43030 + Interview Questions in Mathematics

1.	Evaluate the definite integrals. ∫10xex2dx.
Answer» Evaluate the definite integrals. $\int_{0}^{1} x e^{x^{2}} d x .$

Discussion

2.	The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
Answer» The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Discussion

3.	The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely with the length of the side.
Answer» The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely with the length of the side.

Discussion

4.	Prove that the curves y2=4x and x2+y2−6x+1=0 touch each other at the point (1, 2).
Answer» Prove that the curves $y^{2} = 4 x a n d x^{2} + y^{2} - 6 x + 1 = 0$ touch each other at the point (1, 2).

Discussion

5.	The real order pair (x,y) which satisfies (x4+2xi)−(3x2+yi)=(3−5i)+(1+2yi) is
Answer» The real order pair $(x, y)$ which satisfies $(x^{4} + 2 x i) - (3 x^{2} + y i) = (3 - 5 i) + (1 + 2 y i)$ is

Discussion

6.	A die is thrown repeatedly until a six comes up. What is the sample space for the experiment?
Answer» A die is thrown repeatedly until a six comes up. What is the sample space for the experiment?

Discussion

7.	The set A has 4 elements and the set B had 5 elements then the number of objective mapping that can be defined from A to B is ? Answers is: 120 How to do this question?
Answer» The set A has 4 elements and the set B had 5 elements then the number of objective mapping that can be defined from A to B is ? Answers is: 120 How to do this question?

Discussion

8.	What is the value of x is equals to root 6 + root 6 + root 6 + root 6 upto infinity?
Answer» What is the value of x is equals to root 6 + root 6 + root 6 + root 6 upto infinity?

Discussion

9.	How many three-digit numbers are there, with no digit repeated?
Answer» How many three-digit numbers are there, with no digit repeated?

Discussion

10.	If tan x =n tany, n∈R+, then maximum value of sec2(x−y)=___
Answer» If tan x =n tany, $n \in R^{+}$ , then maximum value of $s e c^{2} (x - y) =$ ___

Discussion

11.	When sinθ + cosθ = 1, then the value of sin2θ is
Answer» When sinθ + cosθ = 1, then the value of sin2θ is

Discussion

12.	The area bounded by y=x2, y=[x+1], x≤1 and the y-axis, where [.] represents the greatest integer function, is A sq. unit, then the value of 9A2 is
Answer» The area bounded by $y = x^{2},$ $y = [x + 1],$ $x \leq 1$ and the $y$ -axis, where $[.]$ represents the greatest integer function, is $A$ sq. unit, then the value of $9 A^{2}$ is

Discussion

13.	The mean and variance of seven observations are 8 and 16 respectiveley. If 5 of the observations are 2,4,10,12,14, then the product of the remaining two observations is:
Answer» The mean and variance of seven observations are $8$ and $16$ respectiveley. If $5$ of the observations are $2, 4, 10, 12, 14,$ then the product of the remaining two observations is:

Discussion

14.	18 mice were placed in two experimental groups and one control group, with all group equally large. In how many ways can the mice be placed into three groups ?
Answer» $18$ mice were placed in two experimental groups and one control group, with all group equally large. In how many ways can the mice be placed into three groups ?

Discussion

15.	How many differnet numbers, greater than 50000 can be formed with the digits 0, 1,1,5,9.
Answer» How many differnet numbers, greater than 50000 can be formed with the digits 0, 1,1,5,9.

Discussion

16.	For the complex roots of a quadratic equation, which of the following is true?
Answer» For the complex roots of a quadratic equation, which of the following is true?

Discussion

17.	Which among the following represents the graph of y=sec−1(x)
Answer» Which among the following represents the graph of $y = s e c^{- 1} (x)$

Discussion

18.	Choose the correct answer If θ is the angle between two vectors a and b, then a.b≥0 only when a) 0<θ<π2 b) 0≤θ<π2 c) 0<θ<π d) 0≤θ≤π
Answer» Choose the correct answer If $θ$ is the angle between two vectors a and b, then $a . b \geq 0$ only when a) $0 < θ < \frac{π}{2}$ b) $0 \leq θ < \frac{π}{2}$ c) $0 < θ < π$ d) $0 \leq θ \leq π$

Discussion

19.	holds for
Answer» holds for

Discussion

20.	The general solution of the equation sin2θ=12 is (nϵZ)
Answer» The general solution of the equation $s i n^{2} θ = \frac{1}{2} i s (n ϵ Z)$

Discussion

21.	The length x of a rectangle is increasing at the rate of 4 cm/s and the width y is decreasing at the rate of 3 cm/s. When x=5 cm and y=6 cm, then the rate of change of the perimeter is
Answer» The length $x$ of a rectangle is increasing at the rate of $4 c m / s$ and the width $y$ is decreasing at the rate of $3 c m / s$ . When $x = 5 c m$ and $y = 6 c m$ , then the rate of change of the perimeter is

Discussion

22.	If the points (1, -1), (2, -1) and (4, -3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.
Answer» If the points (1, -1), (2, -1) and (4, -3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.

