂𝒏𝑨 +

𝒔𝒊𝒏𝑨 𝟏−𝑪𝒐𝒕𝑨

= 𝒔𝒊𝒏𝑨 + 𝒄𝒐𝒔𝑨

OR

From a point 50 m above the ground the angle of elevation of a cloud is 30° and the angle of depression of its reflection is 60°. Find the height of the cloud above the ground. 36.Plan out and find the area of the field from the following notes from

Meters to D

the field work ABCDE. (Scale 20 m = 1 cm). V 37.

150 4 x 4 = 16

In an A.P. if the

12th

term is -13 and the sum of the first four terms

is 24, what isthe sum of the first 10 terms?

OR

The sum of first three terms of a G.P. is 16 and sum of the next three terms is 128. Determine the first term, common ratio and sum to n terms

to E 80

100

70 to C

80

40 to B

30 From A

of the G.P. 38.Solve graphically: 2x2 - x - 3 = 0. 39.In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Prove. 40.Construct two direct common tangents to two circles of radii 5 cm and 2.5 cm whose centres are 11 cm apart. Measure its length. 36 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers

MATHEMATICS

Set - 13

1. The relationship between the dividend {a), divisor {b), quotient (q) and the remainder {r) is (a) a = (b + q) x r

(b) a = (b - q) + r

(c) a = (b - r) x q

(d) a = (b x q ) + r

2.The formula used to find the coefficient of variation is (a) CV =

𝝈

𝑿𝟏𝟎𝟎 𝑿

(b)CV =

𝑿

𝑿𝟏𝟎𝟎 𝝈

(c)CV = σ XX𝟏𝟎𝟎 (d)CV =

𝛔 𝐗𝐗 𝟏𝟎𝟎

3. In the adjoining figure XY II BC. ThenAX/BXis equal to (a) AX/AY 4.The value of

𝒕𝒂𝒏𝜽 𝒄𝒐𝒕𝜽

(a) 0 5.

(c)AY/AC

(d)AC/AY

(b) 1

(c)1/cotѲ

(d)1/ tanѲ

(c)AC/ AB

(d) AC/BC

is

In this figure, the slope of AC is (a)AB/BC

6.

(b) AX/XB

(b) BC/AB

TA and TB are tangents to a circle from an external point T. If ∟ATB = 60°, then the

triangle TAB is (a) right angled triangle (c)obtuse angled triangle 7.

(b) equilateral triangle (d) isosceles triangle

Two dice marked 1 to 6 on each is rolled once simultaneously. The probability of getting

equal numbers on their top is (a) 3/ 36

(b) 36/6

(c) 1

(d)0

(c) 1

(d)0

8. If f (x) = x2 + x-1, then the value of f(1) is (a) 3

(b) -1

II

1 x6=6

9.If A and B are disjoint sets, then what is value of n(A U B) 10. In a sequence if Tn = n2 + 4 and Tn = 200, find the value of n. 11.If nC8 = nC12, find the value of n. 12.Find the zeroes of the polynomial x2 + 5x -14. 13.Find the distance between the origin and the point (12, -6). 14.Find the surface area of a hemispherical bowl of diameter 14 cm. III

2 x 16 = 32

15.Prove that √3 + √2 is an irrational number. 16.In a group of passengers 100 can speak Kannada 50 can speak English and 25 can speak both Kannada and English. Find the total number of passengers and find how many can speak only Kannada. 37 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 17.Classify the following into permutations and combinations. (a)Arrangement of 7 books in a shelf taking 3 books at a time. (b)Number of shake hands by 10 people among themselves. (c)Number of ways by which 5 people occupy 5 seats. (d)Choosing a committee of 7 by 10 people. 18.The maximum number of diagonals in a polygon is 14. Find the number of sides. 19.There are 6 red, 7 white and 7 black marbles in a box. Two balls are drawn from the box at random. Find the probability that both the balls are red. 𝟒

