Subject- Mathematics Class- X- std

1

Subject- Mathematics

Class- X- std

SAMPLE TABLE OF CONTENTS

CHAPTERS NAME OF THE CHAPTER PAGE NO.

1 Real Numbers MCQ’S:- 3to4

A and R:-27 to 28

CASE STUDY:- 41 to 44

COMP.:-63 to 66

2 Polynomials MCQ’S:- 5 to 7

A and R:-28 to 29

CASE STUDY:-45 to 48

COMP.:- 67 to 69

3 Pair of equations in two

variables

MCQ’S:- 7 to 10

A and R:-30 to 31


COMP.:- 71

6 Triangles MCQ’S:-10 to 14

A and R:-32 to 33


COMP.:- 71 to 73

7 Co-ordinate Geometry MCQ’S:- 14 to 16

A and R:- 34 to 35


COMP.:- 73

8 Trigonometric Functions MCQ’S:- 16 to 18

A and R:- 35 to 36


COMP.:- 74

12 Areas related to circles MCQ’S:-19 to 21

A and R:- 36 to 38


COMP.:- 75 to 79

15 Probability MCQ’S:-22 to 26

A and R:-38 to 40

2


COMP.:-79 to 81

MULTIPLE CHOICE QUESTIONS-

CH1. REAL NUMBERS

1)Two positive number have their HCF 12 and their product as 6336.The number

pairs possible for the number is

a) 2

b) 3

3

c) 4

d) 5

2) If n is an even natural number, then the largest ,then the largest natural number

by which n(n+1)(n+2) is divisible is

a) 6

b) 8

c) 12

d) 24

3) The rational form of is in the form of then (p+q) is

a) 14

b) 55

c) 69

d) 79

4) The least number which is a perfect square and is divisible by each of 16,20,and

24 is

a) 240

b) 1600

c) 2400

d) 3600

5) For any natural number n,9n cannot end with the digit

a) 1

b) 2

c) 9

d) 5

6) H.C.F of 6,72 and 120 is

a) 6

b) 2

c) 4

d) 5

4

7) If a = bq +r ,least value of r is

a) 1

b) 0

c) 8

d) 4

8) is which type of number

a) Irrational

b) Rational

c) square

d) whole

9) The sum of exponents of the prime factors in the prime factorization of 196 is

a) 1

b) 4

c) 2

d) 6

10) If HCF of 65 and 117 is expressible in the form of 65m-117, then the value of

m is

a) 1

b) 2

c) 4

d) 3

CH2. POLYNOMIALS

11) If are the zeros of the polynomial f(X) = x2 +x+1 ,then

a) 1

b) -1

c) 0

5

d) none

12) If one zero of the polynomial f(x)= ( k2 + 4)x

2 + 13x +4k is reciprocal of the

other then k =

a) 2

b) -2

c) 1

d) -1

13) If the sum of the zeros of the polynomial f(x)= 2x3- 3kx

2 +4x -5 is 6 ,then the

value of k is

a) 2

b) 4

c) -2

d) -4

14) If the polynomial f(X)=ax3+ bx –c is divisible by the polynomial g(x) =x

2 +bx

+c then ab=

a) 1

b) c

c) -c

d) -1

15) If two of the zero of the cubic polynomial ax3 + bx

2 + c x+ d are each equal to

zero ,then the third zero is

a)

b)

c)

6

d)

16) If the zeros of x3 + x

2 -5x -5 are then third zero is

a) 1

b) -1

c) -2

d) 2

17) What should be added to the polynomial x2-16 x +30, so that 15 is the zero of

the resulting polynomial?

a) 1

b) 2

c) 4

d) 5

18) If the product of zeros of the polynomial f(x) = ax3 -6x

2 +11x -6 is 4 then a =

a)

b)

c)

d)

19) If the square of difference of the zeros of the quadratic polynomial x2 +px +45

is equal to 144,then the value of p is

a)

b)

c)

d)

7

20) find the zeros of the quadratic polynomial y2 -3y +2 with the help of graph

a) 1,-2,

b) 2 ,4

c) 1,2

d) 6,-1

CH3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

21) The pair of equations x = a and y = b graphically represents the lines which

are……..

a)Parallel

b)intersecting at (a,b)

c) Coincident

d) intersecting at (b,a)

22) The value of k for which the pair of equations and

will have no solutions is

a) 3

b) -3

c) 2

d) no value

23) The sum of the digits of a two digit number is 9. If 27 is added to it , the

digits of the numbers get reversed. The number is

a)36

b) 72

c) 63

d) 25

8

24) The sum of the numerator and denominator of a fraction is 12. If the

denominator is increased by 3, the fraction becomes half, then the fraction is

a)

b)

c)

d)

25) Sum of two numbers is 35 and their difference is 13, then the numbers are

a)24 and 12

b) 24 and 11

c) 12 and 11

d) none of these

26) Five years ago , A was thrice as old as B and ten years later A shall be twice

as old as B, then the present age of A is

a)20

b) 50

c) 30

d) none of these

27) ABCD is a cyclic quadrilateral. The values of and y are

9

a)15 and -25

b) 15 and 25

c) -15 and 25

d) none of these

28) 2 men and 7 boys can do a piece of work in 4 days. The same work is done

in 3 days by 4 men and 4 boys . How long would it take one man and one

boy to do it alone.

a)15 days

b) 60 days

c) 15 days

d) 12 days

10

29) The solution of the system of linear equations

are

a) ,

b) ,

c) ,

d) none of these

30) If and , then is

a) 0

b) -1

c) 1

d) 2

CH6. TRIANGLES

31) It is given that with , then is equal to

a)9

b) 3

c)

d)

32) A ladder is placed against a wall such that its foot is at distance of 2.5m from

the wall and its top reaches a window 6m above the ground. The length of the

ladder is

a)6.5m

b) 7.5m

c) 8.5m

d) 9.5m

11

33) , area of , area of and

QR = 6cm, then length of BC is

a)4cm

b) 4.5cm

c) 9cm

d) 12cm

34) In the given figure, if then the value of is

a)6cm

b) 10cm

c) 8cm

d) 12.5cm

12

35) In the given figure, if then the value of is

a)1cm

b) 2cm

c) 3cm

d) 4cm

36) In the given below figure, the value of is

a)

b)

c)

d)

13

37) In the following figure and , then AQ is

a)15 units

b) 8units

c) 5 units

d) 9 units

38) Two isosceles triangles have equal angles and their areas are in the ratios

16 : 25. The ratio of their corresponding heights is

a)3:2

b) 5 : 4

c) 5 : 7

d) 4 : 5

14

39) Two poles of height 6m and 11m stand vertically upright on a plane ground.

