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SSLC MATHEMATICS 100MARKS
2:30HRS
Section – I Choose the correct answer 1)If A= { p, q, r, s }, B = { r, s, t, u }, then A\B is (A) { p, q } (B) { t, u } (C) { r, s }
(D) {p, q, r, s }
2)If k+2, 4k–6, 3k–2 are the three consecutive terms of an A.P, then the value of k is (A) (B) 3 (C) 4 (D) 5 3) If the product of the first four consecutive terms of a G.P is 256 and if the common ratio is 4 and the first term is positive, then its 3rd term is
(A) 8
(B) 1/16
(C)1/32
(D) 16.
4)The sum of two zeros of the polynomial f (x)= 2x2+(p +3)x+ 5 is zero, then the value of p is (A) 3 (B) 4 (C) –3 (D) –4
www.asiriyar.com 5) Let b = a + c . Then the equation ax2+ bx+ c=0 has equl roots, if A) a = c (B) a = – c (C) a = 2c (D) a = –2c
6) If A is of order 3 # 4 and B is of order 4 # 3, then the order of BA is (A) 3 # 3
(B) 4 # 4
(C) 4 # 3
(D) not defined
7) Which one of the following statements is not true? (A) A scalar matrix is a square matrix B) A diagonal matrix is a square matrix (C) A scalar matrix is a diagonal matrix D) A diagonal matrix is a scalar matrix.
8)The slope of the straight line 7y - 2x = 11 is equal to (A)- 7/2 (B)7/2 (C)2/7 (D)-2/7 9) If the tangents PA and PB from an external point P to circle with centre O are inclined to each other at an angle of 400, then ∟POA = (A) 700 .(B) 800 (C)500 (D)600
10) The sides of two similar triangles 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 11)9tanƟ2-9sec2Ɵ=
(A)1(B) 0(C) 9
(D) -9
12)man is 28.5 m away from a tower. His eye level above the ground is 1.5 m. The angle of elevation of the tower from his eyes is 45c.Then the height of the tower is (A) 30 m (B) 27.5 m (C) 28.5 m (D) 27 m
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13)If the diameter and height of a right circular cone are 12 cm and 8 cm respectively, then the slant height is (A) 10 cm (B) 20 cm (C) 30 cm (D) 96 cm 14) If the standard deviation of a set of data is 1.6, then the variance is (A) 0.4 (B) 2.56 (C) 1.96 (D) 0.04 15) The probability that a student will score centum in mathematics is 4/5 . The probability That he will not score centum is (A)
1 5
2
3
5
5
(B) (C)
(D)
4 5
Section – II Answer any ten. Question no 30 is compulsory. 16)Let P = {a,b,c}, Q = {g,h, x, y} and R = {a,e, f, s}. Find the R\ (P ∩Q). −𝑥, 𝑥 < 0 where x ϵR. Does the relation 𝑥, 𝑥 ≥ 0 { (x,y) | y = | x|, x ϵR } define a function? Find its range. 17) ) 𝑓 𝑥 =
18) Simplify
𝑥3 𝑥−2
+
8 2−𝑥
www.asiriyar.com 19) A =
4 −2 8 2 and B = find 6A- 3B 5 −9 −1 −3
20) Construct a 2x 3 matrix A =[aij], whose elements are aij= 2i − 3j
21) If (7,3),(6,1), (8,2)and (p, 4)are the vertices of a parallelogram taken in order, then find the value of p. 22) Find the equations of the straight lines parallel to the coordinate axes and passing through the point (-5,-2).
23) E and F are points on the sides PQ and PR respectively, of a 3PQR. For each of the following cases, verify EF ΙΙQR.(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm.
