Question Set E

CBSE 10th Maths Circles Sample Question Papers Study Material - QB365

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Questions:

Multiple Choice Question

80 x 1 = 80

If the height of the tower is equal to the length of its shadow, then the angle of elevation of the Sun is

(a)

30°

(b)

45°

(c)

60°

(d)

90°

In figure, if \(\angle A O B=125^{\circ} \text {, then } \angle C O D\) is equal to

(a)

62.5°

(b)

45°

(c)

35°

(d)

55°

The origin divides the line segment AB joining the points A (1, -3) and B(3, 9) in the ratio

(a)

3 : 1

(b)

1 : 3

(c)

2 : 3

(d)

1 : 1

The value of k, if (6, k) lies on the line represented by x - 3y + 6 = 0, is

(a)

-4

(b)

(c)

-12

(d)

(x, y) is 5 units from the origin. How many such points lie in the third quadrant?

(a)

(b)

(c)

(d)

infinitely many

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)

\(\frac{7}{90}\)

(b)

\(\frac{1}{9}\)

(c)

\(\frac{4}{45}\)

(d)

\(\frac{9}{89}\)

Let k be the probability that a player wins a medium prize in his first attempt. If a player wins a small and a large prize in his first two attempts, then the probability that he wins a medium prize in his third attempt is

(a)

equal to k

(b)

less than k

(c)

more than k

(d)

cannot be determined using the given information

If a pair of linear equations in two variables is consistent, then the lines represented by the two equations are

(a)

always intersecting

(b)

parallel

(c)

always coincident

(d)

intersecting or coincident

The common difference of the AP whose nth term is given by \(a_n=3 n+7\), is

(a)

(b)

(c)

(d)

10.

The two roots of the equation \(3 x^2-2 \sqrt{6} x+2=0\) are

(a)

real and distinct

(b)

not real

(c)

real and equal

(d)

rational

11.

The ratio of a two-digit number and the sum of its digits is 7:1. How many such two-digit numbers are possible?com

(a)

(b)

(c)

(d)

infinitely many

12.

The value of k for which the system of equstions kx + 2y = 5 and 3x + 4y = 1 have no solution is

(a)

\(k=\frac{3}{2}\)

(b)

\(k \neq \frac{3}{2}\)

(c)

\(k \neq \frac{2}{3}\)

(d)

k = 15

13.

If the lines represented by equations 3x - 2m y = 2 and 2x + 5y + 1= 0 are parallel, then the value of m is

(a)

\(\frac{2}{5}\)

(b)

\(-\frac{5}{4}\)

(c)

\(\frac{3}{2}\)

(d)

\(\frac{15}{4}\)

14.

The given pair of linear equations is non-intersecting. Which of the following statement is true?

(a)

\(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

(b)

\(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

(c)

\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}=\frac{c_1}{c_2}\)

(d)

\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

15.

In the given figure, if PT is a tangent to a circle with centre O and \(\angle\)TPO = 35°, then the measure of \(\angle\)x is

(a)

110°

(b)

115°

(c)

120°

(d)

125°

16.

The probability of guessing the correct answer to a certain test question is \(\frac{x}{6}\). If the probability of not guessing the correct answer to this question is \(\frac{2}{3}\), then the value of x is

(a)

(b)

(c)

(d)

17.

The common difference of the AP \(\frac{1}{2 x}, \frac{1-4 x}{2 x}, \frac{1-8 x}{2 x}\), ... is

(a)

-2x

(b)

-2

(c)

(d)

18.

If one of the zeroes of the cubic polynomial ax + bx + cx + d is zero, then product of other two zeroes is

(a)

\(\frac{-c}{a}\)

(b)

\(\frac{c}{q}\)

(c)

(d)

\(\frac{-b}{a}\)

19.

If α and β are the zeroes of the polynomial x² - 1, then the value of α + ß is

(a)

(b)

(c)

-1

(d)

20.

If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and -3, then

(a)

a = -7 and b = -1

(b)

a = 5 and b = -1

(c)

a = 2 and b = -6

(d)

a = 0 and b = -6

21.

What should be added from the polynomial x² - 5x + 4, so that 3 is the zero of the resulting polynomial?

(a)

(b)

(c)

(d)

22.

Given HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 x k, then the value of k is

(a)

1650

(b)

1600

(c)

165

(d)

1625

23.

If n is a natural number, then 2(5ⁿ + 6ⁿ) always ends with

(a)

(b)

(c)

(d)

24.

If the distances of the point P(x, y) from (1,0) and (0,1) are equal, then which of the following is true?