Discussion

23.	Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.
Answer» Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.

Discussion

24.	If the term free from x in the expansion of (√x−kx2)10 is 405, find the value of k.
Answer» If the term free from x in the expansion of ${(\sqrt{x} - \frac{k}{x^{2}})}^{10}$ is 405, find the value of k.

Discussion

25.	Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king ?
Answer» Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king ?

Discussion

26.	If A(-2, 2, 3) and B(13, -3, 13) are two points. Find the locus of a point P which moves in such a way that 3PA = 2PB.
Answer» If A(-2, 2, 3) and B(13, -3, 13) are two points. Find the locus of a point P which moves in such a way that 3PA = 2PB.

Discussion

27.	If tan−1 x = π10 for some x ∈ R, then the value of cot−1 x is
Answer» If ${tan}^{- 1} x = \frac{π}{10} for some x \in R,$ then the value of $c o t^{- 1} x is$

Discussion

28.	Prove that: sin 2θ1+cos 2θ=tan θ
Answer» Prove that: $\frac{s i n 2 θ}{1 + c o s 2 θ} = t a n θ$

28.

Prove that: sin 2θ1+cos 2θ=tan θ

Answer»

Prove that:

$\frac{s i n 2 θ}{1 + c o s 2 θ} = t a n θ$

Discussion

29.	Consider the following three statements: P : 5 is a prime number Q : 7 is a factor of 192 R : L.C.M. of 5 and 7 is 35 Then the truth value of which one of the following statements is true?
Answer» Consider the following three statements: $P : 5$ is a prime number $Q : 7$ is a factor of 192 $R : L.C.M. of 5 and 7 is 35$ Then the truth value of which one of the following statements is true?

Discussion

30.	For the options given below, the function f(x) = [x] is discontinuous at x =
Answer» For the options given below, the function f(x) = [x] is discontinuous at x =

Discussion

31.	From the given figure if speed of end B of rod of length 4 m at an instant when θ=30∘ is 4 m/s then angular velocity of rod is. [angle between wall is 135∘] Write upto two digits after the decimal point. (Take cos15=√3+12√2 and √3=1.7)
Answer» From the given figure if speed of end B of rod of length 4 m at an instant when $θ = 30^{\circ}$ is 4 m/s then angular velocity of rod is. [angle between wall is $135^{\circ}$ ] Write upto two digits after the decimal point. (Take $cos 15 = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$ and $\sqrt{3} = 1.7$ )

Discussion

32.	Let f:R→R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f′(y)+f′(x)f(y) for all x,y∈R. Then, the value of loge(f(4)) is
Answer» Let $f : R \to R$ be a differentiable function with $f (0) = 1$ and satisfying the equation $f (x + y) = f (x) f^{'} (y) + f^{'} (x) f (y)$ for all $x, y \in R .$ Then, the value of ${log}_{e} (f (4))$ is

Discussion

33.	If f:Z→Z is defined by f(x)={x2 if x even0 if x odd then f is
Answer» If $f : Z \to Z$ is defined by $f (x) = {\begin{matrix} \frac{x}{2} if x even 0 if x odd \end{matrix}$ then f is

Discussion

34.	Let P(4,−4) and Q(9,6) be two points on the parabola y2=4x. If X is any point on the arc POQ of the parabola, where O is the vertex such that the area of △PXQ is maximum, then 4 times the maximum area (in sq. units) is
Answer» Let $P (4, - 4)$ and $Q (9, 6)$ be two points on the parabola $y^{2} = 4 x$ . If $X$ is any point on the arc $P O Q$ of the parabola, where $O$ is the vertex such that the area of $△ P X Q$ is maximum, then $4$ times the maximum area (in sq. units) is

Discussion

35.	What is De morgan's law?
Answer» What is De morgan's law?

Discussion

36.	Let S be the sample space of all 3×3 matrices with entries from the set {0,1}. Let the events E1 and E2 be given by E1={A∈S:detA=0} and E2={A ∈S: sum of entries of A is 7} If the matrix is chosen at random from S, then the conditional probability P(E1\|E2) equals
Answer» Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set {0,1}. Let the events $E_{1}$ and $E_{2}$ be given by $E_{1} = {A \in S : d e t A = 0}$ and $E_{2} =$ {A $\in S :$ sum of entries of $A$ is $7$ } If the matrix is chosen at random from $S,$ then the conditional probability $P (E_{1} \| E_{2})$ equals

Discussion

37.	If 2ax2+3bx+5c=0, a∈R−{0},c>0 does not have any real roots, then which of the following is/are always true?
Answer» If $2 a x^{2} + 3 b x + 5 c = 0, a \in R - {0}, c > 0$ does not have any real roots, then which of the following is/are always true?

