Question Set C

CBSE 10th Maths Probability Model Questions Papers Study Material - QB365

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Questions:

Multiple Choice Question

88 x 1 = 88

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°

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle is drawn. Then, the area of the quadrilateral PQOR is

(a)

60 cm²

(b)

65 cm²

(c)

30 cm²

(d)

32.5 cm²

Here is a circle with centre O.

Manu wants to draw a tangent RS to the circle. What is the number of points at which the line RS will meet the circle?

(a)

(b)

(c)

(d)

In the figure given below, PQRS is a quadrilateral. PR is perpendicular to QR and PS

Based on the above information, answer the following questions.
What is the length of RS?

(a)

8 units

(b)

10 units

(c)

8 √2 units

(d)

16/3 √3 units

In the figure given below, PQRS is a quadrilateral. PR is perpendicular to QR and PS

Based on the above information, answer the following questions.
What is the value of tan Q?

(a)

3/5

(b)

1/2

(c)

(d)

4/3

The value of (tan² 45° - cos² 60°) is

(a)

1/2

(b)

1/4

(c)

3/2

(d)

3/4

The median of first seven prime numbers is

(a)

(b)

(c)

(d)

The time in seconds, taken by 150 athletes to run a 100m hurdle race are tabulated below

Time (sec)	13-14	14-15	15-16	16-17	17-18	18-19
Number of Athletes	2	4	5	71	48	20

The number of athletes who completed the race in less than 17 sec, is

(a)

(b)

(c)

(d)

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)

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

10.

Two coins are tossed together. The probability of getting atleast one tail is

(a)

\(\frac{1}{4}\)

(b)

\(\frac{1}{2}\)

(c)

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

(d)

11.

Which of the following numbers cannot be the probability of happening of an event?

(a)

(b)

\(\frac{7}{0.01}\)

(c)

0.07

(d)

\(\frac{0.07}{3}\)

12.

Which of these is a quadratic equation having one of its roots as zero?
(i) \(x^3+x^2=0\)
(ii) \(x^2-2 x=0\)
(iii) \( x^2-9=0\)

(a)

Only (i)

(b)

Only (ii)

(c)

Only (i) and (ii)

(d)

Only (ii) and (iii)

13.

The pair of equations ax + 2y = 9 and 3x - by = 18 represent parallel lines, where a, b are integers, if

(a)

a=b

(b)

3a = 2b

(c)

2a = 3b

(d)

ab = 6

14.

If the square of difference of the zeroes of the quadratic polynomial x² + px + 45 is equal to 144, then the value of p is

(a)

土9

(b)

土12

(c)

土15

(d)

土18

15.

HCF of two numbers is 27 and their LCM is 162 of the number is 54, then the other number is

(a)

(b)

(c)

(d)

16.

The LCM of smallest two-digit number and smallest composite number is

(a)

(b)

(c)

(d)

17.

If the mean and median of a data are 10 and 11 respectively, then mode of the data is

(a)

(b)

(c)

(d)

18.

The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is

(a)

(a + b + c)²

(b)

(c)

(a + b + c)

(d)

abc

19.

If AOBC is a rectangle whose three vertices are A(0, 3), 0(0,0) and B(5, 0), then the length of its diagonal is

(a)

(b)

(c)

(d)

20.

The given figure shows a disc on which a player spins an arrow twice.

The fraction \(\frac{x}{y}\) is formed, where 'a' is y the number of sectors on which the arrow stops on the first spin and 'b' is the number of the sectors in which the arrow stops on the second spin. In each spin, each sector has equal chance of selection by the arrow, then the probability that the fraction \(\frac{x}{y}\) ≥ 1.

(a)

\(\frac{7}{12}\)

(b)

\(\frac{5}{12}\)

(c)

\(\frac{11}{12}\)

(d)

\(\frac{1}{2}\)

21.

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

22.

If cos 9 \(\alpha\) = sin \(\alpha\) and value of tan 5 \(\alpha\) is 9 \(\alpha\) < 90°, then the

(a)

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

(b)

\(\sqrt{3}\)

(c)

(d)

23.

A graph of quadratic polynomial is given below

If we rotate the axes at an angle of 90° in anti-clockwise direction, the figure remains at the same position. Find the equation of the graph.

(a)

y² + 3y + 2

(b)

y² -3y + 2

(c)

y² + 2y + 3

(d)

y² - 2y + 3

24.

The sum of the series 45² - 43² + 442 - 42² + 43² - 41²+ 42² - 40² + ... upto 30 terms.

