SLIP TEST 1 - 2016 MATHEMATICS

10 -Std

Marks : 30

Chapter - 1 : SETS AND FUNCTIONS

Section I

Section I [ 5 x 2 = 10

1) If A=

3) 4) 5)

Marks : 30

Chapter - 1 : SETS AND FUNCTIONS Answer all the questions

2)

10 -Std

SLIP TEST 2 - 2016 MATHEMATICS

, B= and; C= , then find; A(BC) If A,B are two sets and ; U is the universal set such that n(A)=200, n(B)=300, n( AB )=100, n(U )=700 find; n(A B) IfA= andB= , verify the commutative property of set Union. If R= represents the identity function , find the values of a, b, c and d. Let A= B=N and f:A B , f(x)=x2 then find the range of f . Identify the type of function . Section II

Answer all the questions

[ 4 x 5 = 20

6) A (BC) = (AB)(AC) Verify by using Venn

diagram. 7) If U= , A= and B= then show that (AB) = A B 8) Let A= , B= and f(x)= then Represent f by an arrow diagram, a set of ordered pairs, a table and a graph 9) A function f:[-3,7)  R is Find (i) f(5) + f(6) (iii) f(-2) – f(4) www.asiriyar.com

(ii) f(1) - f(-3) (iv)

Answer all the questions [ 5 x 2 = 10 1) If AB then find A B and A\B by using Venn diagram. 2) If A= andB=

verify the commutative property of set Intersection. 3) If A= and f= then write down the range of f . Is f a function from A to B ? 4) Write the pre images of 2 and 3 in the function f= 5) For the given function

F= domain and range. Section II Answer all the questions 6) If A = ,B=

, write the

[ 4 x 5 = 20

and

C= then show that A\(BC) = (A\B)(A\C) 7) A\(BC) = (A\B)(A\C) Verify by using Venn diagram. 8) Let A= , B= and; f(x)=2x+1 then Represent f by a table , an arrow diagram, a set of ordered pairs, a table and a graph 9) In a village of 120 families, 93 families use firewood for cooking, 63 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 24 families use kerosene and cooking gas, 27 families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas.

10 -Std

SLIP TEST 3 - 2016 MATHEMATICS

Marks : 30

Chapter - 1 : SETS AND FUNCTIONS Section I Answer all the questions [ 5 x 2 = 10 1) Draw Venn diagram if A and B are disjoint but both are subsets of C. , A= and 2) If U=

B= then find (AB) 3) If A= , B= and; C= then find A\ (C\B) 4) If

x 5 6 8 10 f(x) a 11 b 1 and f(x)= 2x-1 then find the values of a and b . 5) Let X= . Examine whether f : X  X f= is a function . Explain. Section II Answer all the questions [ 4 x 5 = 20 6) A\(BC) = (A\B)  (A\C) Verify by using Venn

diagram. 7) If A= ,B= and; C= then show that; A(BC) = (AB)(AC) 8) In a town85% of the people speak Tamil, 40% of the people speak English and 20% speak Hindi. Also , 32% speak English and Tamil , 13% speak Tamil and Hindi , 10% speak English and Hindi find the percentage of people who can speak all the three languages. 9) A function f:[-7,6) R is

Find (i) 2f(-4)+3f(2) (ii) f(-7) - f(-3) (iii) www.asiriyar.com

10 -Std

SLIP TEST 4 - 2016 MATHEMATICS

Marks : 30

Chapter - 1 : SETS AND FUNCTIONS Section I Answer all the questions 1) If A= , B= and; C=

[ 5 x 2 = 10

then find; A(BC) 2) A(B\C) – Draw Venn diagram. 3) If A= , and B= then verify the commutative property of set Union. 4) Determine from A= to B= f= is a function > If f is a function find its range. 5)

= Does the relation f define a function? Find its range.

Section II Answer all the questions , B= 6) If A=

[ 4 x 5 = 20

and; C= then show that A(BC) = (AB)C 7) If A= , B= and; C= then show that A\(B\C) (A\B)\C. Justify your answer. 8) (AB) = A B Verify by using Venn diagram. 9) In a survey of university students, 64 had taken mathematics course , 94 had taken computer science course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and computer science, 22 had taken computer science and physics course , and 14 had taken all the three courses. Find the number of students who were surveyed. Find how many had taken one course only.

