43030 + Interview Questions in Mathematics

1.	In the expansions of (x+a)n, the sum of odd terms is P and sum of even terms is Q, then the value of (P2−Q2) will be
Answer» In the expansions of $(x + a)^{n}$ , the sum of odd terms is P and sum of even terms is Q, then the value of $(P^{2} - Q^{2})$ will be

Discussion

2.	If z=32+cosθ+isinθ, then locus of z is
Answer» If $z = \frac{3}{2 + cos θ + i sin θ}$ , then locus of $z$ is

Discussion

3.	The order and the degree of differential equation are respectively
Answer» The order and the degree of differential equation are respectively

3.

The order and the degree of differential equation are respectively

Answer»

The order and the degree of differential equation are respectively

Discussion

4.	Domain for √\|x\|-x
Answer» Domain for √\|x\|-x

Discussion

5.	Interrogation of √tan x
Answer» Interrogation of √tan x

Discussion

6.	Find I=∫π20log(4+3sinx4+3cosx)dx
Answer» Find $I = \int_{0}^{\frac{π}{2}} l o g (\frac{4 + 3 s i n x}{4 + 3 c o s x}) d x$

Discussion

7.	prove that: sin5x-2sin3x+sinx/cos5x-cosx= tanx
Answer» prove that: sin5x-2sin3x+sinx/cos5x-cosx= tanx

7.

prove that: sin5x-2sin3x+sinx/cos5x-cosx= tanx

Answer»

prove that:

sin5x-2sin3x+sinx/cos5x-cosx= tanx

Discussion

8.	In a G.P.,the product of the first four terms is 4 and the second term is reciprocal of the fourth term. The sum of infinite terms of the G.P. is
Answer» In a G.P.,the product of the first four terms is 4 and the second term is reciprocal of the fourth term. The sum of infinite terms of the G.P. is

Discussion

9.	The product of two numbers is 2475 and their quotient is 11/9. Find the numbers.
Answer» The product of two numbers is 2475 and their quotient is 11/9. Find the numbers.

Discussion

10.	A = {1, 2, 3}, B = {2, 3, 4}, C = {4, 5}. Find (A ∩ B) × C.
Answer» A = {1, 2, 3}, B = {2, 3, 4}, C = {4, 5}. Find (A ∩ B) $\times$ C.

Discussion

11.	If cosx+cosy+cosz=0=sinx+siny+sinz, then
Answer» If $cos x + cos y + cos z = 0 = sin x + sin y + sin z,$ then

Discussion

12.	General solution of ydydx+by2=acosx,0<x<1 is
Answer» General solution of $y \frac{d y}{d x} + b y^{2} = a cos x, 0 < x < 1$ is

Discussion

13.	Find the area enclosed between the parabola y2=8ax and its latus rectum in the first quadrant.
Answer» Find the area enclosed between the parabola $y^{2} = 8 a x$ and its latus rectum in the first quadrant.

Discussion

14.	Show that the solution set of the following linear inequations is empty set: (i) x−2y≥0,2x−y≤−2,x≥0,y≥0 (ii) x+2y≤3,3x+4y≥12,y≥1,x≥0 and y≥0
Answer» Show that the solution set of the following linear inequations is empty set: (i) $x - 2 y \geq 0, 2 x - y \leq - 2, x \geq 0, y \geq 0$ (ii) $x + 2 y \leq 3, 3 x + 4 y \geq 12, y \geq 1, x \geq 0 a n d y \geq 0$

14.

