32581 + Interview Questions in Mathematics Page 9 InterviewSolution

401.	Prove that the ratio of the perimeters of two similar triangle is the same as the ratio of their corresponding sides
Answer» Prove that the ratio of the perimeters of two similar triangle is the same as the ratio of their corresponding sides

Discussion

402.	Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….
Answer» Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….

Discussion

403.	If A (–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
Answer» If A (–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.

Discussion

404.	The join of (-2,6) and (2,0) is divided by y axis in the ratio 1:1, then the point on y axis is
Answer» The join of (-2,6) and (2,0) is divided by y axis in the ratio 1:1, then the point on y axis is

Discussion

405.	What percentage is 500 m of 5 km?
Answer» What percentage is 500 m of 5 km?

Discussion

406.	what is the difference between zero polynomial and zero of polynomial
Answer» what is the difference between zero polynomial and zero of polynomial

Discussion

407.	A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is(a) 176 m3(b) 196 m3(c) 200 m3(d) 110 m3
Answer» A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is (a) 176 m³ (b) 196 m³ (c) 200 m³ (d) 110 m³

Discussion

408.	When two dice are tossed together, find the probability that the sum of numbers on their tops is less than 7.
Answer» When two dice are tossed together, find the probability that the sum of numbers on their tops is less than 7.

Discussion

409.	The perimeter of two similar triangles are 81 cm and 63 cm respectively. If one side of the first triangle be 18 cm, then the corresponding side of the smaller triangle is ___ cm long.
Answer» The perimeter of two similar triangles are 81 cm and 63 cm respectively. If one side of the first triangle be 18 cm, then the corresponding side of the smaller triangle is ___ cm long.

Discussion

410.	The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. Let’s say x toys were produced on a day, what is the total cost of production in terms of x?
Answer» The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. Let’s say $x$ toys were produced on a day, what is the total cost of production in terms of $x$ ?

Discussion

411.	If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. S1+S2+2S3+3S4+....(n−1) Sn=1n+2n+3n+...+nn.
Answer» If $S_{1}, S_{2}, . . . . S_{n}$ are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. $S_{1} + S_{2} + 2 S_{3} + 3 S_{4} + . . . . (n - 1)$ $S_{n} = 1^{n} + 2^{n} + 3^{n} + . . . + n^{n}$ .

411.

If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. S1+S2+2S3+3S4+....(n−1) Sn=1n+2n+3n+...+nn.

Answer»

If $S_{1}, S_{2}, . . . . S_{n}$ are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. $S_{1} + S_{2} + 2 S_{3} + 3 S_{4} + . . . . (n - 1)$

$S_{n} = 1^{n} + 2^{n} + 3^{n} + . . . + n^{n}$ .

Discussion

412.	Prove the following trigonometric identities.tan θ+1tan θ=sec θ cosec θ
Answer» Prove the following trigonometric identities. $\tan θ + \frac{1}{\tan θ} = \sec θ cosec θ$

Discussion

413.	Rationalize the denominator.(i) 35 (ii) 114 (iii) 57 (iv) 693 (v) 113
Answer» Rationalize the denominator. (i) $\frac{3}{\sqrt{5}}$ (ii) $\frac{1}{\sqrt{14}}$ (iii) $\frac{5}{\sqrt{7}}$ (iv) $\frac{6}{9 \sqrt{3}}$ (v) $\frac{11}{\sqrt{3}}$

Discussion

414.	The sum of a number and twice its square is 105. Find the number.
Answer» The sum of a number and twice its square is 105. Find the number.

Discussion

415.	Show that a1,a2,.....,an form an AP where an is defined as below: (i) an=3+4n (ii) an=9−5n Also find the sum of the first 15 terms in each case.
Answer» Show that $a_{1}$ , $a_{2}$ ,....., $a_{n}$ form an AP where an is defined as below: (i) $a_{n}$ =3+4n (ii) $a_{n}$ =9−5n Also find the sum of the first 15 terms in each case.

Discussion

416.	If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are [CBSE 2012](a) (−6, 7) (b) (6, −7) (c) (4, 2) (d) (5, 3)
Answer» If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are [CBSE 2012] (a) (−6, 7) (b) (6, −7) (c) (4, 2) (d) (5, 3)

Discussion

417.	36.The distance between the centers of two circles of radii 3cm and 8cm respectively is 13 cm. If PQ is the direct common tangent of the circles then the length of PQ is
Answer» 36.The distance between the centers of two circles of radii 3cm and 8cm respectively is 13 cm. If PQ is the direct common tangent of the circles then the length of PQ is

Discussion

418.	The angle of depression from the top of a tower of a point A on the ground is 30∘ . On moving a distance of 20 metres from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60∘. Find the height of the tower and its distance from the point A.
Answer» The angle of depression from the top of a tower of a point A on the ground is $30^{\circ}$ . On moving a distance of 20 metres from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is $60^{\circ}$ . Find the height of the tower and its distance from the point A.