(a)

x + y = 0

(b)

x = y + 1

(c)

y = x + 1

(d)

x = y

25.

If common tangents AB and CD of two circles with centres O and O' intersect at E, then OEO' is

(a)

a triangle

(b)

a line

(c)

an arc

(d)

None of these

26.

A ladder rests against a vertical wall at an inclination a to the horizontal. If its foot is pulled away from the wall through a distance p, so that its upper end slides at distance down the wall and then the ladder makes an angle β to the horizontal, then \(\frac{\cos \beta-\cos \alpha}{\sin \alpha-\sin \beta}\) is equal to

(a)

p / a

(b)

p / q

(c)

(d)

1 / pq

27.

In the following figure, from the top of a building AB, 60 m high, the angles of depression of the top and the bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively.

Find the horizontal distance between BA and CO.

(a)

60\(\sqrt3\)m

(b)

40\(\sqrt3\)m

(c)

20\(\sqrt3\)m

(d)

10\(\sqrt3\)m

28.

A letter is chosen at random from the letters of the word 'ASSASSINATION', then the probability that the letter chosen is a vowel is in the form of \(\frac{6}{2 x+1}\) ,then x is equal to

(a)

(b)

(c)

(d)

29.

A circle artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground, then the height of pole, if the angle made by the rope with the ground level is 30°, is

(a)

5 m

(b)

10 m

(c)

15 m

(d)

20 m

30.

If(sec A + tan A) (see B + tan B)(secC + tan C) = (see A - tan A) (sec B - tan B)(sec C- tan C) = X, then the value/ values of x is /are

(a)

\(\pm 1\)

(b)

(c)

\(\pm 2\)

(d)

31.

If \(0<\theta<\frac{\pi}{4}\) then the simplest form of \(\sqrt{1-2 \sin \theta \cos \theta} \text { is }\)

(a)

sin \(\theta\) - cos \(\theta\)

(b)

cos \(\theta\) - sin \(\theta\)

(c)

cos \(\theta\) + sin \(\theta\)

(d)

sin \(\theta\) cos \(\theta\)

32.

If x sin ³ \(\theta\) + y cos³ \(\theta\) = sin \(\theta\) cos \(\theta\) and x sin \(\theta\) = ycos \(\theta\), then x² + y²is equal to

(a)

(b)

1 / 2

(c)

(d)

3 / 2

33.

A long a road line, an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried the job with one of the end stone by carrying them in succession. In carrying, all the stones he covered a distance of 3 km. Then, the total number of stones is

(a)

(b)

(c)

(d)

34.

Is -8 is a solution of the equation 3x² + 8x + 2 = 0?

(a)

Yes

(b)

(c)

Cannot be determined

(d)

None of these

35.

The 10th term of an AP is 52 and 16 th term is 82, then 32nd term of the AP is

(a)

152

(b)

159

(c)

162

(d)

156

36.

In an AP,if d = - 4,n = 7 and an = 4,thena is equal to

(a)

(b)

(c)

(d)

37.

If one of the zeroes of the quadratic polynomial (k - 1)x² + kx + 1 is -3, then the value of k is

(a)

\(\frac{4}{3}\)

(b)

\(\frac{-4}{3}\)

(c)

\(\frac{2}{3}\)

(d)

\(\frac{-2}{3}\)

38.

The product of a non-zero rational and an irrational number is

(a)

always irrational

(b)

always rational

(c)

rational or irrational

(d)

one

39.

Find the fifth term of an A.P whose first term is -1 and common difference is -3

(a)

-13

(b)

(c)

-16

(d)

40.

Find the sum of first 40 integers divisible by 6

(a)

4000

(b)

4920

(c)

2460

(d)

4290

41.

Given an A.P. few of whose terms are x, y, 2, 4, 6, 8,………. What must be the values of x and y?

(a)

x = -4, y = 2

(b)

x = -2, y = 0

(c)

x = 0, y = -2

(d)

x = 2, y = -4

42.

The roots of quadratic equation ax² + bx + c = 0 is given by

(a)

\(\frac { b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

(b)

\(\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

(c)

\(\frac { b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

(d)

\(\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

43.

The roots of quadratic equation x² – 9 = 0 are

(a)

± 3

(b)

± 6

(c)

± 4

(d)

± 9

44.

For what value of k, the equation kx² – 6x – 2 = 0 has equal roots?

(a)

-9/2

(b)

-7/2

(c)

7/2

(d)

-3

45.

Which of the following equations has the sum of its roots as 3

(a)

2x²-3x+6=0

(b)

x²+5x+6=0

(c)

-x²+3x-3=0

(d)

3x²-3x+3=0

46.