10 -Std

SLIP TEST 5 - 2016 MATHEMATICS

Marks : 30

Marks : 30

Chapter - 2 : SEQUENCES AND SERIES OF REAL

Chapter - 2 : SEQUENCES AND SERIES OF REAL

NUMBERS

NUMBERS

Section I

Section I

Answer all the questions

[ 5 x 2 = 10

1) Find the common difference and 15th term of the A.P

125,120,115,110,…

Answer all the questions

[ 5 x 2 = 10

1) How many terms are there in the Arithmetic Progression

7, 13, 19, …, 205 3

3

3

3

2) Find the sum of the series : 1 + 2 + 3 + … + 20 = ? 3) Which term of the geometric sequence 1, 2, 4, 8, … is

1024 > 4) If 13 + 23+ 33+ … + k3 = 8281 then find 1 + 2 + 3 + … + k =?. 5)

10 -Std

SLIP TEST 6 - 2016 MATHEMATICS

If the 4 th and 7 th term of a GP are 54 and 1458

3) If 1 + 2 + 3 + … + p = 171 then find 13 + 23+ 33+ … + p3 = ?. 4) If F1 = F2 =1 and; Fn = Fn-1 + Fn-2 , n=3,4,… then write

the first five terms. 5) Find the 10 th term and common ratio of the GP

respectively, find the G.P.

,

Section II Answer all the questions

2) Find the sum of the series : 12 + 22 + 32 + … + 252 = ?

, 1, -2, …

[ 4 x 5 = 20

6) Find the total area of 12 squares whose sides are

12cm, 13cm, … , 23cm. respectively. 7) If the 10 th and 18 th term of an AP are 41 and 73

Section II Answer all the questions

[ 4 x 5 = 20

6) Find the sum of the series: 163 + 173 + 183 + … + 353 = ? 7) If the 4th and 7th term of a GP are

and ;

respectively,,

th

respectively, find the 27 term of the A.P. 8) Find the sum of the first 2n terms of the following series.

12 - 22 + 32 - 42 + … 9) If S1, S2 and S3 are the sum of first n, 2n and 3n terms

of a geometric series repectively, then prove that S1(S3 - S2) = (S2 - S1)2 www.asiriyar.com

find the G.P. 8) The sum of three consecutive terms in an A.P is 6 and

their product is – 120 . Find the three numbers . 9) Find the sum of all natural numbers between 300 and

500 which are divisible by 11.

SLIP TEST 7 - 2016 MATHEMATICS

10 -Std

Marks : 30

10 -Std

SLIP TEST 8 - 2016 MATHEMATICS

Marks : 30

Chapter - 2 : SEQUENCES AND SERIES OF REAL

Chapter - 2 : SEQUENCES AND SERIES OF REAL

NUMBERS

NUMBERS

Section I

Section I

Answer all the questions

[ 5 x 2 = 10

Answer all the questions 1) If 13 + 23+ 33+ … + k3 = 8281 then find;

1) If a=50, n=25, d=-4 in an A.P then find Sn 2) Find the sum of the series : 1 + 3 + 5 + … 25 terms. 3) Which term of a geometric progression 5, 2, ,

is

,…,

2) 3)

?

4) How many terms are there in the Arithmetic

4)

Progression 7, 13, 19, …, 205 5) If the first term and 5th term of a GP are 3 and 1875

Answer all the questions

Section II [ 4 x 5 = 20

6) If the 4 th and 7 th term of a GP are 54

and ;

1458 respectively, find the G.P. 7) If 9th term of an A.P is zero , prove that its 29th term is

double (twice) the 19th term . 8) Find the sum of all 3 digit natural numbers which are

divisible by 8. 9) If a2,b2,c2 are in A.P. then show that ;

are also in A.P.