𝟑

20.Find the product of √𝟐 𝑿 √𝟑 . 21.Rationalise the denominator and simplify

√𝟓 + 𝟑 𝟑− √𝟓

22. If P(x) = x3 + 4x2 - 5x + 6 and g(x) = x +1. Divide P(x) by g(x) and verify division algorithm. OR The polynomials ax3 + 3x2 -13 and 2x3 - 4x + a are divided by (x - 3). If the remainder is same in each case, find the value of a. 23.Solve by using the formula: 2 y2 + 6 y = 3. 24.In this figure. ∟PQR = 90° and QS┴PR. If PQ =1.5 cm and QR = 2 cm, calculate the length of QS. 𝟏 + 𝐬𝐢𝐧Ѳ

25. Show that 𝟏− 𝐬𝐢𝐧Ѳ = ( secѲ + tanѲ)2 26.

Find the equation of the line whose angle of inclination is 60° and y-intercept is-2.

27.

Draw a circle of diameter 6 cm and construct two tangents at the ends of the radii such

that the angle between the radii is 110°. 28.

The slant height and diameter of the base of a conical tomb are 25 m and 14 m

respectively. Find the cost of painting its curved surface are at the rate of Rs. 50 per square meter.

OR

To D in meters

A circus tent is cylindrical upto a height of 3 m and conical above it. If

140

the diameter of the base is 105 m and the slant height of the conical part is 53 m, find the area of canvas required to cover the tent. 29.A rectangular sheet of paper, 44 cm × 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder so formed. 30.

Plan out the field using the following measurements

100 to E 100

60 to C

80 20 From A

(use the scale 20 m = 1 cm)

38 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

75 to B

Model Maths Papers To Get Success IV

3 x 6 = 18

31.The sum of 6 terms which forms an AP is 345. The difference between the first and last terms is 55. Find the terms. 32.Calculate the standard deviation of the following scores by assumed mean method. (Assumed mean = 60). 33.Mohan had bought certain number of books for Rs. 48. If he had bought 4 Scores (X) Frequency (f) more for the same amount, then the cost of each book would have bean

50

4

reduced by 1 rupee. Find the number of books bought by him.

55

6

60

10

A man travels a distance of 196 km by train and returns in a car which

65

6

travels at a speed of 21 km/hour faster than the train. If the total journey

70

4

OR

takes 11 hours, find the speed of train and car. 𝝅

𝝅

34. If π = 180°, A = 𝟑 and B =𝟔 , prove that tan(A - B) = Prove that:

𝟏+𝒄𝒐𝒔𝜽 𝟏−𝒄𝒐𝒔𝜽

+

𝟏− 𝒄𝒐𝒔𝜽 𝟏+𝒄𝒐𝒔𝜽

𝒕𝒂𝒏𝑨−𝒕𝒂𝒏𝑩 𝟏+𝒕𝒂𝒏𝑨 𝒕𝒂𝒏𝑩

OR

= 4cotѲ cosѲ

35.If two circles touch each other, prove that their centres and their point of contact are collinear. 36.

In a trapezium, prove that the line joining the midpoints of

non-parallel sides are parallel to the parallel sides of the trapezium. OR In trapezium ABCD, AB II CD. If AO = 3x -19,OC = X - 5, BO = X - 3 and OD = 3, find x V

4X4 =16

37.In a right angled triangle, prove that the square on the hypotenuse is equal to sum of the squares on the other two sides. 38.Solve graphically: x2 + x - 2 = 0. 39.Draw two circles of radii 4.5 cm and 2 cm at a distance of 11 cm apart from their centres. Construct direct common tangents to them and measure their length. 40.The sum of three terms of an AP is 21 and the product of first and third term exceeds the second term by 6. Find three terms.

OR

The third term of an AP is 7 and the 7th term exceeds 3 times the third term by 2. Find the first term and the common difference and the sum of first 20 terms. 39 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers Time : 3 hours

MATHEMATICS

MATHEMATICS PAPER

Set - 14

Marks: 80

I.