Discussion

38.	Let S1 and S2 be two unit circles with centres at C1(0,0) and C2(1,0) respectively. Let S3 be another circle of unit radius, passing through C1 and C2 and its centre is above the x-axis. If equation of common tangent to S1 and S3, which does not pass through S2, is ax+by+2=0, then the value of a2−b is
Answer» Let $S_{1}$ and $S_{2}$ be two unit circles with centres at $C_{1} (0, 0)$ and $C_{2} (1, 0)$ respectively. Let $S_{3}$ be another circle of unit radius, passing through $C_{1}$ and $C_{2}$ and its centre is above the $x$ -axis. If equation of common tangent to $S_{1}$ and $S_{3}$ , which does not pass through $S_{2}$ , is $a x + b y + 2 = 0$ , then the value of $a^{2} - b$ is

Discussion

39.	The value of 4∑r=0 4Cr 4Cr+ 4Cr+1 is
Answer» The value of $4 \sum r = 0 \frac{^{4} C_{r}}{^{4} C_{r} +^{4} C_{r + 1}}$ is

Discussion

40.	The vertex of a parabola is the point (a,b) and latus rectum is of the length l. If the parabola is upward opening and its axis is parallel to the y−axis, then its equation is
Answer» The vertex of a parabola is the point $(a, b)$ and latus rectum is of the length $l .$ If the parabola is upward opening and its axis is parallel to the $y -$ axis, then its equation is

Discussion

41.	The locus of the midpoints of chords of the circle x2+y2=1 which subtends a right angle at the origin is
Answer» The locus of the midpoints of chords of the circle $x^{2} + y^{2} = 1$ which subtends a right angle at the origin is

Discussion

42.	If A and B are two invertible matrices of the same order, then adj (AB) is equal to
Answer» If A and B are two invertible matrices of the same order, then adj (AB) is equal to

Discussion

43.	The solution of differential equation x sec(yx)(y dx+x dy)=y cosec(yx)(x dy−y dx) is
Answer» The solution of differential equation $x s e c (\frac{y}{x}) (y d x + x d y) = y c o s e c (\frac{y}{x}) (x d y - y d x)$ is

43.

The solution of differential equation x sec(yx)(y dx+x dy)=y cosec(yx)(x dy−y dx) is

Answer»

The solution of differential equation

$x s e c (\frac{y}{x}) (y d x + x d y) = y c o s e c (\frac{y}{x}) (x d y - y d x)$ is

Discussion

44.	Show that the function f:R→{x∈R:−1<x<1} defined by f(x)=x1+\|x\|, x∈R is one one and onto function.
Answer» Show that the function $f : R \to {x \in R : - 1 < x < 1}$ defined by $f (x) = \frac{x}{1 + \| x \|}, x \in R$ is one one and onto function.

Discussion

45.	In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
Answer» In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is

Discussion

46.	Find the foot of perpendicular from the point (2,3,-8) to 4−x2=y6=1−z3. Also, find the perpendicular distance from the given point to the line.
Answer» Find the foot of perpendicular from the point (2,3,-8) to $\frac{4 - x}{2} = \frac{y}{6} = \frac{1 - z}{3}$ . Also, find the perpendicular distance from the given point to the line.

Discussion

47.	The points on the parabola y2=36x whose ordinate is three times the abscissa are
Answer» The points on the parabola $y^{2} = 36 x$ whose ordinate is three times the abscissa are

Discussion

48.	limx→5ex−e5x−5
Answer» ${lim}_{x \to 5} \frac{e^{x} - e^{5}}{x - 5}$

Discussion

49.	If x, y, z are in H.P., then the value of expression log(x + z) + log(x - 2y + z) will be
Answer» If x, y, z are in H.P., then the value of expression log(x + z) + log(x - 2y + z) will be

Discussion

50.	The number of three element subsets of {1, 2 ......10} sum of whose elements is even is :
Answer» The number of three element subsets of {1, 2 ......10} sum of whose elements is even is :

50.

The number of three element subsets of {1, 2 ......10} sum of whose elements is even is :

Answer»

The number of three element subsets of {1, 2 ......10} sum of whose elements is even is :

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate the definite integrals. ∫10xex2dx.

The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely with the length of the side.

Prove that the curves y2=4x and x2+y2−6x+1=0 touch each other at the point (1, 2).

The real order pair (x,y) which satisfies (x4+2xi)−(3x2+yi)=(3−5i)+(1+2yi) is

A die is thrown repeatedly until a six comes up. What is the sample space for the experiment?

The set A has 4 elements and the set B had 5 elements then the number of objective mapping that can be defined from A to B is ? Answers is: 120 How to do this question?