(a)

1110

(b)

2220

(c)

3330

(d)

4440

25.

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

26.

The 21st term of an AP whose first two terms are - 3 and 4, is

(a)

(b)

137

(c)

143

(d)

-143

27.

When a man travels equal distance at speed x km/h and y km/h. his average speed is 4 km/h. But when he travels at these speed for equal time, his average speed is 4.5 km/h.The difference of the two speed is

(a)

2 km/h

(b)

4 km/h

(c)

3 km/h

(d)

5 km/h

28.

If the square of difference of the zeroes of the quadratic polynomial x² + px + 45 is equal to 144, then the value of p is

(a)

\(\pm9\)

(b)

\(\pm12\)

(c)

\(\pm15\)

(d)

\(\pm18\)

29.

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)

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

30.

If x andy are odd positive integers, then X² + y²is

(a)

even and divisible by 4

(b)

even and not divisible by 4

(c)

odd and divisible by 4

(d)

odd and not divisible by 4

31.

If two positive integers p and q can be expressed as p = ab² and q = a³ b;where a, b being prime numbers, then LCM (p, q) is equal to

(a)

(b)

a²b²

(c)

a³b²

(d)

a³b³

32.

The common difference and the next two terms of the A.P are….75, 67, 59, 51,……

(a)

2, 3, 5

(b)

10, 30, 40

(c)

-8, 43, 35

(d)

3, 6, 9

33.

If a- b, 0 and a + b are consecutive terms of an AP then

(a)

a can take any real value and b = 0

(b)

a = 0 and b can take any real value

(c)

a = 1 and b= 0

(d)

a = 0 and b = 1

34.

If for an A.P s_n= + 3n What is the n^th term?

(a)

2n-3

(b)

n-4

(c)

2n+4

(d)

2n+2

35.

For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?

(a)

(b)

(c)

(d)

36.

What is the sum of the first 50 multiples of 3?

(a)

4325

(b)

3255

(c)

3825

(d)

4455

37.

If a,b,c are real and b²-4ac >0 then roots of equation are

(a)

real roots

(b)

real and unequal

(c)

No real roots

(d)

real and equal

38.

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)

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

39.

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

40.

The condition for equation ax² + bx + c = 0 to be quadratic is

(a)

a ≠ 0

(b)

a > 0

(c)

a ≠ 0, b ≠ 0

(d)

a < 0

41.

If 1/2 is a root of the equation x²+ kx-5/4 = 0 then the other root of the quadratic equation is

(a)

1/4

(b)

-5/2

(c)

-2

(d)

1/2

42.

The equation x-1/x = -2 in standard form ax² + bx + c = 0 is written as

(a)

x² – 2x -1 = 0

(b)

x² + 2x -1 = 0

(c)

x² – 2x +1 = 0

(d)

x² + 2x +1 = 0

43.

For the following frequency distribution

Class	Frequency
0-5	2
5-10	7
10-15	18
15-20	10
20-25	8
25-30	5

If the mode and the median are 12.9 and 14.44 respectively, then the mean is

(a)

15.2

(b)

(c)

(d)

44.

For the following distribution the modal class is

Marks below	10	20	30	40	50	60
Number of students	2	11	25	45	57	75

(a)

20-30

(b)

40-50

(c)

30-40

(d)

10-20

45.

For a symmetrical distribution, which is correct

(a)

Mean = Median = Mode

(b)

Mean < Mode < Median

(c)

Mean > Mode > Median

(d)

Mode = Mean + Median/2

46.

Median of the data represented below is

(a)

(b)

Less than 4

(c)

(d)

Between 2-4

47.

The relation connecting the measures of central tendencies is

(a)

Mode = 2 median + 3 mean

(b)

Mode = 3 median – 2 mean

(c)

Mode = 3 median + 2 mean

(d)

Mode = 2 median – 3 mean

48.

If sin (A – B) = 1/2 and cos (A + B) =1/2 then the value of B is

(a)

15°

(b)

45°

(c)

0°

(d)

60°

49.

The express sin A in terms of cot A is

(a)

\(\frac { \sqrt { 1+{ cot }^{ 2 }\quad A } }{ cot\quad A } \)

(b)

\(\frac { \sqrt { 1-{ cot }^{ 2 }\quad A } }{ cot\quad A } \)

(c)

\(\sqrt { \frac { 1-{ cot }^{ 2 }\quad A }{ cot\quad A\quad } } \)

(d)

\(\frac { 1 }{ \sqrt { 1+{ cot }^{ 2 }\quad A } } \)

50.