Choose the most appropriate answer for the following questions/ statements and write the correct answer along with their options in the space provided to each of the following 1*8 = 8 1. The next term of the G.P 2 , 2 , 1 ------ is A.

1 2

B. 2

C.

1 2

D. 2

2. If n C r  n Pr then ‘r’ = ---------------A. 0 B. 1 C. 2 D. 3 3. The probability of getting a perfect square numbers form the number 1 to 10 is -A.

1 2

B.

3 10

C.

2 5

D.

1 5

4. Standard Deviation : 2x : : variance : ----A. 2 x B. 2x2 C. 4x2 D. 4x 5. The degree of the polynomial p ( x ) = x3 – 7x2 + 5x + 10 is A. 0 B.1 C. 2 D. 3 6. If 2 sin  = 3 , then the value of  is A. 300 B. 450 C. 600 D. 900 7. The inclination of the line is 300 , then the slop is ---------A.

1 3

B. 3

C. 0

D. 1

8. Distance between origin and the point ( - 5 , 12 ) is A. 17 B. 7 C. 13 D. 20 II. Answer the following questions 1* 6 = 6 9. If U = { 0 , 1,2,3,4} and A = { 2,3,4} Find A1 10.Express 129 as the product of prime factors. 11.If f(x) – 3x2 + 5x – 10, then find the value of f( 0) 12.How many direct common tangents can be drawn to two concentric circles? 13.State the converse of Pythagoras theorem 14.Write the formula used to calculate the surface area of a Hallow hemisphere III. 2*16 = 32 15.In a group of 40 peoples, 37 like coffee, 52 like Tea how many like both coffee and tea? 16.Prove that 2 + 3 is a irrational number 40 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 1 1  17.Find the value of 4! 2!

18.In how many ways 5 men and 4 women are seated in a row, such that women can occupy even places? 19.Two coins are tossed simultaneously, what is the probability of getting the same faces? 20.Simplify by rationalizing the denominator

3 5 3

21.Find the product of √𝟓 X 𝟑√𝟓 22.If (x – 2 ) is a factor of x2 + 3x + k, find the value of ‘k’ OR Find the remainder and quotient when x3 – 4x2 + 3x + 1 is divided by ( x – 1 ) using synthetic division method 23.Solve x2 – 7x + 12 = 0 using formula method 24.Draw tangents at the end point of a chord of length 5 cm in a circle of radius 3.5 cm 25.In the adjoining figure ABC  900 , AMP  900 Show that CA BC  PA MP

26.Find the value of : tan300 x cot 600 – sin2900 27.Find the equation of line having slope

1 and y – intercept is -2 3

28.The diameter of a garden roller is 1.4 m and 2 m long how much area will it cover in 5 revolutions? 29.Find the curved surface area of a cone if its slant height is 4.5 cm and radius of its base 2.1 cm OR Find the curved surface are of a right circular cylinder, whose height and radius of the base are 3 cm and 4.9 cm To C respectively In metres 30.Draw a plan for the following data 210 ( Scale 20 m = 1cm ) 130 to D 200 IV. 3*6 = 18 110 180 to B 1 1 31.In H.P if T5= and T10 = find T25 12 22 150 to E 80 From A

41 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 32.Calculate the Standard Deviation for the following scores

CLASS -INTERVAL FREQUENCY 1-5 4 6-10 3 11-15 2 16-20 1

33.The product of two consecutive integers is 182. Find the integers OR The length of a rectangular field is 3 times its breadth, if the are of the field is 147 sq cm find its length 34.In the adjoining figure P and Q are the centres of the circles with radii 9 cm and 2 cm respectively, if PRQ  90 0 , PQ = 17cm find the radius of the circle with centre R OR In the given quadrilateral ABCD BC = 38 cm, QB = 27cm DC = 25 cm and AD  DC. Find the radius of the circle 35.In  LAW , LAW  900 , LNA  900 , LN = 3cm, NA = 4 cm, AW = 12 cm , then find LW 36.If A  300 , show that Cos 2A =

