32581 + Interview Questions in Mathematics Page 207 InterviewSolution

10301.	What is the volume of a box whose length is 3 cm, breadth is 3 cm and height is 3 cm?
Answer» What is the volume of a box whose length is 3 cm, breadth is 3 cm and height is 3 cm?

Discussion

10302.	Question 92 (xvii)Factorise the following using the identity a2−b2=(a+b)(a−b).136a2b2−1649b2c2
Answer» Question 92 (xvii) Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$ $\frac{1}{36} a^{2} b^{2} - \frac{16}{49} b^{2} c^{2}$

10302.

Question 92 (xvii)Factorise the following using the identity a2−b2=(a+b)(a−b).136a2b2−1649b2c2

Answer»

Question 92 (xvii)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$\frac{1}{36} a^{2} b^{2} - \frac{16}{49} b^{2} c^{2}$

Discussion

10303.	Mark the correct alternative in the following question:The mean proportional of a and b is 10 and the value of a is four times the value of b. The value of a + b (a > 0, b > 0) is(a) 20 (b) 25 (c) 101 (d) 29
Answer» Mark the correct alternative in the following question: The mean proportional of a and b is 10 and the value of a is four times the value of b. The value of a + b (a > 0, b > 0) is (a) 20 (b) 25 (c) 101 (d) 29

Discussion

10304.	Show that the function x+a-[x-b] is a periodic function. Find its period. (a and b are positive real numbers)
Answer» Show that the function x+a-[x-b] is a periodic function. Find its period. (a and b are positive real numbers)

Discussion

10305.	Find the values of k for which the given equation has real and equal roots: x2−2x(1+3k)+7(3+2k)=0
Answer» Find the values of k for which the given equation has real and equal roots: $x^{2} - 2 x (1 + 3 k) + 7 (3 + 2 k) = 0$

Discussion

10306.	If the ratio of the sum of first 'n' terms of 2APs is (7n+1):(4n+27) find the ratio of their nth terms
Answer» If the ratio of the sum of first 'n' terms of 2APs is (7n+1):(4n+27) find the ratio of their nth terms

Discussion

10307.	A particle is projected from the ground at an angle theeta with horizontal with some velocity for any position of point A. show that tan alpha + tan beta =tan theeta, where theeta is the angle of projection
Answer» A particle is projected from the ground at an angle theeta with horizontal with some velocity for any position of point A. show that tan alpha + tan beta =tan theeta, where theeta is the angle of projection

Discussion

10308.	Two aeroplanes I and II bomb a target in succession. The probabilities of aeroplanes I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first plane misses the target. Find the probability that the target is hit by the secondplane.
Answer» Two aeroplanes I and II bomb a target in succession. The probabilities of aeroplanes I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first plane misses the target. Find the probability that the target is hit by the secondplane.

Discussion

10309.	The ratio of the sums of m and n terms of an A.P, is m^2: n^2. Show that the ratio of m^{th} and n^{th} term is (2m - 1): (2n - 1).
Answer» The ratio of the sums of m and n terms of an A.P, is m^2: n^2. Show that the ratio of m^{th} and n^{th} term is (2m - 1): (2n - 1).

Discussion

10310.	2 men and 7 boys can do a piece of work in 4 days.It can also be done by 4 men and 4 boys in 3 days .How long would it take for man and one boy to do it.
Answer» 2 men and 7 boys can do a piece of work in 4 days.It can also be done by 4 men and 4 boys in 3 days .How long would it take for man and one boy to do it.

Discussion

10311.	Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =(a) 1(b) 2(c) 3(d) none of these.
Answer» Let S_n denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = S_n− kS_n₋₁ + S_n−2, then k = (a) 1 (b) 2 (c) 3 (d) none of these.

Discussion

10312.	32. The probability that there will be 53 Mondays in a randomly chosen year of 22ndcentury, is
Answer» 32. The probability that there will be 53 Mondays in a randomly chosen year of 22ndcentury, is

Discussion

10313.	An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.
Answer» An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

Discussion

10314.	ΔABC is a right triangle right angled at A such that AB = AC and bisector of ∠C intersects the side AB at D. Prove that AC + AD = BC.
Answer» ΔABC is a right triangle right angled at A such that AB = AC and bisector of ∠C intersects the side AB at D. Prove that AC + AD = BC.