Discussion

419.	if the points [3,-5] [4,3] and [-2, k] are collinear then value of k is?
Answer» if the points [3,-5] [4,3] and [-2, k] are collinear then value of k is?

Discussion

420.	From a helicopter vertically above a straight horizontal plane. If the angles of depression of two consecutive kilometer stones on the same side of the helicopter are found to be θ and φ, where θ > φ, then the height of the helicopter from the ground is (in km)
Answer» From a helicopter vertically above a straight horizontal plane. If the angles of depression of two consecutive kilometer stones on the same side of the helicopter are found to be θ and φ, where θ > φ, then the height of the helicopter from the ground is (in km)

Discussion

421.	36. ABCD is quadrilateral in which AD=BC and angle ADC = angle BCD. show that the points A,B,C,D lies on a cirlce.
Answer» 36. ABCD is quadrilateral in which AD=BC and angle ADC = angle BCD. show that the points A,B,C,D lies on a cirlce.

Discussion

422.	If the equation x2+2(k+2)x+9=0 has equal roots, then find the values of k.
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 = 0$ has equal roots, then find the values of k.

Discussion

423.	A fast train takes one hour less than a slow train for a journey of 200km. If the speed of the slow train is 10km/hr less than that of the fast train, find the speed of the two trains.
Answer» A fast train takes one hour less than a slow train for a journey of 200km. If the speed of the slow train is 10km/hr less than that of the fast train, find the speed of the two trains.

Discussion

424.	If the lengths of the chords intercepted by the circle x2+y2+2gx+2fy=0 from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is
Answer» If the lengths of the chords intercepted by the circle $x^{2} + y^{2} + 2 g x + 2 f y = 0$ from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is

Discussion

425.	A bucket contains 10 brown balls, 8 green balls, and 12 red balls and one ball is picked randomly without looking. The probability that the picked ball will be brown is _______.
Answer» A bucket contains 10 brown balls, 8 green balls, and 12 red balls and one ball is picked randomly without looking. The probability that the picked ball will be brown is _______.

Discussion

426.	If x = 2/3 and x = −3 are the roots of the equation ax2 + 7x + b = 0, find the values of a and b.
Answer» If x = 2/3 and x = −3 are the roots of the equation ax² + 7x + b = 0, find the values of a and b.

Discussion

427.

The mean of the following data is 42, find the missing frequencies x and y if the sum of the frequencies is 100. Class interval 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency 7 10 x 13 y 10 14 9

Answer» The mean of the following data is 42, find the missing frequencies x and y if the sum of the frequencies is 100.

Class interval	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency	7	10	x	13	y	10	14	9

Discussion

428.	The quadratic equation which has D = 0 and a root as 110 is
Answer» The quadratic equation which has D = 0 and a root as $\frac{1}{10}$ is

Discussion

429.	If tan θ=34, find the value ofsin θ.
Answer» If $t a n θ = \frac{3}{4}$ , find the value of $s i n θ$ .

Discussion

430.	The value of sin^-1(sin10) is
Answer» The value of sin^-1(sin10) is

Discussion

431.	Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is
Answer» Two numbers are respectively 20 $%$ and 50 $%$ more than a third number. The ratio of the two numbers is

Discussion

432.	If the Market Value of a share is greater than the Nominal Value, the share is said to be at _______.
Answer» If the Market Value of a share is greater than the Nominal Value, the share is said to be at _______.

Discussion

433.	Question - 2 (ii) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (ii) a = -2, d = 0
Answer» Question - 2 (ii) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (ii) a = -2, d = 0

Discussion

434.	The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
Answer» The first two terms of a G.P. are 125 and 25 respectively. Find the $5^{t h}$ and the $6^{t h}$ terms of the G.P.

Discussion

435.	0, 3, 9, 18, 30, ?
Answer» 0, 3, 9, 18, 30, ?