1  tan 2 A 1  tan 2 A

OR Two wind mills of height 45 m and 30 m are on either side of the field. If a person observe the top of the wind mills from a point in between the towers such that the angle of elevation is 450 in both the cases, find the distance between the wind mills. III. 4*4 = 16 37.Three numbers are in A.P, whose sum is 12 and the sum of the extremes is twice the middle term, find the numbers. OR The angles of a quadrilateral are in A.P if the smallest angle is 150, find the remaining angles of the quadrilateral 38.Solve x2 – x – 2 = 0 graphically 39.Draw Transverse common tangents to two circles of radii 4 cm and 2.5 cm whose centres are 9 cm apart. Measure and verify the length of the tangents. 40.Prove that “ Area of similar triangles are proportional to the square of their corresponding sides”.

42 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers MATHEMATICS

Set - 15

I. Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its letter in the space provided against each question. 8 x 1 = 8 1.The harmonic mean between 2 and 4 is 𝟖

𝟑

(A)𝟑

𝟖

(B) 𝟖

𝟔

(C) 𝟔

(D) 𝟖 .

2.The value of nC n is (A)n

(B) 0

(C)1

(D) n !

𝟓

3.The probability of winning a game is Then the probability of losing it is 𝟔

𝟓

𝟓

(A)− 𝟔

𝟏

(B) 𝟔

(D) 𝟏.

(C)− 𝟔

𝟔

4.The given pie-chart shows annual agricultural yield of certain place. If the total production is 8100 tons, then the yield of Ragi in tons is (A)225

(C) 22.5

(B)2250

(D) 2.250.

II. 95.

Which of the following is the zeroes of the polynomial x 2 + 4x + 4 ? (A)

6.

2

(B)

-2

(C)4

(D)- 4.

The value of tan 2 60° is 𝟏

(B) 𝟐√𝟑

(A) √𝟑

(C) 𝟑

(D)3.

7.The distance between the points ( 2, 3 ) and ( 6, 6 ) is (A) 5 units

(B) 7 units

(C) 3 units

(D) 4 units.

8.The slope of the line joining the points ( 3, - 2 ) and ( 4, 5 ) is (A) 1

(B) 1

(C) 7

(D) 3.

II Answer the following : 9.

6x1=6

Express 210 as the product of prime factors.

10. If A = { 1, 2, 3, 4 } and B = { 1 } , find A \ B. 11. Mean and standard deviation of runs scored by a cricket player are 80 and 4 respectively. Find coefficient of variation. 12. If f ( x ) = x2 - 4, find f ( 4 ). 13. In ∆ ABC, XY II BC,

𝑨𝒀 𝑪𝒀

=

𝟏 𝟐

and AX = 4. Find BX.

14. In the figure, BC is the diameter. What is the measure of x ? III. 15. Prove that 3 +√𝟓 is an irrational number. 43 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 16. In a class of 100 students, 55 students have passed in Physics and 67 students have passed in Mathematics. Find the number of students passed in Physics only. OR A and B are the two subsets of Universal Set U such that n (U) = 700, n ( A ) = 200, n (B ) = 300 and n ( A n B ) = 100. Find n ( A1 n B1). 17. In how many ways 4-digit numbers can beformedusing

the digits 1, 2, 3, 7, 8, 9

without repetitions ? Howmany of theseare even numbers ? 18. Find the number of sides of a polygon having 35 diagonals. 19. Two dice are thrown simultaneously. Find the probability of getting (a)same number on both faces and (b)both faces having multiples of five. 20. Calculate variance for the following data : X = 2, 4, 6, 8, 10 ( Scores ) 𝟑

21.Find the product of √𝟐 𝒂𝒏𝒅 √𝟓 22. Rationalise the denominator and simplify :

