43030 + Interview Questions in Mathematics

1.	Match the possible scenarios for system of linear equations in 3 variables. Column IColumn IIa. Underdetermined systemi. No solutionb. Over determined systemii. Single solutionc. Exactly determined systemiii. Infinite solution
Answer» Match the possible scenarios for system of linear equations in 3 variables. $\begin{matrix} C o l u m n I & C o l u m n I I a . U n d e r d e t e r m i n e d s y s t e m & i . N o s o l u t i o n b . O v e r d e t e r m i n e d s y s t e m & i i . S i n g l e s o l u t i o n c . E x a c t l y d e t e r m i n e d s y s t e m & i i i . I n f i n i t e s o l u t i o n \end{matrix}$

Discussion

2.	Chintu piggy bank collection has only 2 rupee coins and 5rupee coins .The number of 5 rupee coins exceed the 2 rupee by 10 .If the total value is rupees 155. Find the 2 rupee coins and 5 rupee coins
Answer» Chintu piggy bank collection has only 2 rupee coins and 5rupee coins .The number of 5 rupee coins exceed the 2 rupee by 10 .If the total value is rupees 155. Find the 2 rupee coins and 5 rupee coins

Discussion

3.	Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is
Answer» Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is

Discussion

4.	Let there are (n + 1) white and (n + 1) black balls. In each set, the balls are numbered from 1 to (n + 1). If these balls are to be arranged in a row so that consecutive balls are of different colours, then the number of these arrangements is
Answer» Let there are (n + 1) white and (n + 1) black balls. In each set, the balls are numbered from 1 to (n + 1). If these balls are to be arranged in a row so that consecutive balls are of different colours, then the number of these arrangements is

Discussion

5.	∫π2π4 cos θ cosec2θ dθ=
Answer» $\int_{\frac{π}{4}}^{\frac{π}{2}} c o s θ c o s e c^{2} θ d θ =$

Discussion

6.	Constant functions are monotonically increasing functions.T
Answer» Constant functions are monotonically increasing functions. T

Discussion

7.	If the focus of a parabola is (2, 3) and its latus rectum is 8, then the locus of the vertex of the parabola is
Answer» If the focus of a parabola is (2, 3) and its latus rectum is 8, then the locus of the vertex of the parabola is

Discussion

8.	Can sin−1(dydx)=x+y be solved using the variable separable method?(yes/no) Ans :
Answer» Can ${sin}^{- 1} (\frac{dy}{dx}) = x + y$ be solved using the variable separable method?(yes/no) Ans :

Discussion

9.	Write the number of significant digits in (a) 1001 (b) 100.1, (c) 1001.0, (d) 0.001001.
Answer» Write the number of significant digits in (a) 1001 (b) 100.1, (c) 1001.0, (d) 0.001001.

9.

Write the number of significant digits in (a) 1001 (b) 100.1, (c) 1001.0, (d) 0.001001.

Answer»

Write the number of significant digits in

(a) 1001

(b) 100.1,

(c) 1001.0,

(d) 0.001001.

Discussion

10.	13C3 = ___.
Answer» $^{13} C_{3} =$ ___.

Discussion

11.	The direction cosines of Y-axis are:
Answer» The direction cosines of Y-axis are:

Discussion

12.	Is tan x+ tan x=2tanx?
Answer» Is tan x+ tan x=2tanx?

Discussion

13.	If y=√sin x+√sin x+√sin x+.....∞,then dydx is equal to
Answer» $I f y = \sqrt{s i n x + \sqrt{s i n x + \sqrt{s i n x + . . . . . \infty}}}, t h e n \frac{d y}{d x} i s e q u a l t o$

Discussion

14.	The total number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour, is
Answer» The total number of ways in which $20$ different pearls of two colours can be set alternately on a necklace, there being $10$ pearls of each colour, is

Discussion

15.	Domain of defination of the function f(x)=34−x2+log10(x3−x)
Answer» Domain of defination of the function $f (x) = \frac{3}{4 - x^{2}} + l o g_{10} (x^{3} - x)$

Discussion

16.	The value of cot{∑23n=1cot−1(1+∑nk=12k)} is
Answer» The value of $c o t {\sum_{n = 1}^{23} c o t^{- 1} (1 + \sum_{k = 1}^{n} 2 k)}$ is

Discussion

17.	What will be the effect on capacitance, if the distance between the parallel plates reduced to one-third of its original value?
Answer» What will be the effect on capacitance, if the distance between the parallel plates reduced to one-third of its original value?