If the distance between their foot is 12m, the distance between their tops is

a)14cm

b) 12cm

c) 13cm

d) 11cm

40) The value of for which is

a)

b) 2

c) 1

d) none of these

CH7. COORDINATE GEOMETRY

41) If the distance between the points (8, p) and (4, 3) is 5 then value of p

is…………..

a.6

b. 0

c. both a and b

d. none of these

15

42) The fourth vertex of the rectangle whose three vertices taken in order are

(4,1), (7, 4), (13, –2) is………..

a. (10, –5)

b.(10, 5)

c. (8, 3)

d. (8, –3)

43) If the origin is the mid-point of the line segment joined by the points (2,3)

and (x,y), then the value of (x,y) is……………….

a. (2, -3)

b. (2,3)

c.(-2,3)

d.(-2,-3)

44) The distance of the point P(2, 3) from the x-axis is………………….

a.2

b.3

c.1

d.5

45) Line formed by joining (- 1,1) and (5, 7) is divided by a line x + y = 4 in the

ratio of……………..

a. 1 : 4

b. 1 : 3

c. 1 : 2

d. 3 : 4

46) The distance of A(5, -12) from the origin is…………………………..

a. 12

b.11

c. 13

d. 10

47) Point A(–5, 6) is at a distance of…………….units from the origin.

a.

b.

c. 61

d.11

16

48) The points (2, 5), (4, - 1), (6, - 7) are vertices of an ___________ triangle.

a. isosceles

b. equilateral

c. scalene

d. right angled

49) If P(l, 2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram

PQRS then

a. a = 2, b = 4

b. a = 3, b = 4

c. a = 2, b = 3

d. a = 3, b = 5

50) the ordinate of a point whose abscissa is 10 and which is at a distance of 10

units from the point P(2, -3) is………..

a. 3

b.-9

c. both a or b

d. none of the these

CH8. INTRODUCTION TO TRIGONOMETRY

51) The reciprocal of cosecA is…………

a. sinA

b. cosA

c. secA

d. cotA

52) In right angle , ………….

a. cotA

b. cosecA

c. tanA

d. cosA

17

53) ………………..

b.

c.

d.

54) If and is acute angle then ………..

a. 0

b. 60

c. 90

d. none of these

55) ……….

a. 0

b. 2

c. ½

d. 1

56) If cot =7/8 then …………

a. 7/8

b.8/7

c.49/64

d.64/49

18

57) ……………..

a. 0

b. 1

c.2

d.

58) …………………..

a.

b.

c.

d.

59) The value of if is……

a. 45

b. 30

c. 0

d.15

60) In the fig. AB = BC = 10cm then value of x is…..

a. 45

b. 30

c. 0

d.15

19

CH12. AREAS RELATED TO CIRCLE

61) If the area of the sector of a circle bounded by an arc of length 5 cm is

equal to 20 cm2 then the radius of the circle is

a.12cm

b.16cm

c. 8cm

d.10cm

62) If the area of a sector of a circle is of the area of the circle, then the sector

angle is equal to

a.600

b.900

c. 1000

d.1200

63) The area of the incircle of an equilateral triangle is 154 cm2. The perimeter

of the triangle is

a. 71.5cm

b.71.7 cm

c.72.3 cm

d. 72.7cm

20

64) If the difference between the circumference and radius of a circle is 37

cm, then using the circumference of the circle is

a.154 cm

b. 44 cm

c. 14 cm

d. 7 cm

65) If the perimeter of the circle and square are equal, then the ratio of their

areas will be equal to

a. 14:11

b. 22:7

c. 7:22

d. 11:14

66) In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The

length of the arc is;

a. 20cm

b.21cm

c. 22cm

d. 25cm

21

67) It is proposed to build a single circular park equal in area to the sum of areas

of two circular parks of diameters 16 m and 12 m in a locality. The radius of

the new park would be

a.10 m

b. 15 m

c. 20 m

d. 24 m

68) The wheel of a motorcycle is of radius 35 cm. The number of revolutions per

minute must the wheel make so as to keep a speed of 66 km/hr will be

a. 50

b.100

c. 500

d.1000

69) A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the

form of a square, then its area will be

a. 3520 cm²

b. 6400 cm²

c. 7744 cm²

d. 8800 cm²

70) The ratio of the outer and inner perimeters of a circular path is 23 : 22. If the

path is 5 metres wide, the diameter of the inner circle is

a.55 m

b. 110 m

c. 220 m

d. 230 m

22

CH15. PROBABILITY

71) If two different dice are rolled together, the probability of getting an even

number on both the dice…..

a.

b.

C.

d.

72) What is the probability that a non-leap year has 53 Sundays ?

a.

b.

c.

d.None

23

73) What is the probability that a leap year has 52 Mondays ?

a.

b.

c.

d.None

74) Two dice are rolled simultaneously. The probability that they show different

faces is

a.

b.

c.

d.

24

75) A bag contains cards numbered from 1 to 25. A card is drawn at random

from the bag. The probability that the number on this card is divisible by both

2 and 3 is

a.

b.

c.

d.