√𝟔 + √𝟑 √𝟔 − √𝟑

23.Find the value of a if ( x - 5 ) is a factor of (x 3 - 3x 2 + ax - 10 ) OR What must be added to the polynomial P ( x ) = x4 + 2x 3 - 2x 2 + x - 1 so that the resulting polynomial is exactly divisible by x 2 +2x - 3 24.Solve the equation by using formula : x2 - 4x + 2 = 0. 25. In A ABC, AD is the median and PQ II BC. Prove that PE = EQ 26. In the given figure, find the values of cos 𝜽 and tan 𝜽 . 27.Find the perimeter of a triangle whose vertices have the coordinates ( 3, 10 ), ( 5, 2 ) and ( 14, 12 ). IV. 28. Draw a circle of radius 3 cm and construct two tangents to it from an external point 8 cm away from the centre. 29. A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones each of diameter 1cm and height 3cm. Find the number of cones so formed.

44 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 30. Draw a plan of a level ground using the given information : Metre To D

[ Scale : 20 m = 1 cm ] 𝟏

150

𝟏

31.In a harmonic progression, T3 =𝟕 and T7 = 𝟓. Find T15

100

32. Aniruddha bought some books for Rs. 60. Had he bought 5 more books for the same amount, each book would have cost him 1 rupee less. Find the number of books bought by Aniruddha.

80 to C

To E 60 80 40

OR

The ages of Kavya and Karthik are 11 years and 14 years respectively. In

40 to B

From A

how many years time will the product of their ages will be 304 ? 33. In ∆ABC, ∠A = 90°, AD ⊥ BC and ∠B = 45°. If AB = x, find AD in terms of x. OR ABC is a right angled triangle with ∠ C = 90°, BC = a , AC = b, CD ⊥ AB and CD = P. Show that 𝟏 𝑷𝟐

34.

=

𝟏 𝒂𝟐

+

𝟏 𝒃𝟐

Prove that

𝐬𝐞𝐜 𝛉 − 𝐭𝐚𝐧 𝛉 𝐬𝐞𝐜 𝛉 + 𝐭𝐚𝐧 𝛉

= 1 - 2 sec θ . tan θ + 2 tan 2 θ.

OR

𝟏 + 𝐜𝐨𝐬 𝛉

Prove that √ 𝟏 − 𝐜𝐨𝐬 𝛉 = cosec θ + cot θ. V. 35. Prove that ‘the tangents drawn from an external point to a circle are equal’. 36. A solid cylinder has a total surface area of 462 cm2. Its curved surface area is one-third of its total surface area. Find the radius of the cylinder.

OR

From the top of a cone of base radius 12 cm and height 20 cm, a small cone of base radius 3 cm is to be cut off. How far down the vertex is the cuts should be made ? Find the volume of the frustum so obtained. 37. The sum of three consecutive terms in an arithmetic progression is 6 and their product is 120. Find the three numbers.

OR

The product of three consecutive terms in a geometric progression is 216 and sum of their products in pairs is 156. Find the three terms. 38. ‘In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.’ Prove. 39. Construct direct common tangents to two circles of radii 4 cm and 2 cm whose centres are 9 cm apart from their centres. Measure their length and write the length of direct common tangents. 40. Solve the equation graphically : x2 + x - 6 = 0.

45 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers MATHEMATICS

Set - 16

I. Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its letter in the space provided against each question. 8 x 1 = 8 1.By applying Euclid’s division lemma 72 and 28 can be expressed as (A)28 = ( 72 - 16 ) x 2

(B) 72 = ( 28 x 2 ) + 1

(C) 72 = ( 28 x 2 ) - 16

(D) 16 = 72 - ( 28 + 2 ).

2. A and B are two sets. If n ( A ) = 20, n ( B ) = 30 and n ( A U B ) = 40, then n ( A ∩B ) is equal to (A)50

(B)10

(C)40

3.If a, b and c are in Arithmetic progression then (A)

𝒃

(C)1

𝒂

(D)70. 𝒃−𝒂 𝒄−𝒃

i s equal to

(B)0

(D)

2 a.

4.“The occurrence of one event excludes the occurrence of other event.” In a random experiment of probability theory it is called (A) Complementary event

(B) Impossible event

(C) Mutually exclusive event

(D) Certain event.