Discussion

18.	Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years[MNR 1986]
Answer» Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years [MNR 1986]

18.

Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years[MNR 1986]

Answer»

Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years

[MNR 1986]

Discussion

19.	If the ratio of sum of first n terms of two A.P.s is 2n+8:5n−3, then the ratio of nth terms of those two A.P.s is
Answer» If the ratio of sum of first $n$ terms of two A.P.s is $2 n + 8 : 5 n - 3,$ then the ratio of $n^{th}$ terms of those two A.P.s is

Discussion

20.	Two parallel chords of a circle of radius 2 units are at a distance √3+1 units apart. If the chords subtend at the centre, angles of πk and 2πk, where k>0, then the value of [k] (where [k] denotes the largest integer less than or equal to k) is ___
Answer» Two parallel chords of a circle of radius 2 units are at a distance $\sqrt{3} + 1$ units apart. If the chords subtend at the centre, angles of $\frac{π}{k}$ and $\frac{2 π}{k}$ , where $k > 0$ , then the value of [k] (where [k] denotes the largest integer less than or equal to k) is ___

Discussion

21.	Four persons independently solve a certain problem correctly with probabilities 12,34,14,18.Then the probability that the problem is solved correctly by at least one of them is
Answer» Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$ .Then the probability that the problem is solved correctly by at least one of them is

Discussion

22.	Find the acute angle between the lines 2x−y+3=0 and x+y+2=0.
Answer» Find the acute angle between the lines $2 x - y + 3 = 0$ and $x + y + 2 = 0$ .

Discussion

23.	If the sum of two unit vector is a unit vector, then find the magnitude of their difference.
Answer» If the sum of two unit vector is a unit vector, then find the magnitude of their difference.

Discussion

24.	If xϵ[−1,0], then cos−1(2x2−1)−2sin−1x is equal to
Answer» If $x ϵ [- 1, 0]$ , then $c o s^{- 1} (2 x^{2} - 1) - 2 s i n^{- 1} x$ is equal to

Discussion

25.	If x2+px+1 is a factor of the expression ax3+bx+c, then
Answer» If $x^{2} + p x + 1$ is a factor of the expression $a x^{3} + b x + c$ , then

Discussion

26.	If the roots of the equation x2−(p+1)x+p2+p−8=0 are on opposite sides with respect to the line x = 2 then the range of ‘p’ is
Answer» If the roots of the equation $x^{2} - (p + 1) x + p^{2} + p - 8 = 0$ are on opposite sides with respect to the line x = 2 then the range of ‘p’ is

Discussion

27.	Find k so that limx→2 f(x) may exist, where f(x)={2x+3,x≤2x+k,x>2
Answer» Find k so that ${lim}_{x \to 2}$ f(x) may exist, where $f (x) = {\begin{matrix} 2 x + 3, & x \leq 2 x + k, & x > 2 \end{matrix}$

Discussion

28.	Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble?
Answer» Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble?

Discussion

29.	The number of real solutions of sinex.cosex = 2x−2+2−x−2 is
Answer» The number of real solutions of $s i n e^{x} . c o s e^{x}$ = $2^{x - 2} + 2^{- x - 2}$ is

Discussion

30.	If the range of values of parameter a for which the point of minimum of the function f(x)=1−a2x+2x3 satisfy the inequality x2+2x+4x2−√6x−36<0 is given by (−b,b)−{0}, then b is
Answer» If the range of values of parameter $a$ for which the point of minimum of the function $f (x) = 1 - a^{2} x + 2 x^{3}$ satisfy the inequality $\frac{x^{2} + 2 x + 4}{x^{2} - \sqrt{6} x - 36} < 0$ is given by $(- b, b) - {0}$ , then $b$ is

