32581 + Interview Questions in Mathematics Page 191 InterviewSolution

9501.	In the given figure, two circles intersect each other at the points A & B. If PQ & PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR
Answer» In the given figure, two circles intersect each other at the points A & B. If PQ & PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR

9501.

In the given figure, two circles intersect each other at the points A & B. If PQ & PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR

Answer»

In the given figure, two circles intersect each other at the points A & B. If PQ & PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR

Discussion

9502.	Question 6Find the radius of a sphere whose surface area is 154 cm2.[Assume π=227]
Answer» Question 6 Find the radius of a sphere whose surface area is $154 c m^{2}$ . $[A s s u m e π = \frac{22}{7}]$

9502.

Question 6Find the radius of a sphere whose surface area is 154 cm2.[Assume π=227]

Answer»

Question 6

Find the radius of a sphere whose surface area is $154 c m^{2}$ .

$[A s s u m e π = \frac{22}{7}]$

Discussion

9503.	From the polynomial p(x) = x2 + x + 1, do we get p(x) = 0 for any x? What about p(x) = 1? And p(x) = −1?
Answer» From the polynomial p(x) = x² + x + 1, do we get p(x) = 0 for any x? What about p(x) = 1? And p(x) = −1?

Discussion

9504.	Question 1(i)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(i) 4x2–3x–1
Answer» Question 1(i) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (i) $4 x^{2} - 3 x - 1$

Discussion

9505.	The formula for lateral surface area of a cylinder of radius 'r' and height 'h' is
Answer» The formula for lateral surface area of a cylinder of radius 'r' and height 'h' is

Discussion

9506.	If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices parallelogram ABCD, find the values of a and b.
Answer» If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices parallelogram ABCD, find the values of a and b.

Discussion

9507.	In an envelope there are some 5 rupee notes. Total amount these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than number of 10 rupee notes. Then find number of 5 rupee and 10 rupee notes
Answer» In an envelope there are some 5 rupee notes. Total amount these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than number of 10 rupee notes. Then find number of 5 rupee and 10 rupee notes

Discussion

9508.	The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ____________.
Answer» The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ____________.

Discussion

9509.	Question 14 Circumference of a circle is always (a) more than three times of its diameter (b) three times of its diameter (c) less than three times of its diameter (d) three times of its radius
Answer» Question 14 Circumference of a circle is always (a) more than three times of its diameter (b) three times of its diameter (c) less than three times of its diameter (d) three times of its radius

Discussion

9510.	If the sum of the areas of two circles with radii r1 and r2 is equal to the area of circle of radius r, then(a) r = r1 + r2 (b) r12 + r22 = r2 (c) r1 + r2 < r (d) r12 + r22 < r2
Answer» If the sum of the areas of two circles with radii $r_{1}$ and $r_{2}$ is equal to the area of circle of radius $r$ , then (a) $r = r_{1} + r_{2}$ (b) ${r_{1}}^{2} + {r_{2}}^{2} = r^{2}$ (c) $r_{1} + r_{2} < r$ (d) ${r_{1}}^{2} + {r_{2}}^{2} < r^{2}$

Discussion

9511.	Shubendhu rolls a dice. If he obtains a prime number, he tosses a coin and if he gets an even number, he rolls a dice again. What is the cardinality of the sample space? ___
Answer» Shubendhu rolls a dice. If he obtains a prime number, he tosses a coin and if he gets an even number, he rolls a dice again. What is the cardinality of the sample space? ___

Discussion

9512.	From an external point P, two tangents PA and PB are drawn to the circle with centre O. Then the angle between OP and AB is_______.
Answer» From an external point P, two tangents PA and PB are drawn to the circle with centre O. Then the angle between OP and AB is_______.

Discussion

9513.	What is the area of the quadrilateral AMND in the given figure (in cm2)?
Answer» What is the area of the quadrilateral AMND in the given figure (in $c m^{2}$ )?

Discussion

9514.	In the given fig, XY \|\| seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.
Answer» In the given fig, XY \|\| seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.

Discussion

9515.	The point A(2,-4) is reflected about the line x = 0 . Which of the following points could be its image?
Answer» The point A(2,-4) is reflected about the line x = 0 . Which of the following points could be its image?

Discussion

9516.	The difference between the circumference and radius of a circle is 37cm. Using π=227 , find the circumference of the circle. [CBSE 2013]
Answer» The difference between the circumference and radius of a circle is 37cm. Using $π = \frac{22}{7}$ , find the circumference of the circle. [CBSE 2013]

Discussion

9517.	A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30°respectively. Find the width of the river.
Answer» A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30°respectively. Find the width of the river.