5. The standard deviation of a set of scores is 1-6. The variance of these scores is (A)0.4

(C)0.04 𝟑

(B)1.96

(D) 2.56.

𝟑

6.The product of 2√𝟐 and 3√𝟒 is (A) 6

(B) 8

(C)10

(D) 12.

7. In the following figure ∠ABC = 90° and BD ⊥ AC. If AD = 8 cm, CD = 2 cm, then the length of BD is

(A) 4 cm

(B) 8 cm

(C) 16 cm

(D) 10 cm.

8. In the following figure AB ⊥ BC and ∠ACB = 30°, given BC = √𝟑𝟎𝟎 m. The length of AB is (A)10m

(C)

II. Answer the following :

10√𝟑 m

(B)100 m

(D)100√𝟑 m.

6x1=6

9.If Tn = 2n2 + 5 then find T3. 10. Write the degree of the polynomial 19x + √𝟑 x3 + 14. 11. Rationalise the surd (√𝟓 + √𝟐 )) to get a rational number. 12. PQ and PR are tangents to given circle as shown in the figure. If ∠RPQ = 90° and PQ = 8 cm, find the radius of the circle. 46 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 13. Write the ‘discriminant’ of the equation ax2 + bx + c = 0. 14. Write the formula to find the total surface area of a right circular cylinder. Answer the following : 15. Show that 3 + √𝟓 is an irrational number. 16. Draw Venn diagrams to illustrate the following sets : (i)( A U B ) 1 𝟏

(ii) A1 n B.

𝟏

17. In a Harmonic Progression T5 = 𝟏𝟐 and T11 =𝟏𝟓 Find T1. 18. If np2 = 90 , then find the value of n. 19. An unbiased cubical die whose faces are numbered 1 to 6 is rolled once. Find the probability of getting a square number on the top face. 20. Rationalise the denominator and simplify : 21. Find the roots of the equation x2 + 7 x + 12 = 0 by using the formula. OR Solve x2 + 6x - l = 0 by the method of completing the square. 22. The length of a rectangular playground is 2 m longer than its breadth. If the area of the playground is 195 sq.m, find the length and breadth of the field. 23. In the following figure, AC || BD and CE || DF. If OA = 12 cm, AB = 9 cm, OC = 8 cm and EF = 4.5 cm, find OE.

OR

If the area of two similar triangles are equal, then they are congruent. Prove. 24. If 24 tan𝜽= 7, then find (i) sin𝜽 , (ii)cos𝜽. 25. Find the equation of a straight line having angle of inclination 60° and Y-intercept 2. 26. The distance between the points ( 3, 1 ) and ( 0, x ) is 5 units. Find x. 27. In the given figure, AB, BC and AC are tangents to the circle at P, Q and R. If AB = AC, show that Q is the mid-point of BC.

28. The radii of two circular ends of a frustum of a cone shaped dust bin are 15 cm and 8 cm. If its depth is 63 cm, find the volume of the dust bin.

To D ( m )

29. Draw a plan for the recordings from Surveyor’s field work book given

150

below :[ Scale : 20 m = 1 cm ]

120

30.A petrol tank is in the shape of a cylinder with hemispheres of same

60 to C

To E 60 80

radius attached to both ends. If the total length of the tank is 6m and the

30

radius is 1m, what is the capacity of the tank in litres.

From A

47 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

40 to B

Model Maths Papers To Get Success V. 31. Prove that

𝒏𝑪𝒓 𝒏 = (𝒏−𝟏)𝑪𝒓−𝟏 𝒓

where 1< r < n.

OR A polygon has 44 diagonals. Find the number of sides of the polygon. 32. Calculate the standard deviation of the following

C.I.