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5)

1+2+3+…+k If a=5, n=30, l=121 in an A.P then find Sn Find the sum of all two digit natural numbers, which are divisible by 13. If 1 + 2 + 3 + … + n = 120 then find; 13 + 23+ 33+ … +n3 Which term of the geometric sequence 1, 2, 4, 8.... is 1024? Section II

respectively, then find the common ratio . Answer all the questions

[ 5 x 2 = 10

,

,

[ 4 x 5 = 20

6) Find the sum of the series: 113 + 123 + 133 + … + 283 = ? 7) If the first term and 6th term of a GP are

and ;

respectively, find the G.P. 8) The sum of first three terms of a geometric sequence is ; and their product is -1 . Find the common ratio and the terms. 9) If a,b,c are in A.P then prove that (a - c)2 = 4 (b2 - ac)

SLIP TEST 9 - 2016 MATHEMATICS

10 -Std

10 -Std

Chapter - 3 : ALGEBRA

Chapter - 3 : ALGEBRA

Section I

Section I

Answer all the questions 1) Solve :

Marks : 30

SLIP TEST 10 - 2016 MATHEMATICS

[ 5 x 2 = 10

Answer all the questions

Marks : 30

[ 5 x 2 = 10

1) The cost of 11 pencils and 3 erasers is 50 and the

3x + 5y = 25 ; 7x + 6y = 30

cost of 8 pencils and 3 erasers is 38. Find the cost of each

2) Simplify : .

pencil and each eraser.

3) If the sum and product of the roots of the quadratic 2

2) Form the quadratic equation whose roots are 3+

equation ax - 5x + c = 0 are both equal to 10, then find

3) x2y + xy2 , x2 + xy : Find the LCM.

the values of a and c.

4) The sum of a number and its reciprocal is 5 .

and; 3-

Find the number.

4) 3(a-1) , 2(a-1)2 , (a2-1) : Find the LCM. 5) Determine the nature of the roots : x2 - 11x - 10 = 0

5) Determine the nature of the roots : 2x2 - 3x + 4 = 0 Section II

Section II Answer all the questions

Answer all the questions [ 4 x 5 = 20

6) Find the values of a and b if

the polynomial

ax4 - bx3 + 40x2 + 24x + 36 is perfect square. 7) Factorize : x3 - 3x2 - 10x + 24



8)

: Simplify.

9) A car left 30 minutes later than the scheduled time. In

order to reach its destination 150 km away in time, it has to increase its speed by 25 km/hr from its usual speed. Find its usual speed.

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6) Find the values of a and b if

[ 4 x 5 = 20

the polynomial

ax4 + bx3 + 109x2 - 60x + 36 is perfect square. 7) Factorize : x3 - 23x2 + 142x – 120 8) If the roots of the equation (a2 + b2)x2 - 2(ac+bd)x +c2+d2 = 0 a

c

where a , b , c and d  0 , are equal, prove that b = d 9) The base of a triangle is 4cm longer than its altitude. If the area of the triangle is 48 sq.cm, then find its base and altitude.

10 -Std

SLIP TEST 11 - 2016 MATHEMATICS

Marks : 30

Chapter - 3 : ALGEBRA

Chapter - 3 : ALGEBRA

Section I

Section I

Answer all the questions

[ 5 x 2 = 10

+

Answer all the questions

[ 5 x 2 = 10

2) Form the quadratic equation whose roots are 3, 4

: Simplify

3) Find the quadratic polynomial if the sum and product

3) c2 - d2 , c(c - d) : Find the GCD. 4) If α , β are the roots of 2x2 - 3x - 1 = 0 , then find the

of its zeros are , -4 respectively..

value of α - β (where α > β)

4) m2 - 3m - 18, m2+5m+6 : Find the GCD. 5) If α , β are the roots of 3x2 - 6x + 4 = 0 , then find the

5) If the roots of the equation 12x2 + 4kx + 3 = 0 are real

and equal find the value of k .

value of ; α2 + β2

Section II

Section II Answer all the questions 6) Find the values of m and n if

[ 4 x 5 = 20

the polynomial

m - nx + 28x2 + 12x3 + 9x4 is perfect square. 7) Factorize : x3 - 7x + 6 8) Find a quadratic equation whose roots are the

reciprocal of the roots of the equation 4x2 - 3x - 1 = 0 . 9) The speed of a boat in still water is 15 km/hr. It goes

30 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.

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Marks : 30

1) Simplify :

1) Solve : x + 2y = 7 ; x - 2y = 1 2)

10 -Std

SLIP TEST 12 - 2016 MATHEMATICS

Answer all the questions

[ 4 x 5 = 20

6) Find the values of a and b if

the polynomial

4x4 - 12x3 + 37x2 + ax + b is perfect square. 7) Factorize : 2x3 + 11x2 - 7x – 6 8) If α , β are the roots of x2 - 3x - 1 = 0 , form a quadratic

equation whose roots are

.