76) A bag contains three green marbles, four blue marbles and two orange

marbles. If a marble is picked at random, then the probability that it is not an

orange marble is

a.

b.

c.

d.

25

77) A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9.

The probability that the selected number is their average is

a.

b.

c.

d.

78) Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya

purchased a ticket, what is the probability of Priya winning a prize ?

a.

b.

c.

d.

26

79) A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at

random from the box, the probability that it bears a prime number less than

23, is

a.

b.

c.

d.

80) If a number x is chosen from the numbers 1,2,3 and a number is selected

from the numbers 1, 4, 9, then P (xy < 9)

a.

b.

c.

d.

27

ASSERTION AND REASONING BASED QUESTIONS

CH1. REAL NUMBERS

In the following question a statement of Assertion (A) is followed by a statement

of Reason (R),pick the correct option.

a) Both (A) and (R) are true and R is the correct explanation of ( A)

b) Both (A) and (R) are true but R is not the correct explanation of ( A)

c) (A) is true but (R) is false

d) (A) is false but (R) is true

1) Assertion : 2 is a rational number

Reason: The square root of all positive integers are irrational

Ans- c

2) Assertion : n2+n is divisible by 2 for every positive integer n

Reason: If x and y are odd positive integers ,from x2 + y

2 is divisible by 4

Ans –a

3) Assertion: Two numbers have 15 as their HCF and 175 as their LCM

Reason : LCM of two number should be exactly divisible by their HCF

Ans- d

4) Assertion :The least number that divisible by all number between 1 and 10

is 2520

Reason : The required number is the LCM of 1,2,3,4,5,6,7,8,9,10

Ans- a

5) Assertion :The HCF of two number is 12 and their product 1800,their LCM

is 140

Reason: If a,b are two positive integers ,then H.C.F X L.C.M =a xb

Ans –d

28

6) Assertion: 8n ends with digit zero ,where n is natural number.

Reason: Any number ends with zero, if its prime factors is of the form 2m x

5n,where m,n are natural number

Ans- d

7) Assertion :The denominator of has terminating decimal expansion of the

form 2m x 5

n

Reason: is rational number

Ans: c

8) Assertion: If x and y are odd positive integers then x2 + y

2 is even but not

divisible by 4.

Reason: n2 + 1 is divisible by 8

Ans : c

9) Assertion: There are very few positive integers

Reason: Let a be a positive integer and p be prime number such that p| a2 ,

then p| a

Ans: d

10) Assertion: For some integer m , every even integer is of the form 2m.

Reason: Integer contains all negative as well as positive values.

Ans: a

CH2. POLYNOMIALS

11) Assertion: x2 +x has only one real zero

Reason : A polynomial of nth degree must have n real zeros

Ans: c

12) Assertion: Degree of the zero polynomial is not defined.

Reason : Degree of a non zero constant polynomial is 0

Ans: b

29

13) Assertion: (2- is one zero of the quadratic polynomial then other zero

will be (2 + .

Reason: Irrational zeroes (roots) always occurs in pairs.

Ans: a

14) Assertion: Zeroes of f(x) = x2 – 4x – 5 are 5,-1

Reason: The polynomial whose zeroes are 2+ , 2- is x2 – 4x+7

Ans: c

15) Assertion: x2 + 4x +5 has two zeroes

Reason: A quadratic polynomial can have at the most two zeroes.

Ans: d

16) Assertion: The graph of linear pomynomial is astraight line

Reason: Polynomial p(x) =ax+b is a linear polynomial

Ans: a

17) Assertion : If are the zeros of quadratic polynomial ax2 +bx +c

Reason : = , =- ca

Ans : b

18) Assertion: If both the zeroes of quadratic polynomial x2 – 2kx +2 are equal

in magnitude but opposite in sign then the value of k is ½.

Reason: Sum of zeroes of quadratic polynomial ax2 +bx+ c is –b/a

Ans: d

19) Assertion: If p(x)= ax+b then zero of p(x) is –b/a

Reason: Every polynomial equation has atleast one real root

Ans: c

20) Assertion: Degree of quadratic polynomial is less than or equal to two.

Reason: A polynomial of degree n has exactly n zeroes.

Ans: d

30


21) Assertion : If the system of equations and

has infinitely many solutions then 2a-b=0

Reason : The system of equations and has a

unique solution.

Ans :-c

22) Assertion : and represents parallel

lines if k = 8.

Reason : and represent parallel

lines if

Ans :-a

23) Assertion : For k = 6, the system of linear equations and

is inconsistent.

Reason :The system of linear equations and

is inconsistent if

Ans :-c

24) Assertion : If the pair of lines are coincident , then we say that pair of lines

is consistent and it has a unique solution.

Reason : If the pair of lines are parallel, then the pair has no solution and is

called inconsistent pair of equations.

Ans :-d

25) Assertion : Pair of linear equations and

have infinitely many solutions.

Reason : The system of linear equations and

have infinitely many solutions if

Ans :-a

31

26) Assertion : The lines and are parallel lines.

Reason : The system of linear equations and

have infinitely many solutions if

Ans :-b

27) Assertion : and have infinite number of

solutions if k =14

Reason : , have a unique solution

if

Ans :-b

28) Assertion : The linear equations and

have exactly one solution.

Reason : The linear equations and have

a unique solution.

Ans :-c

29) Assertion : and has no solution if k = 2.

Reason : and are consistent if

Ans :-b

30) Assertion : The value of , if is the solution of the line

Reason : The solution of the line will satisfy the equation of the line.

Ans :-a

32

CH6. TRIANGLES

31) Assertion : If in a , a line , intersects AB in D and AC in E

, then

Reason : If a line is drawn parallel to one side of a triangle intersecting the

other two sides, then the other two sides are divided in the same ratio.