Show that the solution set of the following linear inequations is empty set: (i) x−2y≥0,2x−y≤−2,x≥0,y≥0 (ii) x+2y≤3,3x+4y≥12,y≥1,x≥0 and y≥0

Answer»

Show that the solution set of the following linear inequations is empty set:

(i) $x - 2 y \geq 0, 2 x - y \leq - 2, x \geq 0, y \geq 0$

(ii) $x + 2 y \leq 3, 3 x + 4 y \geq 12, y \geq 1, x \geq 0 a n d y \geq 0$

Discussion

15.	If a point P on the axis of the parabola y2=4x is taken such that the point is at shortest distance from the circle x2+y2+2x−2√2y+2=0.Common tangents are drawn to the circle and the parabola from P.If the area of the ΔPAB is √a sq. units where A and B are the points of contact on two distinct tangents from P on circle and parabola respectively, then a=
Answer» If a point $P$ on the axis of the parabola $y^{2} = 4 x$ is taken such that the point is at shortest distance from the circle $x^{2} + y^{2} + 2 x - 2 \sqrt{2} y + 2 = 0$ .Common tangents are drawn to the circle and the parabola from $P$ .If the area of the $Δ P A B$ is $\sqrt{a}$ sq. units where $A$ and $B$ are the points of contact on two distinct tangents from $P$ on circle and parabola respectively, then $a =$

Discussion

16.	Find a vector of magnitude 5 units and parallel to the resultant of the vectors a=2^i+3^j−^k and b=^i−2^j+^k.
Answer» Find a vector of magnitude 5 units and parallel to the resultant of the vectors $a = 2^i + 3^j -^k a n d b =^i - 2^j +^k .$

Discussion

17.	Write the differential equation representing the curve y2=4ax, where a is an arbitrary constant.
Answer» Write the differential equation representing the curve $y^{2} = 4 a x$ , where a is an arbitrary constant.

Discussion

18.	What is a scalar matrix and square matrix ?
Answer» What is a scalar matrix and square matrix ?

Discussion

19.	A point particle moves along a straight line such that x=√t where t is time. Then ratio of acceleration to cube of the velocity is
Answer» A point particle moves along a straight line such that $x = \sqrt{t}$ where $t$ is time. Then ratio of acceleration to cube of the velocity is

Discussion

20.	If sin(x+y)sin(x−y)=a+ba−b,then tan xtan y is equal to
Answer» $I f \frac{s i n (x + y)}{s i n (x - y)} = \frac{a + b}{a - b}, t h e n \frac{t a n x}{t a n y} i s e q u a l t o$

Discussion

21.	If (ax+b)cyx=x, then show that X3(d2ydx2)=(xdydx−y)2
Answer» If $(a x + b) c \frac{y}{x} = x$ , then show that $X^{3} (\frac{d^{2} y}{d x^{2}}) = {(x \frac{d y}{d x} - y)}^{2}$

Discussion

22.	Using properties of determinants, prove that ∣∣∣∣∣a32ab32bc32c∣∣∣∣∣=2(a−b)(b−c)(c−a)(a+b+c).
Answer» Using properties of determinants, prove that $∣ ∣∣∣ ∣ \begin{matrix} a^{3} & 2 & a b^{3} & 2 & b c^{3} & 2 & c \end{matrix} ∣ ∣∣∣ ∣ = 2 (a - b) (b - c) (c - a) (a + b + c)$ .

Discussion

23.	For the matrices A and B, verify that (AB)' =B'A', where A=⎡⎢⎣012⎤⎥⎦, B =[1 5 7]
Answer» For the matrices A and B, verify that (AB)' =B'A', where A= $⎡ ⎢ ⎣ \begin{matrix} 012 \end{matrix} ⎤ ⎥ ⎦$ , B =[1 5 7]

Discussion

24.	Find the unit vector in the direction of vector PQ where P and Q are the points (1,2,3) and (4,5,6), respectively.
Answer» Find the unit vector in the direction of vector PQ where P and Q are the points (1,2,3) and (4,5,6), respectively.

Discussion

25.	If f(x)=3x2+15x+5, then the approximate value of f(3.02) is ? (a) 47.66 (b) 57.66 (c) 67.66 (d) 77.66
Answer» If $f (x) = 3 x^{2} + 15 x + 5,$ then the approximate value of f(3.02) is ? (a) 47.66 (b) 57.66 (c) 67.66 (d) 77.66

Discussion

26.	Find the angle between the lines whose directions cosines are given by the equation l+m+n=0 and l2+m2−n2=0.
Answer» Find the angle between the lines whose directions cosines are given by the equation l+m+n=0 and $l^{2} + m^{2} - n^{2} = 0.$

Discussion

27.	Evaluate Cos to the power4 A - Sin to the power 4A
Answer» Evaluate Cos to the power4 A - Sin to the power 4A

27.