9) One year ago , a man was 8 times as old as his son.

Now his age is equal to the square of his son’s age. Find their present ages.

10 -Std

SLIP TEST 13 - 2016 MATHEMATICS

Marks : 30

Chapter - 4 : MATRICES Section I Answer all the questions [ 5 x 2 = 10 1) Construct a 2x2 matrix A =(aij) whose elements are

given by aij = ij , then find AT and (AT)T

2) If A = 3) If A =

and B =

10 -Std

SLIP TEST 14 - 2016 MATHEMATICS

Chapter - 4 : MATRICES Section I Answer all the questions [ 5 x 2 = 10 1) Construct a 3x2 matrix (aij) whose elements are

aij = , then verify that (AT)T = A

2) If A =

then find;

3) If A =

6A - 3B

Marks : 30

and B =

then prove that

A+B = B+A 4) Find the product , if exists

4) Prove that

and;

are inverses to

and if so , state the order of the product .

each other under matrix multiplication . 5) If A =

Section II Answer all the questions

and B=

then find A+B .

6) If A =

Section II Answer all the questions 6) If A =

[ 4 x 5 = 20

and B =

5) Determine the product PQ if P=(pij)4x3 , Q=(qij)4x3

then verify that

[ 4 x 5 = 20

and B =

then verify

(AB)T = BT AT 7) If A =

,B=

and

(AB)T = BT AT 7) If A =

then verify that A2 - 4A + 5I2 = O

C= then verify that A + (B + C) = (A + B) + C

8) Solve „

+3

9) If A=

, B=

=

8) If A=

and C=

verify that A(B+C) = AB + AC

then

and

C=

then;

verify that (AB)C = A(BC) 9) If A=

AB, BA www.asiriyar.com

, B=

and B =

then find ;

10 -Std

SLIP TEST 15 - 2016 MATHEMATICS

Marks : 30

10 -Std

Chapter - 4 : MATRICES

Chapter - 4 : MATRICES

Section I

Section I

Answer all the questions

[ 5 x 2 = 10

1) Construct a 2x2 matrix A =(aij) whose elements are

Answer all the questions

Marks : 30

[ 5 x 2 = 10

1) Construct a 2x3 matrix A =(aij) whose elements are

given by aij = 2i -j

given by aij =

2) If

=

then find the

values of x,y,z 3) If A =

SLIP TEST 16 - 2016 MATHEMATICS

2) If A =

then Verify A I = I A = A

3) Prove that A =

and B =

then find the matrix

C = 2A+B

and; B =

are

inverses to each other under matrix multiplication . 4) Find the product , if exists for the following :

4) Determine the product A1x3 and; B4x3 and if so , state

the order of the product AB. 5) Solve „

5) If A =

=

and B =

matrix AB .

Section II

Section II

Answer all the questions 6) If A=

[ 4 x 5 = 20

, B=

and C=

then prove

that (AB)C = A(BC) 7) If A =

then find the

Answer all the questions 6) If A = 7) If A=

and B =

then find AB, BA Are

[ 4 x 5 = 20

then verify that A2 - 4A + 5I2 = O , B=

and C=

then find;

(A+B)C and AC + BC. Is (A+B)C = AC + BC

they equal ? =

8) 9) If 2x + 3y =

matrices X and Y. www.asiriyar.com

, 3x + 2y =

Solve the equation. then find the

8) Solve „ 9)

If A =

+3

= and B =

that (A+B)2  A2 + 2AB + B2

then prove

10 -Std

SLIP TEST 17 - 2016 MATHEMATICS

Marks : 30

10 -Std

SLIP TEST 18 - 2016 MATHEMATICS

Marks : 30

Chapter - 5 : CO - ORDINATE GEOMETRY Section I Answer all the questions [ 5 x 2 = 10 1) Find the centroid of the triangle whose vertices are

Chapter - 5 : CO - ORDINATE GEOMETRY Section I Answer all the questions [ 5 x 2 = 10 1) Find the slope and Y-intercept of the straight line

A(4,-6),B(3,-2) and; C(5,2) . Find the equation of the straight line passing through the points (-2,5) and (3,6) . Find the area of the triangle formed by the points (1,2), (-3,4) and; (-5,-6) . Find the equation of the straight line perpendicular to the line x - 2y + 3 = 0 and passing through the point (1,-2) . Find the equation of the straight line whose X and Y-intercepts are and respectively.