Discussion

9518.	Two pipes running together can fill a tank in 1119minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Answer» Two pipes running together can fill a tank in $11 \frac{1}{9} minutes$ . If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Discussion

9519.	Find(a) S3 : S6 for the series 4 + 12 + 36 + …….(b) S4 : S8 for the series 5 + 10 + 20 + ……..
Answer» Find (a) S₃ : S₆ for the series 4 + 12 + 36 + ……. (b) S₄ : S₈ for the series 5 + 10 + 20 + ……..

9519.

Find(a) S3 : S6 for the series 4 + 12 + 36 + …….(b) S4 : S8 for the series 5 + 10 + 20 + ……..

Answer»

Find

(a) S₃ : S₆ for the series 4 + 12 + 36 + …….

(b) S₄ : S₈ for the series 5 + 10 + 20 + ……..

Discussion

9520.	A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is(a) 2r(b) 3r(c) r(d) 4r
Answer» A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is (a) 2r (b) 3r (c) r (d) 4r

Discussion

9521.	Question 4State whether the following is true or false.A pair of tangents can be constructed to a circle inclined at an angle of 170∘.[Thinking process :If the angle between a pair of tangents is greater than 180∘, then the pair of tangent can never be constructed to a circle.]
Answer» Question 4 State whether the following is true or false. A pair of tangents can be constructed to a circle inclined at an angle of $170^{\circ}$ . [Thinking process : If the angle between a pair of tangents is greater than $180^{\circ}$ , then the pair of tangent can never be constructed to a circle.]

Discussion

9522.	Question 4In the figure,QRQS=QTPR and∠1=∠2.Show that ΔPQS∼ΔTQR.
Answer» Question 4 In the figure, $\frac{Q R}{Q S} = \frac{Q T}{P R} a n d$ $∠ 1 = ∠ 2$ . $S h o w t h a t Δ P Q S \sim Δ T Q R$ .

Discussion

9523.	A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.
Answer» A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.

Discussion

9524.	Find the sum of the series452−432+442−422+432−412+422−402+⋯15 terms.
Answer» Find the sum of the series $45^{2} - 43^{2} + 44^{2} - 42^{2} + 43^{2} - 41^{2} + 42^{2} - 40^{2} + \dots 15 t e r m s$ .

Discussion

9525.	Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.
Answer» Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

Discussion

9526.	If 5a+2b5a−2b=53, then find the value of a : b.
Answer» If $\frac{5 a + 2 b}{5 a - 2 b} = \frac{5}{3}$ , then find the value of a : b.

Discussion

9527.	The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface and volume of the frustum.
Answer» The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface and volume of the frustum.

Discussion

9528.	Find the equation of the line parallel to the line 3x+2y=8 and passing through the point (0,1).
Answer» Find the equation of the line parallel to the line $3 x + 2 y = 8$ and passing through the point $(0, 1)$ .

Discussion

9529.	Question 4 (iii)Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1,If the lines represented by these equations are intersecting at a unique point.
Answer» Question 4 (iii) Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1, If the lines represented by these equations are intersecting at a unique point.

Discussion

9530.	If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π=3.14 )
Answer» If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( $π = 3.14$ )

Discussion

9531.	4 + (3 / 3) = ____
Answer» 4 + (3 / 3) = ____

Discussion

9532.	Solve the following systems of equations:x7+y3=5x2-y9=6
Answer» Solve the following systems of equations: $\frac{x}{7} + \frac{y}{3} = 5 \frac{x}{2} - \frac{y}{9} = 6$

Discussion

9533.	The equation of the straight line passing through the points (3, 2) and perpendicular to the line y = x is(a) x – y = 5(b) x + y = 5(c) x + y = 1(d) x – y = 1
Answer» The equation of the straight line passing through the points (3, 2) and perpendicular to the line y = x is (a) x – y = 5 (b) x + y = 5 (c) x + y = 1 (d) x – y = 1

Discussion

9534.	A circle is drawn through the vertices P, Q and R of a triangle PQR with PQ = 52 cm, QR = 56 cm and PR = 60 cm as shown in the given figure. Find the diameter of the circle.
Answer» A circle is drawn through the vertices P, Q and R of a triangle PQR with PQ = 52 cm, QR = 56 cm and PR = 60 cm as shown in the given figure. Find the diameter of the circle.