Evaluate Cos to the power4 A - Sin to the power 4A

Answer»

Evaluate

Cos to the power4 A - Sin to the power 4A

Discussion

28.	Let a, b, c be the sides of the triangle. No two of them are equal and λ∈R. If the roots of the equation x2+2(a+b+c)x+3λ(ab+bc+ca)=0 are real then :
Answer» Let a, b, c be the sides of the triangle. No two of them are equal and $λ \in R$ . If the roots of the equation $x^{2} + 2 (a + b + c) x + 3 λ (a b + b c + c a) = 0$ are real then :

Discussion

29.	The coefficient of x9 in the expansion of 1+x)((1+x2) (1+x3) ⋯ (1+x100) is
Answer» The coefficient of $x^{9}$ in the expansion of $1 + x) ((1 + x^{2})$ $(1 + x^{3})$ $\dots$ $(1 + x^{100})$ is

Discussion

30.	If 12 identical balls are to be placed in 3 different boxes, then the probability that a particular box contains exactly 3 balls, is?
Answer» If 12 identical balls are to be placed in 3 different boxes, then the probability that a particular box contains exactly 3 balls, is?

Discussion

31.	∫10 x Sin−1x√1−x2dx=
Answer» $\int_{0}^{1} \frac{x S i n^{- 1} x}{\sqrt{1 - x^{2}}} d x =$

Discussion

32.	The variance of data 1001,1003,1006,1007,1009,1010 is
Answer» The variance of data $1001, 1003, 1006, 1007, 1009, 1010$ is

Discussion

33.	The total number of 7-letter words that can be formed using the letters of the word MATHEMATICS such that the repeating letters should be placed in odd places, whereas the non-repeating letters should be placed in even places, is
Answer» The total number of $7$ -letter words that can be formed using the letters of the word $M A T H E M A T I C S$ such that the repeating letters should be placed in odd places, whereas the non-repeating letters should be placed in even places, is

Discussion

34.	If x2−3x+2 be a factor of x4−px2+q, then (p, q) =
Answer» If $x^{2} - 3 x + 2$ be a factor of $x^{4} - p x^{2} + q$ , then (p, q) =

Discussion

35.	Let P be the image of the point (3,1,7) with respect to the plane x−y+z=3. Then the equation of the plane passing through P and containing the straight line x1=y2=z1 is
Answer» Let $P$ be the image of the point $(3, 1, 7)$ with respect to the plane $x - y + z = 3.$ Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1} = \frac{y}{2} = \frac{z}{1}$ is

Discussion

36.	The value of ‘a’ for which ax2+sin−1(x2−2x+2)+cos−1(x2−2x+2)=0 has a real solution is
Answer» The value of ‘a’ for which $a x^{2} + s i n^{- 1} (x^{2} - 2 x + 2) + c o s^{- 1} (x^{2} - 2 x + 2) = 0$ has a real solution is

Discussion

37.	1(2+x)4 =
Answer» $\frac{1}{(2 + x)^{4}}$ =

Discussion

38.	A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S={1,2,3,4,5,6,7} and reports that it is even. The probability that it is actually even is
Answer» A man speaks truth $2$ out of $3$ times. He picks one of the natural numbers in the set $S = {1, 2, 3, 4, 5, 6, 7}$ and reports that it is even. The probability that it is actually even is

Discussion

39.	Differentiate the following functions with respect to x : sin x−x cos xx sin x+cos x
Answer» Differentiate the following functions with respect to x : $\frac{s i n x - x c o s x}{x s i n x + c o s x}$

39.