10x + 15y + 6 =0 Find the equation of the straight line passing through the points (-1,1) and (2,-4) . Find the equation of the straight line parallel to the straight line x-8y+13 =0 and passes through the point (2,5) . If the area of a triangle formed by A(0,0),B(4,a) and; C(6,4) is 17 sq.units , then find the value of a . Find the equation of the straight line whose X and Y-intercepts are 2 and 3 respectively.

2) 3) 4)

5)

Section II Answer all the questions [ 4 x 5 = 20 6) Using the concept of slope, show that the points (-2,-1),

(4,0), (3,3) and; (-3,2) taken in order form a parallelogram. 7) Find the area of the quadrilateral formed by the points (6,9), (7,4), (4,2) and; (3,7) . 8) Find the equation of the straight line passing through the point of intersection of the ines 5x - 6y = 1 and 3x + 2y + 5 = 0 and is perpendicular to the straight line ; 3x - 5y + 11 = 0 . 9) If the points (a,1), (1,2) and; (0,b+1) are collinear, then show that + =1

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2) 3)

4) 5)

Section II Answer all the questions [ 4 x 5 = 20 6) Using the concept of slope, show that the points (1,2),

(-2,2), (-4,-3) and; (-1,-3) taken in order form a parallelogram. 7) Find the area of the quadrilateral formed by the points (-4,-2), (-3,-5), (3,-2) and; (2,3) . 8) If the vertices of a PQR are P(1,-3),Q(-2,5) and R(-3,4) . Find the equation of the straight line along the median from the vertex R . 9) In what ratio is the line joining the points (-5,1) and ; (2,3), divided by the y-axis ? Also, find the point of intersection.

10 -Std

SLIP TEST 19 - 2016 MATHEMATICS

Marks : 30

Chapter - 5 : CO - ORDINATE GEOMETRY Section I Answer all the questions

[ 5 x 2 = 10

1) Find the equation of the straight line whose slope is -4 2) 3) 4) 5)

and passing through; (1,2) . Find the equation of the straight line parallel to the coordinate axes and passing through the point (3,-4) . Find the value of a if the straight lines 5x-2y-9 = 0 and ay+2x-11 = 0 are perpendicular to each other. If the equation of a straight line is 5x+3y-15=0 then find the X and Y –intercepts . Find the slope and Y-intercept of the straight line 5x = 3y . Section II

Answer all the questions

[ 4 x 5 = 20

6) Show that the opposie sides of a quadrilateral with vertices

A(-2,-4), B(5,-1), C(6,4) and; D(-1,1) taken in order are parallel. 7) Find the area of the quadrilateral formed by the points (-4,5), (0,7), (5,-5) and; (-4,-2) . 8) Find the equation of the median from the vertex A in a ABC with vertices at A(2,1),B(-2,3) and; C(4,5) . 9) In what ratio does the point P(-2,3) divide the line segment joining the points A(-3,5) and; B(4,-9) internally ?

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10 -Std

SLIP TEST 20 - 2016 MATHEMATICS

Marks : 30

Chapter - 5 : CO - ORDINATE GEOMETRY Section I Answer all the questions [ 5 x 2 = 10 1) Find the equation of the straight line whose slope is

and passing through; (5,-4) . 2) Find the ratio in which the x-axis divides the line segment joining the points (6,4) and; (1,-7) . 3) If the three points (h,0), (a,b) and; (0,k) lie on a straight line, then using the area of the triangle formula, show that + = 1 where h , k  0. 4) Find the slope and Y-intercept of the line whose equation

is y = x + 1 . 5) Find the equations of the straight lines parallel to the coordinate axes and passing through the point (3,-4) . Section II Answer all the questions [ 4 x 5 = 20 6) The line joining the points A(-2,3), B(a,5) is parallel to the

line joining the points C(0,5), D(-2,1) . Find the value of a. 7) Find the area of the quadrilateral formed by the points (-3,4), (-5,-6), (4,-1) and; (1,2) . 8) Find the equation of the perpendicular bisector of the straight line segment joining the points (3,4) and (-1,2) . 9) Using the concept of slope, show that the points (1,2), (-2,2), (-4,-3) and; (-1,-3) taken in order form a parallelogram.