Ans:-a

32) Assertion : In a , a line such that ,

, and then

Reason : If a line is drawn parallel to one side of a triangle to intersect the

other two sides in distinct points , then the other two sides are divided in the

same ratio.

Ans:-d

33) Assertion : such that and

, then AB : DE = 6 : 7

Reason : , then

Ans:-a

34) Assertion : is an isosceles triangle right angled of C , then

Reason : In a right , right angled at B ,

Ans:-a

35) Assertion : Two similar triangles are always congruent.

Reason : If the areas of two similar triangles are equal then the triangles are

congruent.

Ans:-d

33

36) Assertion : ABC is an isosceles , right triangle, right angled at C. Then

Reason : In an isosceles triangle ABC if AC = BC and , then

Ans:-d

37) Assertion : ABC and DEF are two similar triangles such that BC = 4cm, EF

= 5cm and area of , then the area of

Reason : The areas of two similar triangles are in the ratio of the squares of

the corresponding altitudes.

Ans:-b

38) Assertion : In the , AB = 24cm, BC = 10cm and AC = 26cm , then

is right angle triangle .

Reason : If in two triangles , their corresponding angles are equal , then the

triangles are similar.

Ans:-b

39) Assertion : D and E are points on the sides AB and AC respectively of a

triangle ABC such that then the value of is 11, when

Reason : If a line divides any two sides of a triangle in the same ratio then it

is parallel to the third side.

Ans:-b

40) Assertion : The length of the side of a square whose diagonal is 16cm , is

cm.

Reason : In a right triangle , the square of the hypotenuse is equal to the sum

of the squares of the other two sides.

Ans:-a

34


41) Assertion (A): The distance between the point P (4,6 ) and Q (6,8) is

units.

Reason(R): The distance between the point P(x1,y1 ) and Q(x2,y2 ) is

PQ=

Ans:-a

42) Assertion (A): The distance between the point P (3,0 ) and Q (0,4) is units

Reason(R): The distance a point P(x1,y1 ) from origin is

PQ=

Ans:-c

43) Assertion (A): Ashima , Bharti and Chandranika are seated in a line at

A(3,1),B(6,4) and C(8,6) respectively

Reason(R): Any three points P,Q and R are in a line then

Ans:-c

44) Assertion (A): Ashima , Bharti and Chandranika are seated in a line at

A(3,1),B(6,4) and C(8,6) respectively

Reason(R): Any three points A,B and C are in a line then

Ans:-a

45) Assertion (A): (5,-2), (6,4) and (7,-2) are the vertices of an isosceles

triangle.

Reason(R): Isosceles triangles are the triangles in which two sides are equal

in measure.

Ans:-a

46) Assertion (A):The value of y is 3 for which the distance between A(2,-3)

and Q(10,y) is 10 units.

Reason(R): The distance between the point P(x1,y1 ) and Q(x2,y2 ) is

PQ=

Ans:-d

35

47) Assertion (A): The value of p=7 for which the points A(6,1), B(8,2), C(9,4)

and D(p,3) are the vertices of Parallelogram, are taken in order.

Reason(R): Mid-point of AC = Mid-point of BD

Ans:-a

48) Assertion (A): The point (-4,6) divides the line segment joining the points

A(-6,10) and B(3,-8) in the ratio 2:7.

Reason(R):The coordinates of point P(x, y) which divides the line segment

joining the points P(x1,y1 ) and Q(x2,y2 ) internally in the ratio m1:m2 are

.

Ans:-a

49) Assertion (A): Mid-point of a line segment divides in the ratio 1:1.

Reason(R): The coordinates of point P(x, y) which divides the line segment

joining the points P(x1,y1 ) and Q(x2,y2 ) internally in the ratio m1:m2 are

.

Ans:-b

50) Assertion (A): The points (0,4) lies on x-axis.

Reason(R): the x coordinate of the point on y-axis is Zero.

Ans:-d


51) Assertion(A) : The value of cos is not possible.

Reason (R): Hypotenuse is the largest side of the any right triangle.

Ans:-d

52) Assertion(A) :

Reason (R): If

Ans:-c

53) Assertion(A) : In a OP=7cm and then

.

Reason (R):

Ans:-a

36

54) Assertion(A) : for any angle

Reason (R): for any angle

Ans:-d

55) Assertion(A) : cosecA is the abbreviation used for cosine of angle A

Reason (R): the study of ratios of the sides of right angled triangle called

trigonometric ratios of the angle

Ans:-d

56) Assertion(A) :Every trigonometric ratio can be written in the form of others.

Reason (R): trigonometric identities can be derived by using Pythagoras

theorem

Ans:-b

57) Assertion(A) :the value of is zero

Reason (R):

Ans:-a

58) Assertion(A) : If cos

Reason (R):

Ans:-d

59) Assertion(A) :

Reason (R):

Ans:-a

60) Assertion(A) :

Reason (R): For any value of

Ans:-d


61) Assertion: If a wire of length 22 cm is bent in the shape of a circle, then

area of the circle so formed is 40 cm2

Reason : Circumference of the circle = length of the wire Ans :d

37

62) Assertion : If the circumference of two circles are in the ratio 2 : 3 then ratio

of their areas is 4 : 9.

Reason: The circumference of a circle of radius r is 2 r and its area is r2.

ans: a

63) Assertion: A wire is looped in the form of a circle of radius 28 cm. It is bent

into a square. Then the area of the square is 1936cm2

Reason: perimeter of semicircular protractor =

ans: b

64) 64. Assertion: The perimeter of a circle having radius 5cm is 31.4cm

Reason: The area of the circle with radius 5 cm is 78.5cm2

ans: b

65) 65. Assertion: The area of the square that can be inscribed in a circle of

radius 8 cm is 128cm2.

Reason: Area of square= Diameter of circle.

ans:c

66) 66.Assertion : If the perimeter of a semi-circular protractor is 36 cm. Then

Its diameter is 14cm.