Discussion

9535.	The value of the polynomial: -5x + 3 at x=0 is
Answer» The value of the polynomial: -5x + 3 at x=0 is

Discussion

9536.	Let A3×m and B4×n be the two matrices such that AB and BA exist. Then the value of m+n is
Answer» Let $A_{3 \times m}$ and $B_{4 \times n}$ be the two matrices such that $A B$ and $B A$ exist. Then the value of $m + n$ is

Discussion

9537.	△AMT∼△AHE. In △AMT,AM=6.3 cm,∠TAM=50∘, AT=5.6 cm.AMAH=75. Construct △AHE.
Answer» $△ A M T \sim △ A H E .$ In $△ A M T, A M = 6.3 c m, ∠ T A M = 50^{\circ}$ , $A T = 5.6 c m . \frac{A M}{A H} = \frac{7}{5} .$ Construct $△ A H E .$

Discussion

9538.	Varun Ltd. issued ₹ 10,00,000 shares of ₹ 100 each at a premium of ₹ 20 for subscription payable as:₹ 10 per share on application,₹ 40 per share and ₹ 10 premium on allotment, and₹ 50 per share and ₹ 10 premium on final payment.Over-payments on application were to be applied towards amount due on allotment and over-payments on application exceeding amount due on allotment was to be returned. Issue was oversubscribed to the extent of 13,000 shares. Applicants for 12,000 shares were allotted only 1,000 shares and applicants for 2,000 shares were sent letters of regret. All the money due on allotment and final call was duly received.Pass necessary entries in the company's books to record the above transactions. Also, prepare company's Balance Sheet on completion of the above transactions.
Answer» Varun Ltd. issued ₹ 10,00,000 shares of ₹ 100 each at a premium of ₹ 20 for subscription payable as: ₹ 10 per share on application, ₹ 40 per share and ₹ 10 premium on allotment, and ₹ 50 per share and ₹ 10 premium on final payment. Over-payments on application were to be applied towards amount due on allotment and over-payments on application exceeding amount due on allotment was to be returned. Issue was oversubscribed to the extent of 13,000 shares. Applicants for 12,000 shares were allotted only 1,000 shares and applicants for 2,000 shares were sent letters of regret. All the money due on allotment and final call was duly received. Pass necessary entries in the company's books to record the above transactions. Also, prepare company's Balance Sheet on completion of the above transactions.

Discussion

9539.	The greatest four digits number which is divisible by 15, 25, 40 and 75 is
Answer» The greatest four digits number which is divisible by 15, 25, 40 and 75 is

Discussion

9540.	A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of 32 cm and its depth is 89 cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape. [CBSE 2015]
Answer» A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of $\frac{3}{2}$ cm and its depth is $\frac{8}{9}$ cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape. [CBSE 2015]

Discussion

9541.	Question 4 (viii)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(viii) −12,−12,−12,−12……
Answer» Question 4 (viii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (viii) $- \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2} \dots \dots$

Discussion

9542.	If 34 and 16 are the arithmetic mean and geometric mean of two positive numbers respectively, Find the numbers
Answer» If 34 and 16 are the arithmetic mean and geometric mean of two positive numbers respectively, Find the numbers

Discussion

9543.	tan2 θ(sec θ−1)2=
Answer» $\frac{{tan}^{2} θ}{(sec θ - 1)^{2}} =$

Discussion

9544.	What is the length of the third side in the above triangle?
Answer» What is the length of the third side in the above triangle?

Discussion

9545.	Four unbiased coins are tossed simultaneously. The probability of getting at most 2 tails is
Answer» Four unbiased coins are tossed simultaneously. The probability of getting at most 2 tails is

Discussion

9546.	Match the correct expression for volume of the following 3D - shapes.
Answer» Match the correct expression for volume of the following 3D - shapes.

Discussion

9547.	88.A boat sails 2 km east,then 4km southeast and then in an unknown direction.Final position of the boat is5km east from starting point. Unknown displacement is?
Answer» 88.A boat sails 2 km east,then 4km southeast and then in an unknown direction.Final position of the boat is5km east from starting point. Unknown displacement is?

Discussion

9548.	Find the sum and product of the roots of the quadratic equations:(1) (2) (3) (4) (5) (6)
Answer» Find the sum and product of the roots of the quadratic equations: (1) (2) (3) (4) (5) (6)

9548.

Find the sum and product of the roots of the quadratic equations:(1) (2) (3) (4) (5) (6)

Answer»

Find the sum and product of the roots of the quadratic equations:

(1)

(2)

(3)

(4)

(5)

(6)

Discussion

9549.	In the following, determine the set of values of k for which the given quadratic equation has real roots: (i)2x2+3x+k=0(ii)2x2+x+k=0(iii)2x2−5x−k=0(iv)kx2+6x+1=0(v)3x2+2x+k=0
Answer» In the following, determine the set of values of k for which the given quadratic equation has real roots: $(i) 2 x^{2} + 3 x + k = 0 (i i) 2 x^{2} + x + k = 0 (i i i) 2 x^{2} - 5 x - k = 0 (i v) k x^{2} + 6 x + 1 = 0 (v) 3 x^{2} + 2 x + k = 0$

Discussion

9550.	Question 8A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
Answer» Question 8 A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, two circles intersect each other at the points A &amp; B. If PQ &amp; PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR

Question 6Find the radius of a sphere whose surface area is 154 cm2.[Assume π=227]

From the polynomial p(x) = x2 + x + 1, do we get p(x) = 0 for any x? What about p(x) = 1? And p(x) = −1?