10 -Std

SLIP TEST 21 - 2016 MATHEMATICS

Marks : 30

10 -Std

SLIP TEST 22 - 2016 MATHEMATICS

Marks : 30

Chapter - 11, 12 : STATISTICS AND PROBABILITY Section I Answer all the questions [ 5 x 2 = 10 1) The standard deviation of 20 observations is . If each

Chapter - 11, 12 : STATISTICS AND PROBABILITY Section I Answer all the questions [ 5 x 2 = 10 1) Find the range and coefficient of range of

observation is multiplied by 2, find the standard deviation and variance of the resulting observations. . The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data. Calculate the standard deviation of the first 13 natural numbers. An integer is chosen from the first twenty natural numbers. What is the probability that it is a prime number? Two coins are tossed together. What is the probability of getting at most one head ?

43, 24, 38, 56, 22, 39, 45 If the coefficient of variation of a collection of data is 57 and its S.D is 6.84 , then find the mean. There are 7 defective items in a sample of 35 items. Find the probability that an itemchosen at random is non-defective. Three rotten eggs are mixed with 12 good ones. One egg is chosen at random. What is the probability of choosing a rotten egg? 20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the card is not a multiple of 6.

2) 3) 4) 5)

Section II

2) 3) 4)

5)

Section II

Answer all the questions [ 4 x 5 = 20 6) 2,5,8,11,14,6,12,10. Calculate the standard deviation

Answer all the questions [ 4 x 5 = 20 6) 38,40,34,31,28,26,34. Calculate the standard deviation

of the data. 7) 18,20,15,12,25 Find the coefficient of variation of the data. 8) A bag contains 10 white, 5 black, 3 green and 2 red balls. One ball is drawn at random. Find the probability that the ball drawn is white or black or green. 9) The probability that a new car will get an award for its design is 0.25, the probability that it will get an award for efficient use of fuel is 0.35 and the probability that it will get both the awards is 0.15. Find the probability that (i) it will get at least one of the awards (ii) it will get only one of the awards.

of the data. 7) 20,18,32,24,26 Find the coefficient of variation of the data. 8) A card is drawn from a deck of 52 cards. Find the probability of getting a King or a Heart or a Red card. 9) The probability that a girl will be selected for admission in a medical college is 0.16. The probability that she will be selected for admission in an engineering college is 0.24 and the probability that she will be selected in both , is 0.11 (i) Find the probability that she will be selected in at least one of the two colleges. (ii) Find the probability that she will be selected either in a medical college onlyor in an engineering college only.

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10 -Std

SLIP TEST 23 - 2016 MATHEMATICS

Marks : 30

10 -Std

SLIP TEST 24 - 2016 MATHEMATICS

Marks : 30

Chapter - 11, 12 : STATISTICS AND PROBABILITY

Chapter - 11, 12 : STATISTICS AND PROBABILITY

Section I

Section I

Answer all the questions

[ 5 x 2 = 10

Answer all the questions

[ 5 x 2 = 10

1) Find the range and coefficient of range of

1) Find the range and coefficient of range of

41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5 A group of 100 candidates have their height 163.6 cm with coefficient of variation 3.2 . What is the standard deviation of their heights? Find the probability that a leap year selected at random will have 53 Fridays. A box contains 4 Green, 5 Blue and 3 Red balls. A ball is drawn at random. Find the probability that the selected ball is not Green in colour. If A and B are two events such that P(A) = , P(B) = and P(A U B) = then find P(A  B)

59, 46, 30, 23, 27, 40, 52, 35, 29 The largest of 50measurements is 3.84 kg. If the range is 0.46 kg, find the smallest measurement. Find the probability that a non-leap year selected at random will have 53 Fridays. Three coins are tossed simultaneously. Find the probability of getting at least one head. A ticket is drawn from a bag containing 100 tickets. The tickets are numbered from one to hundred. What is the probability of getting a ticket with a number divisible by 10?