What is the value of x is equals to root 6 + root 6 + root 6 + root 6 upto infinity?

How many three-digit numbers are there, with no digit repeated?

If tan x =n tany, n∈R+, then maximum value of sec2(x−y)=___

When sinθ + cosθ = 1, then the value of sin2θ is

The area bounded by y=x2, y=[x+1], x≤1 and the y-axis, where [.] represents the greatest integer function, is A sq. unit, then the value of 9A2 is

The mean and variance of seven observations are 8 and 16 respectiveley. If 5 of the observations are 2,4,10,12,14, then the product of the remaining two observations is:

18 mice were placed in two experimental groups and one control group, with all group equally large. In how many ways can the mice be placed into three groups ?

How many differnet numbers, greater than 50000 can be formed with the digits 0, 1,1,5,9.

For the complex roots of a quadratic equation, which of the following is true?

Which among the following represents the graph of y=sec−1(x)

Choose the correct answer If θ is the angle between two vectors a and b, then a.b≥0 only when a) 0&lt;θ&lt;π2 b) 0≤θ&lt;π2 c) 0&lt;θ&lt;π d) 0≤θ≤π

holds for

The general solution of the equation sin2θ=12 is (nϵZ)

The length x of a rectangle is increasing at the rate of 4 cm/s and the width y is decreasing at the rate of 3 cm/s. When x=5 cm and y=6 cm, then the rate of change of the perimeter is

If the points (1, -1), (2, -1) and (4, -3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.

Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.

If the term free from x in the expansion of (√x−kx2)10 is 405, find the value of k.

Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king ?

If A(-2, 2, 3) and B(13, -3, 13) are two points. Find the locus of a point P which moves in such a way that 3PA = 2PB.

If tan−1 x = π10 for some x ∈ R, then the value of cot−1 x is

Prove that: sin 2θ1+cos 2θ=tan θ

Consider the following three statements: P : 5 is a prime number Q : 7 is a factor of 192 R : L.C.M. of 5 and 7 is 35 Then the truth value of which one of the following statements is true?

For the options given below, the function f(x) = [x] is discontinuous at x =

From the given figure if speed of end B of rod of length 4 m at an instant when θ=30∘ is 4 m/s then angular velocity of rod is. [angle between wall is 135∘] Write upto two digits after the decimal point. (Take cos15=√3+12√2 and √3=1.7)

Let f:R→R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f′(y)+f′(x)f(y) for all x,y∈R. Then, the value of loge(f(4)) is

If f:Z→Z is defined by f(x)={x2 if x even0 if x odd then f is

Let P(4,−4) and Q(9,6) be two points on the parabola y2=4x. If X is any point on the arc POQ of the parabola, where O is the vertex such that the area of △PXQ is maximum, then 4 times the maximum area (in sq. units) is

What is De morgan's law?

Let S be the sample space of all 3×3 matrices with entries from the set {0,1}. Let the events E1 and E2 be given by E1={A∈S:detA=0} and E2={A ∈S: sum of entries of A is 7} If the matrix is chosen at random from S, then the conditional probability P(E1|E2) equals

If 2ax2+3bx+5c=0, a∈R−{0},c&gt;0 does not have any real roots, then which of the following is/are always true?

The value of 4∑r=0 4Cr 4Cr+ 4Cr+1 is

The vertex of a parabola is the point (a,b) and latus rectum is of the length l. If the parabola is upward opening and its axis is parallel to the y−axis, then its equation is

The locus of the midpoints of chords of the circle x2+y2=1 which subtends a right angle at the origin is

If A and B are two invertible matrices of the same order, then adj (AB) is equal to

The solution of differential equation x sec(yx)(y dx+x dy)=y cosec(yx)(x dy−y dx) is

Show that the function f:R→{x∈R:−1&lt;x&lt;1} defined by f(x)=x1+|x|, x∈R is one one and onto function.

In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is

Find the foot of perpendicular from the point (2,3,-8) to 4−x2=y6=1−z3. Also, find the perpendicular distance from the given point to the line.

The points on the parabola y2=36x whose ordinate is three times the abscissa are

limx→5ex−e5x−5

If x, y, z are in H.P., then the value of expression log(x + z) + log(x - 2y + z) will be

The number of three element subsets of {1, 2 ......10} sum of whose elements is even is :

Choose the correct answer If θ is the angle between two vectors a and b, then a.b≥0 only when a) 0<θ<π2 b) 0≤θ<π2 c) 0<θ<π d) 0≤θ≤π

If 2ax2+3bx+5c=0, a∈R−{0},c>0 does not have any real roots, then which of the following is/are always true?

Show that the function f:R→{x∈R:−1<x<1} defined by f(x)=x1+|x|, x∈R is one one and onto function.