Discussion

10315.	A shuttle cock used for playing badminton has the shape of the combination of ________ and _________.
Answer» A shuttle cock used for playing badminton has the shape of the combination of ________ and _________.

Discussion

10316.	The first term of a H P whose second term is 52 and third term is 103, is___
Answer» The first term of a H P whose second term is $\frac{5}{2}$ and third term is $\frac{10}{3}$ , is___

Discussion

10317.	A mass of 3kg is placed on a massless piston of area 10cm^2 of a cylindrical vessel containing a gas . Find the fractional change in surface area of sphere if the bulk modulus is 2×10^{4 }N\backslash m^2 and placed inthe given vessel
Answer» A mass of 3kg is placed on a massless piston of area 10cm^2 of a cylindrical vessel containing a gas . Find the fractional change in surface area of sphere if the bulk modulus is 2×10^{4 }N\backslash m^2 and placed inthe given vessel

Discussion

10318.	A manufacturer in Gujarat manufactures a machine and marks it at ₹5000. He sells the machine to a wholesaler in Jharkhand at a discount of 20%. The wholesaler sells the machine to a dealer in West Bengal at a discount of 10% on the MP. If the rate of GST is 28%, find the net tax liability of the wholesaler to the Central Government.
Answer» A manufacturer in Gujarat manufactures a machine and marks it at ₹5000. He sells the machine to a wholesaler in Jharkhand at a discount of 20%. The wholesaler sells the machine to a dealer in West Bengal at a discount of 10% on the MP. If the rate of GST is 28%, find the net tax liability of the wholesaler to the Central Government.

Discussion

10319.	Solve for x and y:0.4x+0.3y=1.70.7x-0.2y=0.8
Answer» Solve for x and y: $0.4 x + 0.3 y = 1.7 0.7 x - 0.2 y = 0.8$

Discussion

10320.	If the line joining the points (k,2,3),(1,1,2) is parallel to the line joining the points (5,4,−1),(3,2,−3) then the value of k is:
Answer» If the line joining the points $(k, 2, 3), (1, 1, 2)$ is parallel to the line joining the points $(5, 4, - 1), (3, 2, - 3)$ then the value of $k$ is:

Discussion

10321.	Question 1Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
Answer» Question 1 Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

Discussion

10322.	α, β are the roots of the equation x2+4x+5. Find the value of α3+β3
Answer» $α, β$ are the roots of the equation $x^{2} + 4 x + 5.$ Find the value of $α^{3} + β^{3}$

Discussion

10323.	Three vertices of a parallelogram are ( a+ b, a -b), (2a+b, 2a- b), (a - b, a + b). Find the fourth vertex.
Answer» Three vertices of a parallelogram are ( a+ b, a -b), (2a+b, 2a- b), (a - b, a + b). Find the fourth vertex.

Discussion

10324.	Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation.
Answer» Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation.

Discussion

10325.	The class interval size and frequency of modal class is Class Frequency 0−52005−1025010−1522515−2030020−25275
Answer» The class interval size and frequency of modal class is $\begin{matrix} C l a s s & F r e q u e n c y 0 - 5 & 200 5 - 10 & 250 10 - 15 & 225 15 - 20 & 300 20 - 25 & 275 \end{matrix}$

10325.

The class interval size and frequency of modal class is Class Frequency 0−52005−1025010−1522515−2030020−25275

Answer»

The class interval size and frequency of modal class is

$\begin{matrix} C l a s s & F r e q u e n c y 0 - 5 & 200 5 - 10 & 250 10 - 15 & 225 15 - 20 & 300 20 - 25 & 275 \end{matrix}$

Discussion

10326.	Without actually drawing figures or looking up tables, can you arrange the numbers below is ascending order?sin 1°, cos 1°, sin 2°, cos 2°
Answer» Without actually drawing figures or looking up tables, can you arrange the numbers below is ascending order? sin 1°, cos 1°, sin 2°, cos 2°

10326.