Which of the following equations has two distinct real roots?

(a)

5x² – 3x + 1 = 0

(b)

x2 + 3x + 2√2 = 0

(c)

2x² – 3√2 x + 9/4 = 0

(d)

x² + x – 5 = 0

47.

If x = -2 is a root of equation x² – 4x + K = 0 then value of K is

(a)

-8

(b)

(c)

-12

(d)

48.

If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p² – q² is equal to:

(a)

b² + a²

(b)

b² – a²

(c)

a² – b²

(d)

a² + b²

49.

If a cosθ + b sinθ = 4 and a sinθ – b cosθ = 3, then a² + b² is

(a)

(b)

None

(c)

(d)

50.

If cos A= 2 sin A, then the value of cosec A is

(a)

(b)

-5

(c)

±5

(d)

±√5

51.

[cos⁴ A – sin⁴A] is equal to:

(a)

2 cos² A + 1

(b)

2 cos² A – 1

(c)

2 sin² A + 1

(d)

2 sin² A – 1

52.

if cosec27o = \(\frac { y }{ x } \), then sec27^o - sin63^o =

(a)

\(\frac { x }{ y } \)

(b)

\(\frac { x^{ 2 } }{ y^{ 2 } } \)

(c)

\(\frac { x^{ 2 } }{ y\sqrt { y^{ 2 }-x^{ 2 } } } \)

(d)

\(\frac { x^{ 2 } }{ \sqrt { y^{ 2 }-x^{ 2 } } } \)

53.

If the given system of equation is 3x + 2y = 2xy; 6x + 2y = 3xy, then the first step to solve such eqs is

(a)

To divide the complete equation by xy

(b)

Add or subtract the two equation

(c)

To equate the coefficients of x

(d)

To equate the coefficients of y

54.

The pair of linear equations 8x – 5y = 7 and 5x – 8y = -7 have

(a)

One solution

(b)

Two solutions

(c)

Many solutions

(d)

No solution

55.

Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?

(a)

6km/hr

(b)

4km/hr

(c)

3km/hr

(d)

7km/hr

56.

If α , β are zeroes of the polynomial f(x) = x² + 5x + 8, then value of (α + β) is

(a)

(b)

-8

(c)

-5

(d)

57.

If “1” is a zero of the polynomial P(a) = x²a² – 2xa + 3x – 2 , then x =

(a)

-2

(b)

-2, 0

(c)

+2, 2

(d)

58.

The zero of the polynomial represented by the given graph

(a)

Does not exist

(b)

Is 3

(c)

Is y = 3

(d)

Is 0

59.

The largest number which divides 70 and 125 leaving remainders 5 and 8, respectively is

(a)

1750

(b)

(c)

(d)

60.

Largest number that divides 679 and 599 leaving remainder 4 is

(a)

(b)

(c)

(d)

61.

The prime factorization of 184 is

(a)

2³ × 3 ×. 23

(b)

8 × 23

(c)

2³ × 23

(d)

46 ×. 4

62.

The number 7 x 11 x 13 + 13 is :

(a)

prime number

(b)

negative integer

(c)

irrational number

(d)

composite number

63.

What is the HCF of 1076 and 584

(a)

(b)

(c)

(d)

64.

The distance between the points P (-6,7) and Q (-1,-5) is

(a)

(b)

(c)

(d)

65.

The distance of the point P(6,-6) from the origin is equal to

(a)

3 √4 units

(b)

8 units

(c)

6 √2 units

(d)

3 units

66.

If A and B are the points (-6, 7) and (-1, -5) respectively, then the distance 2AB is equal to

(a)

(b)

169

(c)

(d)

238

67.

Let P(x, y) be equidistant from the points A (7, 1) and (3, 5).Find a relation between x and y.

(a)

y– x = 4

(b)

y– x = 2

(c)

x – y = 2

(d)

x – y = 4

68.

If the probability of winning a game is 0.3, the probability of losing it is

(a)

1.3

(b)

0.1

(c)

(d)

0.7

69.

A bag has 9 red, 7 green and 4 blue balls. A student randomly selects a ball from the bag. The probability of not getting a blue ball is

(a)

9/20

(b)

1/5

(c)

7/20

(d)

4/5

70.

If three coins are tossed simultaneously, than the probability of getting at least two heads, is

(a)

1/4

(b)

3/8

(c)

1/2

(d)

1/8

71.

What is the probability that a number selected from the numbers (1, 2, 3,..........,15) is a multiple of 4?

(a)

1/5

(b)

4/5

(c)

2/15

(d)

1/3

72.