When 0° <θ< 90° and 3tan²θ – 1 = 0. Then is equal to

(a)

30°

(b)

90°

(c)

60°

(d)

45°

51.

In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

(a)

4/3

(b)

9/4

(c)

8/4

(d)

5/4

52.

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

53.

The sum of the digits of a two-digit number is 9. Also, twice this number is nine times the number obtained by reversing the order of the digits. Find the number

(a)

(b)

(c)

(d)

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.

The pair of linerar equations 2x+ky-3, 6x+ \(\frac { 2 }{ 3 } \)y+7 =0 have a unique solution for all values of k except

(a)

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

(b)

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

(c)

\(k\neq \frac { 2 }{ 9 } \)

(d)

\(k=\frac { 2 }{ 9 } \)

56.

In elimination method_______is an important condition

(a)

Equating only the x co-efficient

(b)

Equating only the y coefficient

(c)

Equating either of the coefficients

(d)

Equating both the coefficients

57.

If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y are

(a)

Â½ and 1

(b)

2 and 1

(c)

1 and 2

(d)

1 and Â½

58.

Find the quadratic polynomial whose zeros are 2 and -6.

(a)

x² + 4x – 12

(b)

x² + 4x + 12

(c)

x² – 4x – 12

(d)

x² – 4x + 12

59.

The zero of the polynomial represented by the given graph

(a)

Does not exist

(b)

Is 3

(c)

Is y = 3

(d)

Is 0

60.

Given a polynomial p(x) of degree ‘n’, the graph of y = p(x) intersects the X-axis

(a)

at most n points

(b)

at most n – 1 points

(c)

at most n + 1 points

(d)

at most 0 points

61.

The graph y= p(x) is shown below. How many zeroes does the polynomial p(x) have?

(a)

(b)

(c)

(d)

62.

If 1 is a zero of the polynomial p(a)=x²a²-2xa+3x-2 . Then x=

(a)

-1, -2

(b)

2, 1

(c)

2,-1

(d)

-2, 1

63.

If a prime number p divides a² , then which one of the following is true?

(a)

p divides a

(b)

p = a

(c)

p > a

(d)

a divides p

64.

There are 135 partcipants in English and 165 in Mathematics in a seminar. What is the minimum number of rooms required to seat them if each room must have the same number of participants from each of the two subjects.

(a)

(b)

(c)

(d)

65.

H.C.F. of two consecutive even numbers is:

(a)

(b)

(c)

(d)

66.

If x and y are odd positive integers then x² + y² is-

(a)

even

(b)

odd or even

(c)

multiple of 2 and 4

(d)

odd

67.

The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?

(a)

2 ,21,11

(b)

1,10,19

(c)

-1 ,8,17

(d)

2 ,11,20

68.

The graph of the equation x = 3 is

(a)

a point

(b)

straight line parallel to y axis

(c)

straight line passing through the origin

(d)

straight line parallel to x axis

69.

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

70.

The values of x and y, if the distance of the point (x,y) from (-3,0) as well as from (3,0) is 4 are

(a)

x = 1, y = 7

(b)

x = 2, y = 7

(c)

x = 0, y = – √7

(d)

x = 0, y = ± √7

71.

Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear

(a)

(b)

(c)

(d)

72.

Find the distance of the point (–6, 8) from the origin

(a)

(b)

(c)

(d)

73.

Which of the following cannot be the probability of an event?

(a)

(b)

(c)

3/2

(d)

2/3

74.

In a lottery, there are 5 prizes and 20 blanks. The probability of getting a prize is

(a)

1/5

(b)

1/2

(c)

1/4

(d)

1/3

75.

An urn contains lottery tickets numbered from 1 to 100. If a ticket is selected at random, then the probability that it is a perfect square is

(a)

0.01

(b)

0.08

(c)

0.09

(d)

0.1

76.

A fair die is cast in the game of ‘Ludo’. The probability of getting a score greater than 6 is

(a)

zero

(b)

2/3

(c)

1/6

(d)

77.

Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

(a)

50 (√3 + 1) m²

(b)

50 √3 m²

(c)

50 m²

(d)

100 m²

78.

A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60° to the horizontal. The length of the string to the nearest metre is

(a)

55 m

(b)

87 m

(c)

100 m

(d)

60 m

79.

A man on a top of a tower observes a truck at an angle of depression α where tanα = 1/ √5 and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to be β where tan β = √5 . If the truck is moving at a uniform speed, then how much more time it will take to reach the base of the tower.

(a)

150√5 sec

(b)

1500 sec

(c)

150 sec

(d)

150/ √5 sec

80.