Without actually drawing figures or looking up tables, can you arrange the numbers below is ascending order?sin 1°, cos 1°, sin 2°, cos 2°

Answer»

Without actually drawing figures or looking up tables, can you arrange the numbers below is ascending order?

sin 1°, cos 1°, sin 2°, cos 2°

Discussion

10327.	What is the ratio ACBC for the line segment AB following the construction method below?Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2,...,A30Step 2. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17 and meet AB at C.
Answer» What is the ratio $\frac{A C}{B C}$ for the line segment AB following the construction method below? Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2}, . . ., A_{30}$ Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ and meet AB at C.

Discussion

10328.	Prove that a line drawn through the end point of the radius and perpendicular to it, is a tangent to the circle.
Answer» Prove that a line drawn through the end point of the radius and perpendicular to it, is a tangent to the circle.

Discussion

10329.	If p, q, r are the roots of the equation x^3 - ax^2 + bx - c = 0, then find the value of 1/p^2 + 1/q^2 + 1/r^2
Answer» If p, q, r are the roots of the equation x^3 - ax^2 + bx - c = 0, then find the value of 1/p^2 + 1/q^2 + 1/r^2

Discussion

10330.	If the equation 9x2+6kx+4=0 has equal roots, then find the value of k.
Answer» If the equation $9 x^{2} + 6 k x + 4 = 0$ has equal roots, then find the value of $k$ .

Discussion

10331.	If LM∥AB, AL=x−3, AC=2x, BM=x−2, and BC=2x+3. What is value of AC? ____
Answer» If $L M ∥ A B, A L = x - 3, A C = 2 x, B M = x - 2,$ and $B C = 2 x + 3.$ What is value of $A C ?$ ____

10331.

If LM∥AB, AL=x−3, AC=2x, BM=x−2, and BC=2x+3. What is value of AC? ____

Answer»

If $L M ∥ A B, A L = x - 3, A C = 2 x, B M = x - 2,$ and $B C = 2 x + 3.$ What is value of $A C ?$

____

Discussion

10332.	Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party the cost of the food for each member increased by Rs 10. How many students participated in the picnic?
Answer» Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party the cost of the food for each member increased by Rs 10. How many students participated in the picnic?

Discussion

10333.	ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area of △ACF : area of △ABE.
Answer» $A B C D$ is a square. Equilateral triangles $A C F$ and $A B E$ are drawn on the the diagonal $A C$ and side $A B$ respectively. Find area of $△ A C F$ : area of $△ A B E$ .

Discussion

10334.	i) In the figure given below,, XY∥BC. Given that AX = 3 cm, BX = 1.5 cm and BC = 6 cm. Write down the value of XY ii) If AXXB=413 and AC = 20.4 cm, find AY. [3 MARKS]
Answer» i) In the figure given below,, $X Y ∥ B C$ . Given that AX = 3 cm, BX = 1.5 cm and BC = 6 cm. Write down the value of XY ii) If $\frac{A X}{X B} = \frac{4}{13}$ and AC = 20.4 cm, find AY. [3 MARKS]

Discussion

10335.	Two tangents PA and PB are drawn to the circle with centre O, such that ∠APB =120∘. Prove thatOP = 2AP ?
Answer» Two tangents PA and PB are drawn to the circle with centre O, such that $∠$ APB $= 120^{\circ}$ . Prove that OP = 2AP ?

10335.

Two tangents PA and PB are drawn to the circle with centre O, such that ∠APB =120∘. Prove thatOP = 2AP ?

Answer»

Two tangents PA and PB are drawn to the circle with centre O, such that $∠$ APB $= 120^{\circ}$ . Prove that

OP = 2AP ?

Discussion

10336.	The 4th term of a G.P is square of its second term and the first term is - 3. Determine the Common Ratio of the G.P.
Answer» The 4th term of a G.P is square of its second term and the first term is - 3. Determine the Common Ratio of the G.P.

Discussion

10337.	Prove that arc= Radius *angle subtended by the arc
Answer» Prove that arc= Radius *angle subtended by the arc

Discussion

10338.	If the degree of p(x) is 4 and the degree of q(x) is 2, the n what is the degree of p(x) + q(x)?
Answer» If the degree of p(x) is 4 and the degree of q(x) is 2, the n what is the degree of p(x) + q(x)?