0 — 10

10 — 20

20 — 30

30 — 40

40 — 50

f

7

10

15

8

10

data ( by Assumed mean method ). Assumed Mean = 25 33. The polynomials P ( x ) = ax3 + 3x2 - 13 and g ( x ) = 2x3 - 4x + a are divided by ( x - 3 ). If the remainder in each case is the same, find the value of a. OR If the quotient obtained on dividing x 4+ 10x3 + 35x2 + 50x + 29 by ( x + 4 ) is x3 - ax2 + bx + 6 then find a and b. Also find the remainder. ( Hint : Apply Synthetic division ) 𝟓

34. In an equilateral triangle ABC, AD⊥ BC. Prove that AB2 + CD2 = 𝟒 AC2. OR In A ABC, AD 1 BC and BD : CD = 3 : 1. Prove that 2 (AB2 - AC2 ) = BC2. 35.Prove that( sin 𝜽 + cosec θ )2 + ( cos θ + sec θ )2 = 7 + tan2 θ + cot2 θ.

√

Prove that 36.

𝟏 + 𝐜𝐨𝐬 𝛉 𝟏− 𝐜𝐨𝐬 𝛉

OR

= cosec θ + cot θ.

Prove that the tangents drawn to a circle from an external point are equal.

V. 37. The product of three consecutive terms of a geometric progression is 216 and the sum of their products taken in pairs is 156. Find the terms of the progression. OR Find three consecutive terms in an Arithmetic progression whose sum is 18 and sum of their squares is 140. 38.Draw a transverse common tangent to two circles of radii 4 cm and 2 cm whose centres are 9 cm apart. Measure the length of the tangent. 39.Prove that “If two triangles are equiangular, then their corresponding sides are proportional”.

40.Solve the quadratic equation x 2 + x - 6 = 0 graphically. 48 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success S.S.L.C Examination Model Question Papers MATHEMATICS

Set - 17

I. Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its letter in the space provided against each question. 8 x 1 = 8 1. If Tn = n2 + 3 then the value of T3 is (A)6

(B)

9

(C)12

(D)27.

2. Arithmetic mean of 2 and 8 is (A)5

(B)

10

(C)16

(D)3.2

3. If the probability of winning a game is 0.3, then what is the probability of losing it ? (A)0.1

(B)0.3

(C)0.7

(D)1.3.

4. The degree of the polynomial 2x2 - 4x3 + 3x + 5 is (A)0

(B)1

(C)2

(D)3.

5. The distance between the origin and the point ( 4, - 3 ) is (A) 1 unit

(B) 5 units

(C) 7 units

(D) - 12 units.

6. The slope of the straight line whose inclination is 60° is (A)0

(C)

𝟏 √𝟑

(B) - √𝟑

(D) √𝟑

𝟑

7.If sin𝜽 = 𝟓 then the value of cosec𝜽 is 𝟒

𝟓

(A) 𝟓

(C) 𝟑

𝟒

𝟓

(B) 𝟑

.(D)𝟒

8. If the standard deviation of a set of scores is 1-2 and their mean is 10, then the coefficient of variation of the scores is (A) 12

(B) 0.12

(C) 20

(D) 120.

II. Answer the following :

6x1=6

9.If U = { 1, 2, 3, 4, 5 } and A = { 2, 4, 5 } then find A 1. 10.The H.C.F. of 12 and 18 is 6. Find their L.C.M. 11.If f ( x ) = 2x2 + 3x + 2 then find the value of f ( 2 ). 12. Two circles of diameters 10 cm and 4 cm, touch each other externally. Find the distance between their centres. 13.State Pythagoras theorem. 14.Write the formula to find the total surface area of a cylinder. 15.Calculate the maximum number of diagonals that can be drawn in an octagon using the suitable formula. 49 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

Model Maths Papers To Get Success 16.Prove that 2 + √𝟓 is an irrational number. 17.There are 500 wrist watches in a box. Out of these 50 wrist watches are found defective. One watch is drawn randomly from the box. Find the probability that wrist watch chosen is a defective watch. 𝟑