2)

3) 4)

5)

Section II

2) 3) 4) 5)

Section II Answer all the questions

[ 4 x 5 = 20

[ 4 x 5 = 20

6) A test in General knowledge was conducted for a class. The

6) Find the standard deviation of the data 3,5,6,7. Then add 4

marks out of 40, obtained by 6 students were 20,14,16,30,21 and; 25. Find the standard deviation of the data. 7) The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation. 8) If a die is rolled twice, find the probability of getting an even number in the first time or a total of 8. 9) One number is chosen randomly from the integers 1 to 50. Find the probability that it is divisible by 4 or 6.

Answer all the questions

to each item and find the standard deviation of the new data. 7) Interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency; 8 12 17 14 9 7 4 Calculate the standard deviation 8) A die is thrown twice. Find the probability that at least one of the two throws comes up with the number 5 . ( use addition theorem ) 9) Two unbiased dice are rolled once. Find the probability of getting (i) a sum 8 (ii) a doublet (iii) a sum greater than 8. www.asiriyar.com

Two mark questions for practice

15) If A =

1) (BC)\A – Draw Venn diagram. 2) If A,B are two sets and ; U is the universal set such

that n(A)=285, n(B)=195, n( AB )=410, n(U )=500

then

Verify that A + (-A) = O = (-A) + A 16) If A =

and B =

then find

C(-1,5) is 12 sq.units , then find the value of a .

by (i) a table (ii) an arrow diagram 4) If R=

represents the

identity function , find the value of a , b , c and d. A

5) If Cn = (-1)n 3n+2 ,

nN then write the first three terms

6) Find the sum of the series : 31 + 33 + … + 53 = ? 7) If 13 + 23+ 33+ … + n3 = 36100 then find

8) Find the sum of the series : 12 + 22 + 32 + … + 252 9) Solve x + = 2

by using quadratic formula. : Simplify

vertices are (-7,6) and; (8,5) then find the third vertex of the triangle . 19) If P(x,y) is any point on the line segment joining the points

(a,0) and (0,b) , then, prove that

+ = 1 where a , b 0.

= x - p and;

ax + 5 = 3y are parallel to each other. 21) Three dice are thrown simultaneously. Find the probability

of getting the same number on all the three dice. 22) Calculate the standard deviation of the first 10 natural

2

11) If the roots of the equation 2x - 10x + k = 0 are real

and equal find the value of k . 12) Solve : x + =4 ;

18) If the centroid of a triangle is at (1,3) and two of its

20) Find the value of a if the straight lines

1 + 2 + 3 + …+ n

+ 2y = 5

13) Find the product , if exists for the following :

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and O =

17) If the area of a triangle formed by A(a,-3),B(3,a) and;

3) Represent the function f=



, B=

A+B .

find n(A B)

10)

14) Find the product , if exists

numbers. 23) If n = 10,

and ; Σ X2 = 1530, then calculate the

coefficient of variation .

Five mark questions for practice 1) In a school of 4000 students, 2000 know French, 3000

know Tamil and 500 know Hindi, 1500 know French and Tamil, 300 know French and Hindi, 200 know Tamil and Hindi and 50 know all the three languages. (i) How many do not know any of the three languages? (ii) How many know at least one language? (iii) How many know only two languages? 2) A function [ f:[-7,6)  R is : Find (i) 2f(-4) + 3f(2) (ii) f(-7) - f(-3)

(iii)

3) If A=

, B= and; C= the assosiative law of Set intersection A(BC) = (AB)C 4) A function f:[1,6)  R is

14) If A=

(A+B)C and 15) If A =

16) If A =

17)

Find (i) f(5) (ii) f(3) (iii) f(1) (iv) f(2) - f(4) 19)

5) Find the three consecutive terms in an A.P whose sum 6) 7) 8) 9)



10)

+

11) 12) If P =

,Q=

13) If A =

Are they equal? www.asiriyar.com

: Simplify

-

then find the value of and B =

20) 21)

22)

23) 24)

: Simplify

-

then find; AB, BA.

then prove that

A - (a + d)A=(bc - ad) I2

18)

is 18 and the sum of their squares is 140. If ax = by = cz , x  0 , y  0 , z  0 and; b2 =ac , then show that , , are in A.P.. Find the total volume of 15 cubes whose sides are 16cm, 17cm, 18cm … , 30cm. respectively. Find the sum of the first 40 terms of the following series. 12 - 22 + 32 - 42 + … If the equation (1+m2)x2 + 2mcx + c2 - a2 = 0 has real and equal roots , then prove that c2 = a2(1+m2)

and I2 =

2

then prove

(v) 2f(5) - 3f(1)