Discussion

31.	If cos(α−β)=1 and (cos(α+β)=1e, −π<α,β<π, then total number of ordered pair of (α,β) is
Answer» If $c o s (α - β) = 1$ and $(c o s (α + β) = \frac{1}{e}$ , $- π < α, β < π$ , then total number of ordered pair of $(α, β)$ is

Discussion

32.	Find the value of 2(√3)6+18−4(√3)3 ?
Answer» Find the value of $2 (\sqrt{3})^{6} + 18 - 4 (\sqrt{3})^{3}$ ?

Discussion

33.	The solution of the differential equation dydx+x(x+y)=x3(x+y)3−1 is a(x+y)b=c(x2+1)+kex2, then a+b+c is equal to
Answer» The solution of the differential equation $\frac{d y}{d x} + x (x + y) = x^{3} (x + y)^{3} - 1$ is $\frac{a}{(x + y)^{b}} = c (x^{2} + 1) + k e^{x^{2}},$ then $a + b + c$ is equal to

Discussion

34.	If the equation x2+px+q=0 and x2+qx+p=0, have a common root, then p + q + 1 =
Answer» If the equation $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0$ , have a common root, then p + q + 1 =

Discussion

35.	The value of the integral, ∫63√x√9−x+√xdx is
Answer» The value of the integral, $\int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} d x i s$

Discussion

36.	If cosA+cosB=12 and sinA+sinB=14, prove that: tan(A+B2)=12
Answer» If $c o s A + c o s B = \frac{1}{2}$ and $s i n A + s i n B = \frac{1}{4}$ , prove that: $t a n (\frac{A + B}{2}) = \frac{1}{2}$

Discussion

37.	Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
Answer» Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

Discussion

38.	If tangents PQ and PR are drawn from a point on the circle x2+y2=16 to the ellipse x2a2+y212=1 (a<3), so that the fourth vertex S of the parallelogram PQSR lies on the circumcircle of the triangle PQR, then the eccentricity of the ellipse is
Answer» If tangents $P Q$ and $P R$ are drawn from a point on the circle $x^{2} + y^{2} = 16$ to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{12} = 1 (a < 3)$ , so that the fourth vertex $S$ of the parallelogram $P Q S R$ lies on the circumcircle of the triangle $P Q R$ , then the eccentricity of the ellipse is

Discussion

39.	Find the mid-point of the points on x + y = 4 which are at a unit distance from the line 4x + 3y - 10 = 0
Answer» Find the mid-point of the points on x + y = 4 which are at a unit distance from the line 4x + 3y - 10 = 0

Discussion

40.	Three six-faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k (3≤k≤8) is
Answer» Three six-faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k $(3 \leq k \leq 8)$ is

Discussion

41.	On a toss of two dice, A throws a total of 5. Then the probability that he will throw another 5 before he throws 7 is
Answer» On a toss of two dice, A throws a total of 5. Then the probability that he will throw another 5 before he throws 7 is

Discussion

42.	If P1 and P2 are the lengths of the perpendiculars from the points (2,3,4) and (1,1,4) respectively from the plane 3x-6y+2z+11 =0, then P1 and P2 are the roots of the equation
Answer» If $P_{1}$ and $P_{2}$ are the lengths of the perpendiculars from the points (2,3,4) and (1,1,4) respectively from the plane 3x-6y+2z+11 =0, then $P_{1}$ and $P_{2}$ are the roots of the equation

Discussion

43.	Write the sum of 20 terms of the series: 1+12(1+2)+13(1+2+3)+....
Answer» Write the sum of 20 terms of the series: $1 + \frac{1}{2} (1 + 2) + \frac{1}{3} (1 + 2 + 3) + . . . .$

Discussion

44.	Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, -5, 7) and (3, 0, 1)
Answer» Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, -5, 7) and (3, 0, 1)

Discussion

45.	Find the equation of a straight line passing through the point of intersection of x+2y+3=0 and 3x+4y+7=0 and perpenicular to the straight line x-y+0=0
Answer» Find the equation of a straight line passing through the point of intersection of x+2y+3=0 and 3x+4y+7=0 and perpenicular to the straight line x-y+0=0