Discussion

436.	A man bought 360, ten-rupee shares of a company, paying 12 percent per annum. He sold the shares when their price rose to Rs 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at Rs 3.50 per share. Find the annual change in his income.
Answer» A man bought 360, ten-rupee shares of a company, paying 12 percent per annum. He sold the shares when their price rose to Rs 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at Rs 3.50 per share. Find the annual change in his income.

Discussion

437.	In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to(A) 60 (B) 70(C) 80 (D) 90
Answer» In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to (A) 60 (B) 70 (C) 80 (D) 90

437.

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to(A) 60 (B) 70(C) 80 (D) 90

Answer»

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to

(A) 60 (B) 70

(C) 80 (D) 90

Discussion

438.	Mark the correct alternative in each of the following:If fx=x100+x99+ ... +x+1, then f'1 is equal to(a) 5050 (b) 5049 (c) 5051 (d) 50051
Answer» Mark the correct alternative in each of the following: If $f (x) = x^{100} + x^{99} + . . . + x + 1$ , then $f' (1)$ is equal to (a) 5050 (b) 5049 (c) 5051 (d) 50051

Discussion

439.	From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a (i) a face card ( King , Queen ,Jack)(ii) an even number red card
Answer» From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a (i) a face card ( King , Queen ,Jack) (ii) an even number red card

439.

From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a (i) a face card ( King , Queen ,Jack)(ii) an even number red card

Answer»

From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a

(i) a face card ( King , Queen ,Jack)

(ii) an even number red card

Discussion

440.	Question 2 (ii)Do the following equations represent a pair of coincident lines? Justify your answer.– 2x – 3y = 1 and 6y + 4x = - 2
Answer» Question 2 (ii) Do the following equations represent a pair of coincident lines? Justify your answer. – 2x – 3y = 1 and 6y + 4x = - 2

Discussion

441.	If sin (A - B) = 1/2 and cos (A + B) = 1/2, then the value of B is
Answer» If sin (A - B) = ¹/₂ and cos (A + B) = ¹/₂, then the value of B is

Discussion

442.	Mark the correct alternative in the following question:Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to(a) 4 (b) 6 (c) 8 (d) 10
Answer» Mark the correct alternative in the following question: Let S_n denote the sum of first n terms of an A.P. If S₂_n = 3S_n, then S₃_n : S_n is equal to (a) 4 (b) 6 (c) 8 (d) 10

Discussion

443.	Diameter of cylinder Ais 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm andheight is 7 cm. Without doing any calculations can you suggest whosevolume is greater? Verify it by finding the volume of both thecylinders. Check whether the cylinder with greater volume also hasgreater surface area?
Answer» Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

443.

Diameter of cylinder Ais 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm andheight is 7 cm. Without doing any calculations can you suggest whosevolume is greater? Verify it by finding the volume of both thecylinders. Check whether the cylinder with greater volume also hasgreater surface area?

Answer»

Diameter of cylinder A
is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and
height is 7 cm. Without doing any calculations can you suggest whose
volume is greater? Verify it by finding the volume of both the
cylinders. Check whether the cylinder with greater volume also has
greater surface area?

Discussion

444.	The roots of the quadratic equation x2+5x-14=0 is
Answer» The roots of the quadratic equation $x^{2}$ +5x-14=0 is

Discussion

445.	If a and b are two odd positive integers such that a > b, then prove that one of the two numbers a+b2and a-b2is odd and the other is even.
Answer» If a and b are two odd positive integers such that a > b, then prove that one of the two numbers $\frac{a + b}{2} and \frac{a - b}{2}$ is odd and the other is even.

Discussion

446.	A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
Answer» A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?

Discussion

447.	Find ∫(†an^{-1}(secx+†an x))dx
Answer» Find ∫(†an^{-1}(secx+†an x))dx

Discussion

448.	It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?
Answer» It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?

Discussion

449.	Question 2 (iii)Are the following statements ‘True’ or False’? Justify your answer.iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial
Answer» Question 2 (iii) Are the following statements ‘True’ or False’? Justify your answer. iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial

Discussion

450.

Four defenders are standing in the coordinates A(-2,5), B(4,5), C(2,1) and D(-4,1). To stop a striker B and D move two units to the left and right respectively, then what shape does the final position of the four defenders make?

Answer»

Four defenders are standing in the coordinates A(-2,5), B(4,5), C(2,1) and D(-4,1). To stop a striker B and D move two units to the left and right respectively, then what shape does the final position of the four defenders make?

Discussion

Explore topic-wise InterviewSolutions in .

Prove that the ratio of the perimeters of two similar triangle is the same as the ratio of their corresponding sides

Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….