10338.

If the degree of p(x) is 4 and the degree of q(x) is 2, the n what is the degree of p(x) + q(x)?

Answer»

If the degree of p(x) is 4 and the degree of q(x) is 2, the n what is the degree of p(x) + q(x)?

Discussion

10339.	Question 29 The time period after which the interest is added each time to form a new principal, is called the ___.
Answer» Question 29 The time period after which the interest is added each time to form a new principal, is called the ___.

10339.

Question 29 The time period after which the interest is added each time to form a new principal, is called the ___.

Answer»

Question 29

The time period after which the interest is added each time to form a new principal, is called the ___.

Discussion

10340.	To divide a line segment AB in the ratio m : n (m, n are positive integers), draw a ray AX such that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is(a) greater than m and n(b) m + n(c) m + n – 1(d) mn
Answer» To divide a line segment AB in the ratio m : n (m, n are positive integers), draw a ray AX such that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is (a) greater than m and n (b) m + n (c) m + n – 1 (d) mn

Discussion

10341.	Given tan θ=15, what is the value of cosec2 θ-sec2 θcosec2 θ+sec2 θ?
Answer» Given $\tan θ = \frac{1}{\sqrt{5}}$ , what is the value of $\frac{{cosec}^{2} θ - \sec^{2} θ}{{cosec}^{2} θ + \sec^{2} θ}$ ?

Discussion

10342.	What are the different types of taxes?
Answer» What are the different types of taxes?

Discussion

10343.	Question 1 (vii)Which of the following form an AP? Justify your answer.√3,√12,√27,√48⋯
Answer» Question 1 (vii) Which of the following form an AP? Justify your answer. $\sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48} \dots$

Discussion

10344.	A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.
Answer» A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$ . Find the number of blue marbles in the jar.

Discussion

10345.	What is the remainder when x^1999 is divided by (x^2)-1?
Answer» What is the remainder when x^1999 is divided by (x^2)-1?

Discussion

10346.	All kings and queens are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a red face card (ii) a black card. [CBSE 2014]
Answer» All kings and queens are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a red face card (ii) a black card. [CBSE 2014]

Discussion

10347.	12 men's work 9 hour daily can finish a work in 30 days . how many men's working 10 times faster can complete the work if they wprk for 5 hour s daily for 24 days.
Answer» 12 men's work 9 hour daily can finish a work in 30 days . how many men's working 10 times faster can complete the work if they wprk for 5 hour s daily for 24 days.

Discussion

10348.

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24. Age (in years) 0−10 10−20 20−30 30−40 40−50 Number of persons 5 25 ? 18 7

Answer» Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age (in years)	0−10	10−20	20−30	30−40	40−50
Number of persons	5	25	?	18	7

Discussion

10349.	The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m2 . Find the cost of ploughing the field. [Take π=227].
Answer» The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m² . Find the cost of ploughing the field. [Take $π = \frac{22}{7}$ ].

Discussion

10350.

The fig., shows the observation of point C from point A. The angle of depression from A is:

Answer»

The fig., shows the observation of point C from point A. The angle of depression from A is:

Discussion

Explore topic-wise InterviewSolutions in .

What is the volume of a box whose length is 3 cm, breadth is 3 cm and height is 3 cm?

Question 92 (xvii)Factorise the following using the identity a2−b2=(a+b)(a−b).136a2b2−1649b2c2

Mark the correct alternative in the following question:The mean proportional of a and b is 10 and the value of a is four times the value of b. The value of a + b (a > 0, b > 0) is(a) 20 (b) 25 (c) 101 (d) 29

Show that the function x+a-[x-b] is a periodic function. Find its period. (a and b are positive real numbers)

Find the values of k for which the given equation has real and equal roots: x2−2x(1+3k)+7(3+2k)=0

If the ratio of the sum of first 'n' terms of 2APs is (7n+1):(4n+27) find the ratio of their nth terms

A particle is projected from the ground at an angle theeta with horizontal with some velocity for any position of point A. show that tan alpha + tan beta =tan theeta, where theeta is the angle of projection

Two aeroplanes I and II bomb a target in succession. The probabilities of aeroplanes I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first plane misses the target. Find the probability that the target is hit by the secondplane.