Reason: perimeter of semicircular protractor =

ans : a

67) Assertion: A region of a circle is enclosed by any two radii and the arc

intercepted between two radii is called the sector of a circle.

Reason: Circumference of a circle= 2

ans: b

38

68) Assertion: The area of a quadrant of a circle with circumference of 22 cm is

77/8 cm2

Reason: The perimeter of a circle is generally known as circumference of a

circle.

ans: b

69) Assertion: If a wire of length 22 cm is bent in the shape of a circle, then

area of the circle so formed is 40 cm2.

Reason: Circumference of the circle=length of the wire

ans: d

70) Assertion : If the perimeter and the area of a circle are numerically equal,

then the radius of the circle is 2 unit.

Reason: If R and r be the radius of outer and inner circular path respectively

then area of path =π(R2-r

2)

ans:b

CH15. PROBABILITY

71) Assertion : If a box contains 5 white, 2 red and 4 black marbles, then the

probability of not drawing a white marble from the box is .

Reason : P ( not E) = 1 - P(E ), where E is any evnet

Ans:d

72) Assertion : If a die is thrown, the probability of getting a number less than 3

and greater than 2 is zero.

Reason : Probability of an impossible event is zero.

Ans.a

39

73) Assertion : In a simultaneously throw of a pair of a dice. The probability of

getting a double is

Reason:Probability of an event may be negative.

ans c 74) Assertion : The probability of winning a game is 0.4, then the probability of

losing it, is 0.6

Reason : P( E) + P(not E )=1

ans:a

75) Assertion : Card numbered as 1, 2, 3 .......... 15 are put in a box and

mixed thoroughly, one card is then drawn at random. The probability of

drawing an even number is .

Reason : For any event E, we have 0≤P(E) ≤1.

ans: d

76) Assertion:The probability of getting a prime number when a die thrown

once is .

Reason: Prime numbers on a die are 2,3,5.

ans:d

77) Assertion : In rolling a dice, the probability of getting number 8 is zero.

Reason: Its an impossible event.

ans:a

78) Assertion: When two coins are tossed simultaneously then the probability

of getting no tail is .

Reason: When a coin is tossed , probability of getting a head is

ans: a

40

79) Assertion: Probability of an event cannot be negative.

Reason: Probability of an event lies between 0 and 1.

Ans: a

80) Assertion: A card is accidently dropped from a pack of 52 playing cards.

The probability that it is an ace is .

Reason: If P (E) = 0.05, then P (not E) =0.95.

ans: a

41

CASE STUDY QUESTIONS

CH1. REAL NUMBERS

1) A mathematics exhibition is being conducted in the school and one of the

students is making a model of factors tree. One student has some difficulty and

asked for the help to his friend in completing the quiz for the audience. Observe

the following factor tree and answer the following

1) What will be the value of x ?

a) 11130

b) 12130

c) 41120

d) 11430

2) What will be the value of y ?

a) 5563

b) 5565

c) 6555

d) 6355

x

y

1855

371

z

2

3

7

5

42

3) What will be the value of z ?

a) 55

b) 63

c) 53

d) 35

4) The prime factorization for value of x is given by

a) 2x3x5x7

b) 3x4x5x6

c) 5x3x2x7

d) 6x5x4x3

5) According to fundamental theorem of arithmetic the value of x is

a) Composite number

b) Prime number

c) Neither prime nor composite

d) Even number

43

2) A seminar is being conducted by educational organization where the participants

will be educators of different subjects. The number of participants in Physics,

Chemistry and Biology are 18, 24 and 36 respectively.

1)In each room maximum number of participants are to be seated and all of

them being in the same subject.

a) 6

b) 3

c) 9

d) 2

2)What is the number of minimum number of room required during the

event?

a) 11

b) 12

c) 13

d) 14

44

3)The LCM of 18, 24 and 36 is

a) 82

b) 35

c) 99

d) 72

4)The product of HCF and LCM of 18 , 24 and 36

a) 432

b) 342

c) 428

d) 248

5) 36 can be expressed as product of it’s prime as

a) 2x32

b) 23x3

c) 22x3

2

d) 32x2

2

45

CH2. POLYNOMIALS

3) In a classroom, four students Anil, Jay Richa and Suresh were asked to draw the

graph of p(x) = ax2 +bx +c ,following graphs are drawn by the students.

1)How many students have drawn the graph correctly

a) 1

b) 2

c) 3

d) 4

2) Which type of polynomial is represented by Jay’s graph?

a) Linear

b) parabola

c) 3 zig-zag

d) none

3) How many zeros are there for Richa’s graph

a) 1

b) 2

c) 3

Richa Suresh

46

d) 4

4) If p(x)=ax2

+ bx + c and a+b+c =0 ,then one zero is

a) –b/a

b) c/a

c) b/a

d) –c/a

5) If p(x)=ax2

+ bx + c and a+b+c =0 ,then one zero is

a) –b/a

b) c/a

c) b/a

d) –c/a

4)Due to heavy storm an electric wire got bent as shown in the fig. It followed a

mathematical shape .Answer the following question below.

47

1) Name the shape in which the wire is bent

a) spiral

b) ellipse

c) linear

d) parabola

2) How many zeros are there for the polynomial (shape of the wire)

a) 1

b) 2

c) 3

d) 0

3) The zeros of the polynomial are

a) -1,5

b) -2,3

c) -1, 3

d) 4,-2

4) What will be the expression of the polynomial ?

a) x2 +2x -3

b) x2 -2x +3

c) x2 +2x +3

d) x2 -2x -3

48

5) What is the value of the polynomial if x=-1 ?

a) 6

b) 18

c) -18

d) 0


5. Two rails are represented by the equations and

are parallel as shown in figure. Answer the following questions

5. The value of k for which above equations are parallel

a)3

b) 4

c) 2

d) none of these

49

6. The line cuts the x-axis and y-axis that is co-ordinates are

a) (6,0) and (0,3)

b) (0,6) and (3,0)

c) (8,0) and (0,4)

d) (0,8) and (0,4)

50

CH6. TRIANGLES

7.Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8m

above the surface of water and the fly at the end of the string rests on the

water 3.6m away and 2.4m from a point directly under the tip of the rod.