Question 1(i)Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials(i) 4x2–3x–1

The formula for lateral surface area of a cylinder of radius 'r' and height 'h' is

If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices parallelogram ABCD, find the values of a and b.

In an envelope there are some 5 rupee notes. Total amount these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than number of 10 rupee notes. Then find number of 5 rupee and 10 rupee notes

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ____________.

Question 14 Circumference of a circle is always (a) more than three times of its diameter (b) three times of its diameter (c) less than three times of its diameter (d) three times of its radius

If the sum of the areas of two circles with radii r1 and r2 is equal to the area of circle of radius r, then(a) r = r1 + r2 (b) r12 + r22 = r2 (c) r1 + r2 &lt; r (d) r12 + r22 &lt; r2

Shubendhu rolls a dice. If he obtains a prime number, he tosses a coin and if he gets an even number, he rolls a dice again. What is the cardinality of the sample space? ___

From an external point P, two tangents PA and PB are drawn to the circle with centre O. Then the angle between OP and AB is_______.

What is the area of the quadrilateral AMND in the given figure (in cm2)?

In the given fig, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.

The point A(2,-4) is reflected about the line x = 0 . Which of the following points could be its image?

The difference between the circumference and radius of a circle is 37cm. Using π=227 , find the circumference of the circle. [CBSE 2013]

Two pipes running together can fill a tank in 1119minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Find(a) S3 : S6 for the series 4 + 12 + 36 + …….(b) S4 : S8 for the series 5 + 10 + 20 + ……..

A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is(a) 2r(b) 3r(c) r(d) 4r

Question 4State whether the following is true or false.A pair of tangents can be constructed to a circle inclined at an angle of 170∘.[Thinking process :If the angle between a pair of tangents is greater than 180∘, then the pair of tangent can never be constructed to a circle.]

Question 4In the figure,QRQS=QTPR and∠1=∠2.Show that ΔPQS∼ΔTQR.

Find the sum of the series452−432+442−422+432−412+422−402+⋯15 terms.

Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

If 5a+2b5a−2b=53, then find the value of a : b.

The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface and volume of the frustum.

Find the equation of the line parallel to the line 3x+2y=8 and passing through the point (0,1).

Question 4 (iii)Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1,If the lines represented by these equations are intersecting at a unique point.

If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π=3.14 )

4 + (3 / 3) = ____

Solve the following systems of equations:x7+y3=5x2-y9=6

The equation of the straight line passing through the points (3, 2) and perpendicular to the line y = x is(a) x – y = 5(b) x + y = 5(c) x + y = 1(d) x – y = 1

A circle is drawn through the vertices P, Q and R of a triangle PQR with PQ = 52 cm, QR = 56 cm and PR = 60 cm as shown in the given figure. Find the diameter of the circle.

The value of the polynomial: -5x + 3 at x=0 is

Let A3×m and B4×n be the two matrices such that AB and BA exist. Then the value of m+n is

△AMT∼△AHE. In △AMT,AM=6.3 cm,∠TAM=50∘, AT=5.6 cm.AMAH=75. Construct △AHE.

The greatest four digits number which is divisible by 15, 25, 40 and 75 is

Question 4 (viii)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(viii) −12,−12,−12,−12……

If 34 and 16 are the arithmetic mean and geometric mean of two positive numbers respectively, Find the numbers

tan2 θ(sec θ−1)2=

What is the length of the third side in the above triangle?

Four unbiased coins are tossed simultaneously. The probability of getting at most 2 tails is

Match the correct expression for volume of the following 3D - shapes.

88.A boat sails 2 km east,then 4km southeast and then in an unknown direction.Final position of the boat is5km east from starting point. Unknown displacement is?

Find the sum and product of the roots of the quadratic equations:(1) (2) (3) (4) (5) (6)

In the following, determine the set of values of k for which the given quadratic equation has real roots: (i)2x2+3x+k=0(ii)2x2+x+k=0(iii)2x2−5x−k=0(iv)kx2+6x+1=0(v)3x2+2x+k=0

Question 8A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

In the given figure, two circles intersect each other at the points A & B. If PQ & PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR

If the sum of the areas of two circles with radii r1 and r2 is equal to the area of circle of radius r, then(a) r = r1 + r2 (b) r12 + r22 = r2 (c) r1 + r2 < r (d) r12 + r22 < r2