A ladder leaning against a wall makes an angle of 60° with the wall. If its foot is 6.2 m away from the wall, its length is

(a)

10.2 m

(b)

8 m

(c)

14.2 m

(d)

12.4 m

73.

Consider a ladder which makes an angle of 60° with a wall of height 10 m and its top just touches the top of the wall. If the ladder is now rotated in such a way that its top now touches the top of the opposite wall which has a height of 10/√3 m. What is the angle by which the ladder is rotated.

(a)

45°

(b)

60°

(c)

90°

(d)

30°

74.

Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?

(a)

√3 x 10⁵ sec

(b)

10⁴ sec

(c)

√3 x 10⁴ sec

(d)

10⁵ sec

75.

If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree is

(a)

\(\frac { 40 }{ 3 } (3-\sqrt { 3 } )\)

(b)

\(\frac { 20 }{ 3 } (\sqrt { 3 } +3)\)

(c)

\(\frac { 20 }{ 3 } (\sqrt { 3 } +1)\)

(d)

\(\frac { 40 }{ 3 } (\sqrt { 3 } -1)\)

76.

In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is

(a)

10 cm

(b)

16 cm

(c)

18 cm

(d)

12 cm

77.

A line that intersects a circle in exactly one point is called a

(a)

Diameter

(b)

Tangent

(c)

Radius

(d)

Secant

78.

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120°, then ∠OPQ is

(a)

60^o

(b)

30^o

(c)

90^o

(d)

45^o

79.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other an angle of 70° , then find ∠POA.

(a)

60°

(b)

65^o

(c)

55^o

(d)

50^o

80.

in figure , if ㄥAOB = 125^o, then ㄥCOD is equal to

(a)

62^o

(b)

45^o

(c)

35^o

(d)

55^o

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Answers Key:

Multiple Choice Question

80 x 1 = 80

(b)
45°

(d)
55°

(b)
1 : 3

(d)
4

(d)
infinitely many

(a)
equal to k

(d)
intersecting or coincident

(b)
3

10.

11.

(b)
4

12.

(a)
\(k=\frac{3}{2}\)

13.

(d)
\(\frac{15}{4}\)

14.

(b)
\(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

15.

(d)
125°

16.

(a)
2

17.

(b)
-2

18.

(a)
\(\frac{-c}{a}\)

19.

(d)
0

20.

(a)
a = -7 and b = -1

21.

(b)
2

22.

(d)
1625

23.

(d)
6

24.

(d)
x = y

25.

(b)
a line

26.

(b)
p / q

27.

28.

(b)
6

29.

(b)
10 m

30.

(a)
\(\pm 1\)

31.

(b)
cos \(\theta\) - sin \(\theta\)

32.

33.

(d)
25

34.

(b)
No

35.

36.

(d)
28

37.

Given that, one of the zeroes of the quadratic polynomial say p(x) = (k -1)x² + kx + 1 is -3, then
p(-3)=0
\( \Rightarrow\) (k -1)(-3)2 + k(-3) + 1= 0

38.

(a)
always irrational

39.

(a)
-13

40.

(b)
4920

41.

(b)
x = -2, y = 0

42.

(d)
\(\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2c } \)

43.

(a)
± 3

44.

(a)
-9/2

45.

46.

(d)
x² + x – 5 = 0

47.

48.

(b)
b² – a²

49.

50.

(d)
±√5

51.

(b)
2 cos² A – 1

52.

53.

(a)
To divide the complete equation by xy

54.

(a)
One solution

55.

(a)
6km/hr

56.

57.

58.

(a)
Does not exist

59.

(d)
13

60.

(a)
5

61.

62.

(d)
composite number

63.

(b)
4

64.

65.

66.

(a)
26

67.

68.

(d)
0.7

69.

(d)
4/5

70.

71.

(a)
1/5

72.

(d)
12.4 m

73.

74.

(b)
10⁴ sec

75.

(a)
\(\frac { 40 }{ 3 } (3-\sqrt { 3 } )\)

76.

(b)
16 cm

77.

(b)
Tangent

78.

(b)
30^o

79.

80.

Since, the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
i.e ㄥAOB + ㄥCOD = 180^o
⇒ ㄥCOD =180^o - ㄥAOB
⇒ ㄥCOD = = 180^o - 125^o = 55^o

CBSE 10th Maths Circles Sample Question Papers Study Material - QB365 Set E

QB365 Student Learing Managemnet System

Std: 10th Standard CBSE - Maths

chapter: Circles - Sample Question Papers

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Questions:

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Answers Key:

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