She is pulling the string at the rate of 5 cm per second. Nazima’s friend

observe her position and draw a rough sketch by using A, B, C and D

positions ( see the below figure) . Assuming that her string ( from the tip

of her rod to the fly) is taut, answer the following questions

51

7.The length of AC is

a)2m

b) 3m

c) 4m

d) 5m

8. The length of the string pulled in 12 seconds is

a)6m

b) 0.3m

c) 0.6m

d) 3m


9. Four friends Shubham, Onkar , Rahul and Raj are studding are reference to

a well situated at the origin with the following respective coordinates (2,4)

,(-2,4) , (-2,-4) and (2,-4) . based on the information given above answer the

following questions:

1. By ploting these points on graph paper, the figure obtained is ………..

a. square

b. irregular quadrilateral

c. rectangle

d. none

2. Distance between Shubham and Onkar is…………ft.

a. 12

b. 24

c. 4

d.8

3. Rahul stands in which Quadrent?

a. I

b.II

c.III

d.IV

52

4. Ordinate of the point (-2,-4) is …………

a. -2

b. -3

c. -4

d. -5

5. Distance between Onkar and Raj is……….ft.

a. 2

b.3

c.4

d.5

10. One day, Mohan visited his friend’s apartment from his balcony, he

observed that there is flower bed on the ground which is in the shape of

parallelogram. Four red colour poles are there at the corners of the garden.

He draws the sketch of the flower bed on a graph paper as shown in figure

given below:

Based on the information given above answer the following questions:

1. The coordinates of point D are……..

a. (3,2)

b.(-3,3)

c.(3,3)

d.(3,4)

53

2. The coordinates of M are ………

a. (3.5,2)

b.(5,2.5)

c.(5,3)

d.(6,7)

3. At what ratio M divides the line segment joining the points B and D?

a. 1:1

b. 2:3

c. 3:1

d. 4:1

4. What is distance between the red pole B and red pole C

a. m

b.2 m

c.3 m

d. 4 m

5. What will be the coordinates of a point which divides line segment joining

the points M and B in the ratio 1:1?

a. ( 6 ,1)

b. ( 6 ,1.5)

c. ( 6 ,1.75)

d. ( 6 ,1.775)

54


11. In the fig given below m and AB=6cm . based on that information

choose the correct options .

a) m ………

a.

b.

c.

d.

b) ……….cm

a. 6

b. 12

c. 6

d. none of these

c) ……….cm

a. 6

b. 12

c. 6

d. none of these

d) The value of ………….

a.

b.

c. 3

d. none of these

55

e) The value of ………….

a. 2

b. 2/3

c.

d. none of these

12. In the fig. given below ABCD is a parallelogram with m

m and . Based on

information given above choose the correct options :

(a) ………. cm

a. 3

b. 6

c. 9

d.12

(b) ……… cm

a. 3

b. 6

c. 9

d.12

(c) ……….cm

a.

b.2

c.3

d.4

56

(d) The value of ………

a.

b.

c. 2

d. none of these

(e) m …………

a. 60

b. 30

c. 90

d. none of these


13. Ravi went to stadium everyday to enjoy his summer vacation. In

Stadium, there is a circular swimming pool with center O. The

radius of pool is 7 m. There are 2 points on the wall of the pool

separated by equal distance. These 2 points are named A and B.

A rope is attached between A and B. This rope separates the

shallow section of pool from deep section of pool such that

LAOB = 900. The shallow section is the smaller section.

1.What is the area of ∆AOB?

(a) 49 m2

(b) 24.5 m2

(c) 98 m2

(d) 140 m2

57

2.What is the area of minor sector AOB? (Use π = 22/7)

(a) 77 m2

(b) 38.5 m2

(c) 154 m2

(d) 70 m2

3.What is the area of Shallow?

(a) 28 m2

(b) 56 m2

(c) 14 m2

(d) 7 m2

4.What is the area of swimming pool?

(a) 77 m2

(b) 38.5 m2

(c) 154 m2

(d) 70 m2

5.What is the area of deeper section?

(a) 77 m2

(b) 150 m2

(c) 154 m2

(d) 140 m2

14. Mohan went to city along with his friends. He visited a cricket

stadium which is in the trapezium shape. A circular green ground for

playing cricket is inscribed in a trapezium shaped stadium of height

200 m and lengths of parallel sides are equal to 250 m and 400 m.

58

1.What is the area of trapezium shaped stadium?

(a) 65000 m2

(b) 130000 m2

(c) 75000 m2

(d) 100000 m2

2.What is the radius of the circular cricket field?

(a) 200 m

(b) 100 m

(c) 250 m

(d) 400 m

3.What is the area of circular cricket field? (use π = 3.14)

(a) 65000 m2

(b) 33600 m2

(c) 31400 m2

(d) 40000 m2

4.What is the area of blue shaded part of the stadium (other than cricket field)?

(a) 31400 m2

(b) 33600 m2

(c) 25000 m2

(d) 40000 m2

5.What is the area of circular cricket field excluding pitch whose dimension is 22

m x 3 m?(use π = 3.14)

(a) 31400 m2

(b) 33600 m2

(c) 31334 m2

(d) 65000 m2

59

CH15. PROBABILITY

14.On a weekend Vineet was playing cards with his family .The deck has 52 cards.

If her brother drew one card .