, B= and C= then find; AC + BC . Is ; (A+B)C = AC + BC ?

and B =

;

then verify that

(AB)T = BT AT If the vertices of a ABC are A(2,-4),B(3,3) and C(-1,5) . Find the equation of the straight line along the altitude from the vertex B . Find the equation of the straight line joining the point of intersection of the straight lines 3x - y + 9 = 0, x + 2y = 4 and the point of intersection of the straight lines 2x + y - 4 = 0, x - 2y + 3 = 0 . Find the equation of the straight line passes through the point of intersection of the straight lines 2x – 3y + 4 =0 , x – 2y + 3 = 0 and the mid point of the line segment joining the points (3,-2) and (-5,8) . Find the equation of the straight lines passing through the point (6,-2) and the sum of the intercepts is 5 . Amount(‘ ) 0-20 20-40 40-60 60-80 80-100 Numbers 2 7 12 19 5 Calculate the variance and standard deviation. x 70 74 78 82 86 90 f 1 3 5 7 8 12 Calculate the standard deviation 20,18,32,24,26 Find the coefficient of variation of the data. x 3 8 13 18 23 f 7 10 15 10 8 Calculate the standard deviation

1.

Practical Geometry 1. Draw a circle of radius 3.2 cm. Take a point P on this circle and draw a tangent at P. (Using the centre). 2. Draw a circle of radius 4.2 cm, and take any point on the circle. Draw the tangent at that point using the centre. 3. Draw a circle of radius 3.2 cm at a point P on it, draw a tangent to the circle using the tangent - chord theorem. 4. Draw a circle of radius 4.8 cm. Take a point on the circle. Draw the tangent at that point using the tangent - chord theorem. 5. Draw a circle of radius 3 cm. From an external point 7 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. 6. Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 6 cm. Also, measure the lengths of the tangents. 7. Draw a circle of diameter 10 cm. From a point P, 13 cm away from its centre, draw the two tangents PA and PB to the circle, and measure their lengths. 8. Take a point which is 9 cm away from the centre of a circle of radius 3 cm, and draw the two tangents to the circle from that point. 9. Construct a  ABC such that AB = 6 cm,
10. Construct a ABC in which BC = 5.5 cm,
Graph

5. The following table gives the cost and number of notesbooks bought.

1. Draw a graph for the following table and identify the variation. x y

2 8

3

5

12

20

8 32

No. of note books

10

2

4

6

30

60 90

8

10

12

x

40

Cost

Hence, find the value of y when x = 4.

120

150 180

y

2. A cyclist travels from a place A to a place B along the same route at a uniform speed on different days. The following

Draw the graph and hence

table gives the speed of his travel and the corresponding

(i) Find the cost of seven note books.

time he took to cover the distance.

(ii) How many note books can be bought for 16 5.

Speed in km / hr

6. 2

4

6

10

12

60

30

20

12

10

x Time in hrs

Draw the speed - time graph and use it to find. (i) The number of hours he will take if he travels at a speed (ii) The speed with which he should travel if he has to cover

5

7

8

y

2

6

10

14

16

Draw the graph for the above table and hence find (ii) The value of x if y = 12 7. The cost of the milk per litre is 15. Draw the graph for the (i) The proportionality constant. (ii) The cost of 3 litres of milk.

the distance in 40 hrs. 3. A bank gives 10 % S.I on deposits for senior citizens. Draw the graph for the relation between the sum deposited and the interest earned for one year. Hence find. 650.

(ii) The amount to be deposited to earn an interest of 45. 4. A bus travels at a speed of 40 km / hr. Write the distance time formula and draw the graph of it. Hence, find the distance

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3

relation between the quantity and cost. Hence find.

of 5 km / hr.

travelled in 3 hours.

1

(i) The value of y if x - 4

y

(i) The interest on the deposit of

x

8. Draw the graph of xy = 20, x, y > 0. Use the graph to find y when x = 5, and to find x when y = 10. 9. No of workers

3

4

6

8

9

16

96

72

48

36

32

18

x No of days y Draw graph for the data given in the table. Hence find the number of days taken by 12 workers to complete the work.