If A (–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.

The join of (-2,6) and (2,0) is divided by y axis in the ratio 1:1, then the point on y axis is

What percentage is 500 m of 5 km?

what is the difference between zero polynomial and zero of polynomial

A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is(a) 176 m3(b) 196 m3(c) 200 m3(d) 110 m3

When two dice are tossed together, find the probability that the sum of numbers on their tops is less than 7.

The perimeter of two similar triangles are 81 cm and 63 cm respectively. If one side of the first triangle be 18 cm, then the corresponding side of the smaller triangle is ___ cm long.

The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. Let’s say x toys were produced on a day, what is the total cost of production in terms of x?

If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. S1+S2+2S3+3S4+....(n−1) Sn=1n+2n+3n+...+nn.

Prove the following trigonometric identities.tan θ+1tan θ=sec θ cosec θ

Rationalize the denominator.(i) 35 (ii) 114 (iii) 57 (iv) 693 (v) 113

The sum of a number and twice its square is 105. Find the number.

Show that a1,a2,.....,an form an AP where an is defined as below: (i) an=3+4n (ii) an=9−5n Also find the sum of the first 15 terms in each case.

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are [CBSE 2012](a) (−6, 7) (b) (6, −7) (c) (4, 2) (d) (5, 3)

36.The distance between the centers of two circles of radii 3cm and 8cm respectively is 13 cm. If PQ is the direct common tangent of the circles then the length of PQ is

if the points [3,-5] [4,3] and [-2, k] are collinear then value of k is?

From a helicopter vertically above a straight horizontal plane. If the angles of depression of two consecutive kilometer stones on the same side of the helicopter are found to be θ and φ, where θ &gt; φ, then the height of the helicopter from the ground is (in km)

36. ABCD is quadrilateral in which AD=BC and angle ADC = angle BCD. show that the points A,B,C,D lies on a cirlce.

If the equation x2+2(k+2)x+9=0 has equal roots, then find the values of k.

A fast train takes one hour less than a slow train for a journey of 200km. If the speed of the slow train is 10km/hr less than that of the fast train, find the speed of the two trains.

If the lengths of the chords intercepted by the circle x2+y2+2gx+2fy=0 from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is

A bucket contains 10 brown balls, 8 green balls, and 12 red balls and one ball is picked randomly without looking. The probability that the picked ball will be brown is _______.

If x = 2/3 and x = −3 are the roots of the equation ax2 + 7x + b = 0, find the values of a and b.

The mean of the following data is 42, find the missing frequencies x and y if the sum of the frequencies is 100. Class interval 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency 7 10 x 13 y 10 14 9

The quadratic equation which has D = 0 and a root as 110 is

If tan θ=34, find the value ofsin θ.

The value of sin^-1(sin10) is

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

If the Market Value of a share is greater than the Nominal Value, the share is said to be at _______.

Question - 2 (ii) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (ii) a = -2, d = 0

The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.

0, 3, 9, 18, 30, ?

A man bought 360, ten-rupee shares of a company, paying 12 percent per annum. He sold the shares when their price rose to Rs 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at Rs 3.50 per share. Find the annual change in his income.

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to(A) 60 (B) 70(C) 80 (D) 90

Mark the correct alternative in each of the following:If fx=x100+x99+ ... +x+1, then f'1 is equal to(a) 5050 (b) 5049 (c) 5051 (d) 50051

From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a (i) a face card ( King , Queen ,Jack)(ii) an even number red card

Question 2 (ii)Do the following equations represent a pair of coincident lines? Justify your answer.– 2x – 3y = 1 and 6y + 4x = - 2

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

Mark the correct alternative in the following question:Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to(a) 4 (b) 6 (c) 8 (d) 10

The roots of the quadratic equation x2+5x-14=0 is

If a and b are two odd positive integers such that a > b, then prove that one of the two numbers a+b2and a-b2is odd and the other is even.

A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?

Find ∫(†an^{-1}(secx+†an x))dx

It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?

Question 2 (iii)Are the following statements ‘True’ or False’? Justify your answer.iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial

Four defenders are standing in the coordinates A(-2,5), B(4,5), C(2,1) and D(-4,1). To stop a striker B and D move two units to the left and right respectively, then what shape does the final position of the four defenders make?

From a helicopter vertically above a straight horizontal plane. If the angles of depression of two consecutive kilometer stones on the same side of the helicopter are found to be θ and φ, where θ > φ, then the height of the helicopter from the ground is (in km)