24) Prove the identity 𝑠𝑒𝑐 2 Ɵ + 𝑐𝑜𝑠𝑒𝑐 2 Ɵ = cosec𝜃 − 𝑐𝑜𝑡𝜃 25)A ramp for unloading a moving truck, has an angle of elevation of 300. If the top of the ramp is 0.9 m above the ground level, then find the length of the ramp. 26)If the circumference of the base of a solid right circular cone is 236 cm and its slant height is 12 cm, find its curved surface area. 27) A solid wooden toy is in the form of a cone surmounted on a hemisphere. If the radii of the hemisphere and the base of the cone are 3.5 cm each and the total height of the toy is 17.5 cm, then find the volume of wood used in the toy. TakeΠ=22/7
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(28) The largest of 50 measurements is 3.84 kg. If the range is 0.46 kg, find the smallest measurement. 29) Two coins are tossed together. What is the probability of getting at most one head. 1 1 1
30)a)If ax= by= cz ,x,y,z ᴹ≠0 and b2=4ac , then show that , 𝑥 ,𝑦 ,𝑧 , are in A.P b) Form a quadratic equation whose roots are
OR
3+ 7, 3− 7
Section – III Answer any nine. Question no 45 is compulsory. 31)A radio station surveyed 190 students to determine the types of music they liked. The survey revealed that 114 liked rock music, 50 liked folk music, and 41 liked classical music, 14 liked rock music and folk music, 15 liked rock music and classical music, 11 liked classical music and folk music. 5 liked all the three types of music. Find (i) how many did not like any of the 3 types? (ii) how many liked any two types only? (iii) how many liked folk music but not rock music? 32) A function f : [-3,7)→R is defined as follows
4𝑥 2 − 1 −3≤𝑥 <2 𝑓 𝑥 = find (i) f(5)+f(6) 3𝑥 − 22 ≤ 𝑥 ≤ 4 2𝑥 − 34 < 𝑥 < 7 4𝑓 3 +2𝑓(4) (ii) f(1)-f(-3) (iii)𝑓 −2 −3𝑓(1)
www.asiriyar.com 33) Find the sum of all natural numbers between 300 and 500 which are divisible by 11. 34) Find the sum of first nterms of the series 7 + 77 + 777 +... 𝑥
𝑦
1
2𝑄
35) If P =𝑥+𝑦 , Q =𝑥+𝑦 then find 𝑃−𝑄 − 𝑃 2 −𝑄 2 . 36) A takes 6 days less than the time taken by B to finish a piece of work. If both A andB together can finish it in 4 days, find the time that B would take to finish this work by himself. 37) Find the values of a andb if the following polynomials are perfect squares.
ax4-bx3+40x2+24x+36 38) A =
3 −2 5 2 and B = , then show that (AB)T =BTAT −7 5 7 3
39) Find the area of the quadrilateral whose vertices are
(-4, -2), (-3, -5), (3, -2) and (2 , 3).
40)State and prove Angle bisector theorem 41)From the top of a tower of height 60 m, the angles of depression of the top and the bottom of a building are observed to be 30c and 60crespectively. Find the height of the building.
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42) Find the mass of 200 steel spherical ball bearings, each of which has radius 0.7 cm, given that the density of steel is 7.95 g/cm3 . (Mass = Volume XDensity) 43)The mean and the standard deviation of a group of 20 items was found to be 40 and 15 respectively. While checking it was found that an item 43 was wrongly written as 53. Calculate the correct mean and standard deviation. 44) A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are rotten. If a person takes out one fruit at random, find the probability that the fruit is either an apple or a good fruit. 45)a) Find the equation of the straight lines passing through the point (2, 2) and the sum of the intercepts is 9.OR b) An iron right circular cone of diameter 8 cm and height 12 cm is melted and recast into spherical lead shots each of radius 4 mm. How many lead shots can be made?. Section – IV Answer both choosing either of the alternative. 46)a) Construct a cyclic quadrilateral ABCD, given AB = 6 cm, ∟ABC = 70o,BC= 5 cm and ∟ACD = 30o. or b)Construct a ∆ABC such that AB = 6 cm, ∟C = 40o and the altitude from C to AB is of length 4.2 cm.
www.asiriyar.com 47) a) Draw the graph of y= x2- x-8 and hence solve x2- 2x -15. Or b) B)NNo. Of 3 4 6 8 9 workers x No of days 96 72 48 36 32 N No. Of days y
16 18
o. of wDraw graph for the data given in the table. Hence find the number of days taken by 12 workers to complete the work.