Discussion

46.	If the function f(x)={ax+1,if x≤3bx+3,if x>3.is continuous at x = 3 then the relation between a and b is given by
Answer» If the function $f (x) = {\begin{matrix} a x + 1, & i f x \leq 3 b x + 3, & i f x > 3 \end{matrix}$ .is continuous at x = 3 then the relation between a and b is given by

Discussion

47.	limx→∞3x−1+4x−25x−1+6x−2
Answer» ${lim}_{x \to \infty} \frac{3 x^{- 1} + 4 x^{- 2}}{5 x^{- 1} + 6 x^{- 2}}$

Discussion

48.	An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that (i) both the balls are red (ii) one ball is red and the other is black (iii) one ball is white.
Answer» An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that (i) both the balls are red (ii) one ball is red and the other is black (iii) one ball is white.

48.

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that (i) both the balls are red (ii) one ball is red and the other is black (iii) one ball is white.

Answer»

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that

(i) both the balls are red

(ii) one ball is red and the other is black

(iii) one ball is white.

Discussion

49.	If z1,z2,z3 be three non-zero complex number, such that z2≠z1,a=\|z1\|,b=\|z2\| and c=\|z3\| suppose that ∣∣∣∣abcbcacab∣∣∣∣=0, then arg(z3z2) is equal to
Answer» If $z_{1}, z_{2}, z_{3}$ be three non-zero complex number, such that $z_{2} \neq z_{1}, a = \| z_{1} \|, b = \| z_{2} \| a n d c = \| z_{3} \|$ suppose that $∣ ∣∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣∣ ∣ = 0, t h e n a r g (\frac{z_{3}}{z_{2}})$ is equal to

Discussion

50.	Sum of the terms of the series 1+2(1+1n)+3(1+1n)2+.... is given by ________.
Answer» Sum of the terms of the series $1 + 2 (1 + \frac{1}{n}) + 3 (1 + \frac{1}{n})^{2} + . . . .$ is given by ________.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Match the possible scenarios for system of linear equations in 3 variables. Column IColumn IIa. Underdetermined systemi. No solutionb. Over determined systemii. Single solutionc. Exactly determined systemiii. Infinite solution

Chintu piggy bank collection has only 2 rupee coins and 5rupee coins .The number of 5 rupee coins exceed the 2 rupee by 10 .If the total value is rupees 155. Find the 2 rupee coins and 5 rupee coins

Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is

Let there are (n + 1) white and (n + 1) black balls. In each set, the balls are numbered from 1 to (n + 1). If these balls are to be arranged in a row so that consecutive balls are of different colours, then the number of these arrangements is

∫π2π4 cos θ cosec2θ dθ=

Constant functions are monotonically increasing functions.T

If the focus of a parabola is (2, 3) and its latus rectum is 8, then the locus of the vertex of the parabola is

Can sin−1(dydx)=x+y be solved using the variable separable method?(yes/no) Ans :

Write the number of significant digits in (a) 1001 (b) 100.1, (c) 1001.0, (d) 0.001001.

13C3 = ___.

The direction cosines of Y-axis are:

Is tan x+ tan x=2tanx?

If y=√sin x+√sin x+√sin x+.....∞,then dydx is equal to

The total number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour, is

Domain of defination of the function f(x)=34−x2+log10(x3−x)

The value of cot{∑23n=1cot−1(1+∑nk=12k)} is

What will be the effect on capacitance, if the distance between the parallel plates reduced to one-third of its original value?

Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years[MNR 1986]

If the ratio of sum of first n terms of two A.P.s is 2n+8:5n−3, then the ratio of nth terms of those two A.P.s is

Two parallel chords of a circle of radius 2 units are at a distance √3+1 units apart. If the chords subtend at the centre, angles of πk and 2πk, where k&gt;0, then the value of [k] (where [k] denotes the largest integer less than or equal to k) is ___

Four persons independently solve a certain problem correctly with probabilities 12,34,14,18.Then the probability that the problem is solved correctly by at least one of them is

Find the acute angle between the lines 2x−y+3=0 and x+y+2=0.