18. Find the product of √𝟑 𝒂𝒏𝒅 √𝟐 19. Rationalise the denominator and simplify :

√𝟑 + √𝟐 √𝟑 − √𝟐

20.Find out the quotient and the remainder when P ( x ) = x3 + 4x2 - 5x + 6 is divided by g ( x ) = x + 1 OR Find the polynomial which is to be added to P ( x ) = x4 + 2x3 - 2x2 + x - 1 so that the resulting polynomial is exactly divisible by x2 + 2x - 3. 21. In the following figure, DE || AB. If AD = 7 cm, CD = 5 cm and BC = 18 cm, find CE. 22.Given √𝟑tan𝜽 = 1 and 𝜽 is an acute angle. Find the value of sin𝟑𝜽 23.Find the coordinates of the mid-point of the line segment joining the points ( 2, 3 ) and ( 4, 7 ). 24.The radius of a cone is 7 cm and its slant height is 10 cm. Calculate the curved surface area of the cone. OR Calculate the volume of a right circular cylinder whose radius is 7 cm and height is 10 cm. 25. Solve the quadratic equation x2 - 4x + 2 = 0 by formula method. 26. Construct a tangent at any point P on a circle of radius 3 cm. 27. Draw a plan using the information given below :

Metre To D

[ Scale : 20 m = 1 cm ]

160

28. In a group of people, 12 people know music, 15 people know drawing

120

and 7 people know both music and drawing. If people know either

60 to C

40 to E 80

music or drawing then calculate the number of people in the group. 29. A solid hemisphere of wax of radius 12 cm is melted and made into a

40 From A

cylinder of its base radius 6 cm. Calculate the height of the cylinder. 30. Find the sum of first 20 terms of the series 4 + 7 + 10 + ................................ IV. 31. Prove that “If two circles touch each other externally then their centres and the point of contact are collinear”.

50 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354

40 to B

Model Maths Papers To Get Success

Class-intervals frequency 1—5

4

32. Calculate the standard deviation for the following data

6 — 10

3

33. Find how many 4-digit numbers can be formed using the digits 1, 2, 3,

11 — 15

2

16 — 20

1

4, 5, 6 without repetition of the digits. Find out how many of these are less than 5000

OR

N = 10

If 16 . n P3 = 13 . n + 1 P3 then find n. 34. Prove that

𝑺𝒊𝒏(𝟗𝟎𝟎 −𝜽 ) 𝟏+𝑺𝒊𝒏𝜽

+

𝑪𝒐𝑺𝜽 𝟏−𝐜𝐨𝐬(𝟗𝟎𝟎 −𝜽 )

= 2Sec𝜽 OR

If A = 60°, B = 30° then verify that cos ( A + B ) = cos A . cos B - sin A .sin B. 35. Pupils of Xth Standard of a school had arranged for a function at a total cost of Rs. 1,000 which was to be shared equally among them. Since 10 of them failed to join the function each of them had to pay Rs. 5 more. Find the number of pupils in the class. OR If m and n are the roots of the equation x 2 - 5x + 3 = 0, find the values of i)( m + n ) 2 + ( m - n ) 2 ii)( m + n )3 + 4 mn. V. 36.In the right angled triangle ABC, ∠ABC = 90°. AM and CN are the medians drawn from A and C respectively to BC and AB. Show that 4 ( AM2 + CN2 ) = 5 AC2

OR

In the Rhombus ABCD Show that 4AB2 = AC2 +BD2 . 37. Prove that “If two triangles are equiangular then their corresponding sides are in proportion.” 38. Draw two direct common tangents to two circles of radii 4 cm and 2 cm whose centres are 8 cm apart. Measure the length of the tangents. 39. In an arithmetic progression, the sum of first term, third term and the fifth term is 39 and the sum of second term, fourth term and the sixth term is 51. Find the tenth term of the sequence.

OR

In a geometric progression, the sum of the first 3 terms is 7 and the sum of the next 3 terms is 56. Find the geometric progression. 40.

Solve the equation graphically : x2 + x - 2 = 0.

**********# By K V Shivaprasanna . GGPUC- Bifurcated. RC Road. HASSAN ************** 51 | Page Shivaprasanna.K.V.GirlsGovt P UCollege-Bifurcated .Hassan 7411174354