Differentiate the following functions with respect to x : sin x−x cos xx sin x+cos x

Answer»

Differentiate the following functions with respect to x :

$\frac{s i n x - x c o s x}{x s i n x + c o s x}$

Discussion

40.	Solution of the equation cot−1x+sin−11√5=π4
Answer» Solution of the equation $c o t^{- 1} x + s i n^{- 1} \frac{1}{\sqrt{5}} = \frac{π}{4}$

Discussion

41.	Differentiate the following functions with respect to x : px2+qx+rax+b
Answer» Differentiate the following functions with respect to x : $\frac{p x^{2} + q x + r}{a x + b}$

41.

Differentiate the following functions with respect to x : px2+qx+rax+b

Answer»

Differentiate the following functions with respect to x :

$\frac{p x^{2} + q x + r}{a x + b}$

Discussion

42.	Mean and Standard Deviation of 100 items are 50 and 4 respectively. The sum of all squares of the items is...
Answer» Mean and Standard Deviation of $100$ items are $50$ and $4$ respectively. The sum of all squares of the items is...

Discussion

43.	X and Y are partners sharing profits in 5 : 3 ratio admitted Z for 110 share which he acquired equally for X and Y. Calculate new profit sharing ratio.
Answer» X and Y are partners sharing profits in 5 : 3 ratio admitted Z for $\frac{1}{10}$ share which he acquired equally for X and Y. Calculate new profit sharing ratio.

Discussion

44.	If A(1, 2, 3), B(2, 3, 1) and C(3, 1, 2) are the vertices of the triangle. Find the coordinates of its orthocenter (O) and In center (I).
Answer» If $A (1, 2, 3), B (2, 3, 1)$ and $C (3, 1, 2$ ) are the vertices of the triangle. Find the coordinates of its orthocenter $(O)$ and In center $(I)$ .

Discussion

45.	Differentiate the following equation, logx2 x
Answer» Differentiate the following equation, $l o g_{x^{2}} x$

Discussion

46.	The equation of a curve is 3x2+2xy+3y2=10 . Its equation if the axes are rotated through an angle 45° will be .
Answer» The equation of a curve is $3 x^{2} + 2 xy + 3 y^{2} = 10$ . Its equation if the axes are rotated through an angle $45 °$ will be .

Discussion

47.	If ∣ z∣=1 andw=z−1z+1 (where z ≠ −1) ,then Re(w) is
Answer» If $∣ z ∣= 1$ $a n d^{w = \frac{z - 1}{z + 1} (w h e r e z \neq - 1), t h e n R e (w)}$ is

Discussion

48.	Evaluate: ∣∣∣x2−x+1x−1x+1x+1∣∣∣
Answer» Evaluate: $∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

Discussion

49.	Distinguish between advertising and personal selling on any five basis.
Answer» Distinguish between advertising and personal selling on any five basis.

Discussion

50.	The sum of the roots of the equation x+1−2log2(2x+3)+2log4(10−2−x)=0 is
Answer» The sum of the roots of the equation $x + 1 - 2 {log}_{2} (2^{x} + 3) + 2 {log}_{4} (10 - 2^{- x}) = 0$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the expansions of (x+a)n, the sum of odd terms is P and sum of even terms is Q, then the value of (P2−Q2) will be

If z=32+cosθ+isinθ, then locus of z is

The order and the degree of differential equation are respectively

Domain for √|x|-x

Interrogation of √tan x

Find I=∫π20log(4+3sinx4+3cosx)dx

prove that: sin5x-2sin3x+sinx/cos5x-cosx= tanx

In a G.P.,the product of the first four terms is 4 and the second term is reciprocal of the fourth term. The sum of infinite terms of the G.P. is

The product of two numbers is 2475 and their quotient is 11/9. Find the numbers.

A = {1, 2, 3}, B = {2, 3, 4}, C = {4, 5}. Find (A ∩ B) × C.

If cosx+cosy+cosz=0=sinx+siny+sinz, then

General solution of ydydx+by2=acosx,0&lt;x&lt;1 is

Find the area enclosed between the parabola y2=8ax and its latus rectum in the first quadrant.