Two pillars are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the taller pillar is

(a)

a√2^m

(b)

2a m

(c)

a m

(d)

a/√2 m

81.

A tower stands vertically on the ground. From a point C on the ground, which is 20 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45°. The height of the tower is

(a)

10 m

(b)

8 m

(c)

15 m

(d)

20 m

82.

A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 450. The height of the tree is:

(a)

4.5 m

(b)

3 m

(c)

5.2 m

(d)

4 m

83.

Which of the following is rational?

(a)

√3 + √5

(b)

√4 + √9

(c)

√2 + √4

(d)

√6 + √9

84.

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

85.

If figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70o, then ∠TPQ is equal to

(a)

45^o

(b)

5^o

(c)

35^o

(d)

70^o

86.

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

87.

The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :

(a)

10 cm

(b)

5 cm

(c)

√7 cm

(d)

2√7 cm

88.

In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to

(a)

45^o

(b)

60^o

(c)

50^o

(d)

55^o

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Answers Key:

Multiple Choice Question

88 x 1 = 88

(d)
55°

(a)
60 cm²

(b)
1

(d)
16/3 √3 units

(d)
4/3

(d)
3/4

(b)
7

10.

11.

(b)
\(\frac{7}{0.01}\)

12.

13.

(d)
ab = 6

14.

(d)
土18

15.

(a)
36

16.

17.

(d)
13

18.

(b)
0

19.

(b)
3

20.

(a)
\(\frac{7}{12}\)

21.

(b)
10 m

22.

23.

(a)
y² + 3y + 2

24.

(b)
2220

25.

26.

(b)
137

27.

28.

Given that \( f(x)=x^{2}+p x+45 \)
Then, \( \alpha+\beta=\frac{-p}{1}=-p \) and \(\alpha \beta=\frac{45}{1}=45\)
According to given condition,
\((\alpha-\beta)^{2}=144 \)
\(\Rightarrow(\alpha+\beta)^{2}-4 \alpha \beta=144 \)
\(\Rightarrow \quad(-p)^{2}-4(45)=144 \Rightarrow p^{2}=144+180\)
\(\Rightarrow p^{2}=324 \Rightarrow p=\pm 18\)

29.

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

30.

(b)
even and not divisible by 4

31.

32.

33.

(b)
a = 0 and b can take any real value

34.

(d)
2n+2

35.

(a)
5

36.

37.

(b)
real and unequal

38.

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

39.

(a)
-9/2

40.

(a)
a ≠ 0

41.

(b)
-5/2

42.

(b)
x² + 2x -1 = 0

43.

(a)
15.2

44.

(b)
40-50

45.

(a)
Mean = Median = Mode

46.

47.

(b)
Mode = 3 median – 2 mean

48.

(a)
15°

49.

(d)
\(\frac { 1 }{ \sqrt { 1+{ cot }^{ 2 }\quad A } } \)

50.

(a)
30°

51.

(a)
4/3

52.

(a)
To divide the complete equation by xy

53.

(b)
81

54.

(a)
One solution

55.

(d)
\(k=\frac { 2 }{ 9 } \)

56.

57.

58.

(a)
x² + 4x – 12

59.

(a)
Does not exist

60.

(a)
at most n points

61.

(b)
4

62.

(d)
-2, 1

63.

(a)
p divides a

64.

(d)
20

65.

66.

(a)
even

67.

(d)
2 ,11,20

68.

(b)
straight line parallel to y axis

69.

70.

(d)
x = 0, y = ± √7

71.

72.

73.

74.

(a)
1/5

75.

(d)
0.1

76.

(a)
zero

77.

(b)
50 √3 m²

78.

(b)
87 m

79.

80.

(a)
a√2^m

81.

(d)
20 m

82.

(d)
4 m

83.

(b)
√4 + √9

84.

(b)
16 cm

85.

86.

(b)
30^o

87.

88.

Here AC is the diameter of the circle.
∴ ∠ABC = 90°     [ Angle in a semi-circle]
Now, in ΔACB, ∠A + ∠B + ∠C = 180°      [Sum of all interior angles of a triangle is 180°]
⟹     ∠A + 90° + 50° = 180°
⟹ ∠A + 140 = 180
⟹ ∠A = 180^o - 140° = 40°
Or ∠OAB = 40° …(i)
Here, OA ⏊ AT
⟹   ∠OAT = 90°
⟹ ∠OAB + ∠BAT = 90°
⟹   ∠BAT = 90° - 40° = 50°    [Using (i)]
Hence, the value of ∠BAT is 50°.

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