The ratio of the sums of m and n terms of an A.P, is m^2: n^2. Show that the ratio of m^{th} and n^{th} term is (2m - 1): (2n - 1).

2 men and 7 boys can do a piece of work in 4 days.It can also be done by 4 men and 4 boys in 3 days .How long would it take for man and one boy to do it.

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =(a) 1(b) 2(c) 3(d) none of these.

32. The probability that there will be 53 Mondays in a randomly chosen year of 22ndcentury, is

An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

ΔABC is a right triangle right angled at A such that AB = AC and bisector of ∠C intersects the side AB at D. Prove that AC + AD = BC.

A shuttle cock used for playing badminton has the shape of the combination of ________ and _________.

The first term of a H P whose second term is 52 and third term is 103, is___

A mass of 3kg is placed on a massless piston of area 10cm^2 of a cylindrical vessel containing a gas . Find the fractional change in surface area of sphere if the bulk modulus is 2×10^{4 }N\backslash m^2 and placed inthe given vessel

Solve for x and y:0.4x+0.3y=1.70.7x-0.2y=0.8

If the line joining the points (k,2,3),(1,1,2) is parallel to the line joining the points (5,4,−1),(3,2,−3) then the value of k is:

Question 1Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

α, β are the roots of the equation x2+4x+5. Find the value of α3+β3

Three vertices of a parallelogram are ( a+ b, a -b), (2a+b, 2a- b), (a - b, a + b). Find the fourth vertex.

Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation.

The class interval size and frequency of modal class is Class Frequency 0−52005−1025010−1522515−2030020−25275

Without actually drawing figures or looking up tables, can you arrange the numbers below is ascending order?sin 1°, cos 1°, sin 2°, cos 2°

Prove that a line drawn through the end point of the radius and perpendicular to it, is a tangent to the circle.

If p, q, r are the roots of the equation x^3 - ax^2 + bx - c = 0, then find the value of 1/p^2 + 1/q^2 + 1/r^2

If the equation 9x2+6kx+4=0 has equal roots, then find the value of k.

If LM∥AB, AL=x−3, AC=2x, BM=x−2, and BC=2x+3. What is value of AC? ____

Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party the cost of the food for each member increased by Rs 10. How many students participated in the picnic?

ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area of △ACF : area of △ABE.

i) In the figure given below,, XY∥BC. Given that AX = 3 cm, BX = 1.5 cm and BC = 6 cm. Write down the value of XY ii) If AXXB=413 and AC = 20.4 cm, find AY. [3 MARKS]

Two tangents PA and PB are drawn to the circle with centre O, such that ∠APB =120∘. Prove thatOP = 2AP ?

The 4th term of a G.P is square of its second term and the first term is - 3. Determine the Common Ratio of the G.P.

Prove that arc= Radius *angle subtended by the arc

If the degree of p(x) is 4 and the degree of q(x) is 2, the n what is the degree of p(x) + q(x)?

Question 29 The time period after which the interest is added each time to form a new principal, is called the ___.

To divide a line segment AB in the ratio m : n (m, n are positive integers), draw a ray AX such that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is(a) greater than m and n(b) m + n(c) m + n – 1(d) mn

Given tan θ=15, what is the value of cosec2 θ-sec2 θcosec2 θ+sec2 θ?

What are the different types of taxes?

Question 1 (vii)Which of the following form an AP? Justify your answer.√3,√12,√27,√48⋯

A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.

What is the remainder when x^1999 is divided by (x^2)-1?

All kings and queens are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a red face card (ii) a black card. [CBSE 2014]

12 men's work 9 hour daily can finish a work in 30 days . how many men's working 10 times faster can complete the work if they wprk for 5 hour s daily for 24 days.

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24. Age (in years) 0−10 10−20 20−30 30−40 40−50 Number of persons 5 25 ? 18 7

The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m2 . Find the cost of ploughing the field. [Take π=227].

The fig., shows the observation of point C from point A. The angle of depression from A is:

A shuttle cock used for playing badminton has the shape of the combination of and _.