If the sum of two unit vector is a unit vector, then find the magnitude of their difference.

If xϵ[−1,0], then cos−1(2x2−1)−2sin−1x is equal to

If x2+px+1 is a factor of the expression ax3+bx+c, then

If the roots of the equation x2−(p+1)x+p2+p−8=0 are on opposite sides with respect to the line x = 2 then the range of ‘p’ is

Find k so that limx→2 f(x) may exist, where f(x)={2x+3,x≤2x+k,x&gt;2

Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble?

The number of real solutions of sinex.cosex = 2x−2+2−x−2 is

If the range of values of parameter a for which the point of minimum of the function f(x)=1−a2x+2x3 satisfy the inequality x2+2x+4x2−√6x−36&lt;0 is given by (−b,b)−{0}, then b is

If cos(α−β)=1 and (cos(α+β)=1e, −π&lt;α,β&lt;π, then total number of ordered pair of (α,β) is

Find the value of 2(√3)6+18−4(√3)3 ?

The solution of the differential equation dydx+x(x+y)=x3(x+y)3−1 is a(x+y)b=c(x2+1)+kex2, then a+b+c is equal to

If the equation x2+px+q=0 and x2+qx+p=0, have a common root, then p + q + 1 =

The value of the integral, ∫63√x√9−x+√xdx is

If cosA+cosB=12 and sinA+sinB=14, prove that: tan(A+B2)=12

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

If tangents PQ and PR are drawn from a point on the circle x2+y2=16 to the ellipse x2a2+y212=1 (a&lt;3), so that the fourth vertex S of the parallelogram PQSR lies on the circumcircle of the triangle PQR, then the eccentricity of the ellipse is

Find the mid-point of the points on x + y = 4 which are at a unit distance from the line 4x + 3y - 10 = 0

Three six-faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k (3≤k≤8) is

On a toss of two dice, A throws a total of 5. Then the probability that he will throw another 5 before he throws 7 is

If P1 and P2 are the lengths of the perpendiculars from the points (2,3,4) and (1,1,4) respectively from the plane 3x-6y+2z+11 =0, then P1 and P2 are the roots of the equation

Write the sum of 20 terms of the series: 1+12(1+2)+13(1+2+3)+....

Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, -5, 7) and (3, 0, 1)

Find the equation of a straight line passing through the point of intersection of x+2y+3=0 and 3x+4y+7=0 and perpenicular to the straight line x-y+0=0

If the function f(x)={ax+1,if x≤3bx+3,if x&gt;3.is continuous at x = 3 then the relation between a and b is given by

limx→∞3x−1+4x−25x−1+6x−2

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that (i) both the balls are red (ii) one ball is red and the other is black (iii) one ball is white.

If z1,z2,z3 be three non-zero complex number, such that z2≠z1,a=|z1|,b=|z2| and c=|z3| suppose that ∣∣∣∣abcbcacab∣∣∣∣=0, then arg(z3z2) is equal to

Sum of the terms of the series 1+2(1+1n)+3(1+1n)2+.... is given by ________.

Two parallel chords of a circle of radius 2 units are at a distance √3+1 units apart. If the chords subtend at the centre, angles of πk and 2πk, where k>0, then the value of [k] (where [k] denotes the largest integer less than or equal to k) is ___

Find k so that limx→2 f(x) may exist, where f(x)={2x+3,x≤2x+k,x>2

If the range of values of parameter a for which the point of minimum of the function f(x)=1−a2x+2x3 satisfy the inequality x2+2x+4x2−√6x−36<0 is given by (−b,b)−{0}, then b is

If cos(α−β)=1 and (cos(α+β)=1e, −π<α,β<π, then total number of ordered pair of (α,β) is

If tangents PQ and PR are drawn from a point on the circle x2+y2=16 to the ellipse x2a2+y212=1 (a<3), so that the fourth vertex S of the parallelogram PQSR lies on the circumcircle of the triangle PQR, then the eccentricity of the ellipse is

If the function f(x)={ax+1,if x≤3bx+3,if x>3.is continuous at x = 3 then the relation between a and b is given by