1. Find the probability of getting a king of red colour.

a)

b)

c)

d)

2. Find the probability of getting a face card.

a)

b)

c)

d)

60

3. Find the probability of getting a jack of hearts.

a)1/26

b) 1/52

c)

d) None

4. Find the probability of getting a red face card.

a)3/26

b)6/52

c)13/52

d) none

5. Find the probability of getting a spade.

a)

b)

c)

d)

61

15. In summer holidays ,four friends Vani, Vineet, Rohit , Reena were playing

ludo game .In which they used to throw a die…

1.Vani got first chance to roll the dice. What is the probability that she got the

number appearing on the top face of the dice is 2?

a.

b.

c.

d.

2. Vineet got next chance. What is the probability that he got the number

appearing on the top face of the dice is a prime number ?

a.

b.

c.

d.

62

3.Now it was Rohit’s turn. He rolled the dice. What is the probability that he got

number appearing on the top face of the dice is less than 6?

a.

b.

c.

d.

4. Next comes Reena’S turn.what is the probability that a number on top of

the face is an odd number?

a.

b.

c.

d.None

5. Now again comes here Vani’s turn What is the probability that she got number

appearing on the top face of the dice is greater than 6?

a.

b.

c.

d. 0

63

COMPENTENCY BASED QUESTIONS

CH1. REAL NUMBERS

1) Three sets of English , Hindi and Science books dealing with cleanliness have to

be kept in such a way that all books are stored topic wise and height of each is the

same. Number of English books is 96 and that of Hindi and Science are 240 and

336 respectively.

1)Assuming that books are of the same thickness , determine the largest number of

English, Hindi and science books respectively

a) 48

b) 50

c) 52

d) 46

2) Number of stack English books kept

a) 4

b) 5

c) 2

d) 6

3) Number of stack Hindi books kept

a) 4

b) 5

c) 2

d) 6

4) Number of stack Science books kept

a) 4

b) 5

c) 7

d) 6

64

5) Which mathematical concept is used in this problem?

a) HCF

b) LCM

c) Complexity

d) None

2)There is a circular path around the sport field. Elena takes 18 minutes to drive

one round of the field while Rebecca takes 12 minutes for the same. Suppose they

both starts at the same point and at the same time and go in the same direction.

1) After how many minutes they will meet again at the starting point?

a) 32

b) 36

c) 42

d) 46

2) What kind of sports field is mentioned in the problem?

a) Circular

b) Triangular

c) Rectangular

d) None

3) How much hours does Elena took to complete 4 such rounds?

a) 4.2 hrs

b) 2.1 hrs

c) 1.2 hrs

d) 3 hrs

65

4) How much hours does Rebecca took to complete 3 such rounds?

a) 6 hrs

b) 12 hrs

c) 0.3 hrs

d) 0.6 hrs

5) Which mathematical concept is used in this problem?

a) HCF

b) LCM

c) Complexity

d) None

3) A trader was moving along a road selling eggs. An idler who didn’t has much

work to do, started to get the trader into wordy duel. This grew into fight, he puled

the basket with the eggs. The trader requested to panchyat to ask the idler to pay

for broken eggs. The Panchayat asked the trader, how many eggs were broken, he

gave the following responses: If counted in pair, one will remain. If counted in 3,

two will remain. If counted in 4, three will remain. If counted in 5, four will

remain. If counted in 6, five will remain. If counted in 7, nothing will remain.

My basket cannot accommodate more than 150 eggs.

1) If counted in pair, 1 will remain. How will you represent it using Euclid’s

Division Lemma?

a) a=2u+1

b) a=3u+2

c) a=2+5u

d) None

66

2) If counted in 3, two will remain. How will you represent it using Euclid’s

Division Lemma?

a) a=2+t

b) a=3t+2

c) a=2t+1

d) None

3) If counted in 4, three will remain. How will you represent it using Euclid’s

Division Lemma?

a) a=s+4

b) a=3s+2

c) a=4s+3

d) None

4) If counted in six, 5 will remain. How will you represent it using Euclid’s

Division Lemma?

a) a=q+6

b) a=6q+5

c) a=5q+6

d) None

5) How many eggs were there in the basket?

a) 119

b) 130

c) 129

d) 120

67

CH2. POLYNOMIALS

4) David’s mom has given him money to buy some boxes from the market at the

rate of 4x2 +3x -2. The total amount of money is represented by 8x

4 +14x

3 - 2x

2

+7x – 8. Out of this money he donated some amount to child who was studying

under light of street lamp.

1)What is the rate of each box?

a) 4x2 +3x -2

b) 3x2 +4x -1

c) 5x3 +4x -3

d) None

2) How many boxes e purchased from the market?

a) 2x2 -2x +1

b) 2x2 +2x -1

c) 2x2 +4x -2

d) None

3) How much amount of money he donated to the child?

a) 3x -2

b) 16x -12

c) 14x - 10

d) None

68

4) Why David did so?

a) Kindness

b) Care

c) Promoting education

d) All options

5)Total amount of money is represented by which equation? Write the

equation.

Ans : 8x4 +14x

3 - 2x

2 +7x – 8.

5) Mr. Fell has asked his friend to do carpooling for commuting to office because

their offices are located in the same tower of the city. For this, they calculated the

total expense of the fuel and other charges which together is represented by x3 +

8x2 + 16x + 9. If there are x+1 members, who are sharing , find the share of each

member.

1)How many members are there who are sharing?

a) x +1

b) x -1

c) 4x -2

d) None

2) What is the share of each member?

a) x2 -7x -9

b) x2 +7x +9

c) x2 -7x +9

d) None

69

3) Why Mr. Fell has taken this initiative?

a) To control pollution

b) To save fossil fuel

c) Sustainable development

d) All options

4) Total expense of fuel and other charges together represented by which

equation? Write the equation.

Ans: x3 + 8x

2 + 16x + 9

5) What mathematical concept is used?

Ans: Long Division Method.

6) Stefan’s mother has given him money to buy some chocolate from the bakery

at the rate of x2 +2x -3 .The total amount of money given by his mother is

represented by 4x4 +2x

3 -2x

2 +x -1 .out of this money he give some amount to his

friend who always help him in his studies .Find how much amount of money he

must have so that he is able to buy exact and maximum number of chocolate from

the bakery.