Show that the solution set of the following linear inequations is empty set: (i) x−2y≥0,2x−y≤−2,x≥0,y≥0 (ii) x+2y≤3,3x+4y≥12,y≥1,x≥0 and y≥0

Find a vector of magnitude 5 units and parallel to the resultant of the vectors a=2^i+3^j−^k and b=^i−2^j+^k.

Write the differential equation representing the curve y2=4ax, where a is an arbitrary constant.

What is a scalar matrix and square matrix ?

A point particle moves along a straight line such that x=√t where t is time. Then ratio of acceleration to cube of the velocity is

If sin(x+y)sin(x−y)=a+ba−b,then tan xtan y is equal to

If (ax+b)cyx=x, then show that X3(d2ydx2)=(xdydx−y)2

Using properties of determinants, prove that ∣∣∣∣∣a32ab32bc32c∣∣∣∣∣=2(a−b)(b−c)(c−a)(a+b+c).

For the matrices A and B, verify that (AB)' =B'A', where A=⎡⎢⎣012⎤⎥⎦, B =[1 5 7]

Find the unit vector in the direction of vector PQ where P and Q are the points (1,2,3) and (4,5,6), respectively.

If f(x)=3x2+15x+5, then the approximate value of f(3.02) is ? (a) 47.66 (b) 57.66 (c) 67.66 (d) 77.66

Find the angle between the lines whose directions cosines are given by the equation l+m+n=0 and l2+m2−n2=0.

Evaluate Cos to the power4 A - Sin to the power 4A

Let a, b, c be the sides of the triangle. No two of them are equal and λ∈R. If the roots of the equation x2+2(a+b+c)x+3λ(ab+bc+ca)=0 are real then :

The coefficient of x9 in the expansion of 1+x)((1+x2) (1+x3) ⋯ (1+x100) is

If 12 identical balls are to be placed in 3 different boxes, then the probability that a particular box contains exactly 3 balls, is?

∫10 x Sin−1x√1−x2dx=

The variance of data 1001,1003,1006,1007,1009,1010 is

The total number of 7-letter words that can be formed using the letters of the word MATHEMATICS such that the repeating letters should be placed in odd places, whereas the non-repeating letters should be placed in even places, is

If x2−3x+2 be a factor of x4−px2+q, then (p, q) =

Let P be the image of the point (3,1,7) with respect to the plane x−y+z=3. Then the equation of the plane passing through P and containing the straight line x1=y2=z1 is

The value of ‘a’ for which ax2+sin−1(x2−2x+2)+cos−1(x2−2x+2)=0 has a real solution is

1(2+x)4 =

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S={1,2,3,4,5,6,7} and reports that it is even. The probability that it is actually even is

Differentiate the following functions with respect to x : sin x−x cos xx sin x+cos x

Solution of the equation cot−1x+sin−11√5=π4

Differentiate the following functions with respect to x : px2+qx+rax+b

Mean and Standard Deviation of 100 items are 50 and 4 respectively. The sum of all squares of the items is...

X and Y are partners sharing profits in 5 : 3 ratio admitted Z for 110 share which he acquired equally for X and Y. Calculate new profit sharing ratio.

If A(1, 2, 3), B(2, 3, 1) and C(3, 1, 2) are the vertices of the triangle. Find the coordinates of its orthocenter (O) and In center (I).

Differentiate the following equation, logx2 x

The equation of a curve is 3x2+2xy+3y2=10 . Its equation if the axes are rotated through an angle 45° will be .

If ∣ z∣=1 andw=z−1z+1 (where z ≠ −1) ,then Re(w) is

Evaluate: ∣∣∣x2−x+1x−1x+1x+1∣∣∣

Distinguish between advertising and personal selling on any five basis.

The sum of the roots of the equation x+1−2log2(2x+3)+2log4(10−2−x)=0 is

General solution of ydydx+by2=acosx,0<x<1 is