1) What is the rate of each box?

a) x2 +2x -3

b) x2 +4x -1

c) x3 +4x -3

d) None

70

2) How many chocolates he purchased from the bakery?

a) 4x2 -6x +22

b) x2 +2x -1

c) 2x2 -4x -2

d) None

3) How much amount of money he given to his friend?

a) 3x -54

b) 6x -12

c) -61x +65

d) None

4) Why Stefan did so?

a) Kindness

b) Care

c) Promoting education

d) All options

5) Total amount of money is represented by which equation? Write the

equation.

Ans: 4x4 +2x

3 -2x

2 +x -1

71


Two years ago , Salim was thrice as old as his daughter and six years later, he will

be four year older than twice her age.

7. Age of Salim is

a) 42 years

b) 40 years

c) 38 years

d) 36 years

8. Age of Salim’s daughter is

a) 12 years

b) 14 years

c) 19 years

d) 20 years

9. The difference between their ages is

a) 19

b) 24

c) 38

d) 22

CH6. TRIANGLES

10. In the given figure , and then

is

72

a)

b)

c)

d)

11. In the given figure then

a)

b)

c)

73

d) none of these

12. If in the two triangles ABC and PQR, , then

a)

b)

c)

d)


13. the points (5, 4) and (x, y) are equidistant from the point (4, 5), then…..

a. x2 + y

2 – 8x – 10y + 39 = 0.

b. 8x – 10y + 39 = 0.

C. x2 + y

2 – 8x=0

d. none of these

14. If the point P(x, y) is equidistant from the points A(5, 1) and B(–1, 5),

then the relation between ordinate and abscissa is …………

a. x = y

b. x + y = 3

c.x – y = 1

d. none of these

15. the coordinates of the point which divides the line segment joining the

points A(–5, 11) and B(4, –7) in the ration 7 : 2 is ………

a. (2,2)

b. (2,-3)

c.(3,-3)

d. none of these

74


A ladder of length 13m stands on high building and angle made by ladder

with the ground surface is 60 .

16. the distance between the foot of ladder and foot of building is……

a. 6.5 cm

b. 7.5 cm

c. 8.5cm

d. 5.5 cm

17. height of the building is………..

a.

b.

c.

d.none of these.

18. The ratio of the height of the building to the length between foots of

ladder and the building is

a.

b.

c.

d. none of these

75


19. A teacher explained the importance of hardwork , Tolerance, peace and

Honesty by drawing equilateral triangle ABC of side 84 cm with A,B and

C centre arcs are drawn with radius half the length of the side of the

equilateral triangle. Answer the following:

i. The area of the hardwork region is ….. cm2

(a)924

(b)1024

(c)724

(d)824

ii. The sum of the areas of hardwork ,tolerance and peace region is……cm2

(a)7227

(b)2772

(c)7722

(d)2277

iii. The area of the equilateral triangle is….

(a)1774

(b)1274

(c)7417

(d)None

iv. The area of the honesty region is……cm2

(a)(2772-1774

(b)(1764-1774

(c)(1764

(d)None

76

v. The perimeter of the honesty region is…..cm.

(a)110

(b)132

(c)144

(d)154

20. A race track is a special place built for Racing. The racing may be for people,

animals, or vehicles. Examples of animal racing are horse racing.

The given figure depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are

each 106 m long. If the track is 10 m wide, find:

1.What is the distance around the track along its inner edge?

a. m

b.

c. m

d.2084m

2.What is inner circular radius?

a.10m

b.20m

c. 30m

d.40m

77

3. What is the outer circular radius?

a.30m

b. 20m

c.40m

d. 10m

4.What is the area of the track?

a.4320m2

b. 4230m2

c.4310 m2

D. None

5. Which mathematical concept is used in above example?

a.area of circle ,circumference

b. Area of square

c.area of triangle

d. None

78

21. Archery is the sport, practice, or skill of using a bow to shoot arrows. Archery

offers a number of health and fitness benefits.

The figure depicts an archery target marked with its five scoring regions from the

centre outwards as gold, red, blue, black and white. The diameter of the region

representing the gold score is 21 cm and each of the other bands is 10.5 cm wide.

What is the area of the gold region?

1. What is the area of the Red region?

a.346.5cm2

b.364.5cm2

c.384.5cm2

d.344.cm2

2. What is the area of the Blue region?

a. 1733.5cm2

b..1732.5cm2

c.1736.5cm2

d.1748.5cm2

3. What is the area of the Black region?

a.2425.5cm2

b.2423.5cm2

79

c.2444.5cm2

d.None

4. Which Mathematical concept is used in the above problem?

a. area of circle

b.area of triangle

c. circumference of circle

d. None of the above

CH15. PROBABILITY

22. A child has a die whose six faces show the letters as given below: A B C D E A

The die is thrown once.

1. What is the probability of getting A?

a.1/6

b.2/6

c.2/5

d.1/5

2. What is the probability of getting D?

a.1/6

b.2/6

c.2/5

d.1/5

3. What is the probability of getting E?

a.1/6

b.2/6

80

c.2/5

d.1/5

23. Two customers Shyam and Ekta are visiting a particular shop in the same week

(Tuesday to Saturday). Each is equally likely to visit the shop on any day as on

another day.

i)How many Possible Outcomes are there?

a.25

b.20

c.30

d.35

ii) What is the probabilihy that they will visit the shop on the same day?

a.

b.

c.

d.

81

ii)What is the probabilihy that they will visit the shop on the consecutive

days?

a.

b.

c.

d.

iii)What is the probabilihy that they will visit the shop on different days?

a.

b.

c.

d.

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Subject- Mathematics Class- X- std

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Transcript of Subject- Mathematics Class- X- std