43030 + Interview Questions in Mathematics

1.	∫e√x√x(x+√x)dx equals
Answer» $\int \frac{e^{\sqrt{x}}}{\sqrt{x}} (x + \sqrt{x}) d x$ equals

Discussion

2.	Read the following. Then Keq=?
Answer» Read the following. Then $K_{e} q = ?$

Discussion

3.	The rank of the word SUCCESS, If all possible permutations of the word SUCCESS are arranged in dictionary order is
Answer» The rank of the word $S U C C E S S$ , If all possible permutations of the word $S U C C E S S$ are arranged in dictionary order is

Discussion

4.	The value(s) of θ for which cosθ=−12 is/are
Answer» The value(s) of $θ$ for which $cos θ = - \frac{1}{2}$ is/are

Discussion

5.	Of the 10 prizes 5 prizes are of category Platinum, 3 of gold and 2 of silver and they are placed in an enclosure for an olympiad contest. The prizes are awarded by allowing winners to select randomly from the prizes remaining. When the 8th participant goes to collect the prize what the probability that last 3 prizes are 1 of platinum 1 of gold and 1 of silver?
Answer» Of the 10 prizes 5 prizes are of category Platinum, 3 of gold and 2 of silver and they are placed in an enclosure for an olympiad contest. The prizes are awarded by allowing winners to select randomly from the prizes remaining. When the 8th participant goes to collect the prize what the probability that last 3 prizes are 1 of platinum 1 of gold and 1 of silver?

Discussion

6.	The plane containing the line x−11=y−22=z−33 and parallel to the line x1=y1=z4 is
Answer» The plane containing the line $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and parallel to the line $\frac{x}{1} = \frac{y}{1} = \frac{z}{4}$ is

Discussion

7.	Let f be a real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) and g(x)=fx+8x f(t) dt then :
Answer» Let $f$ be a real valued function satisfying $f (x) + f (x + 4) = f (x + 2) + f (x + 6)$ and $g (x) = f_{x}^{x + 8} f (t) d t$ then :

Discussion

8.	If (p∧∼r)⇒(q ∧ r) is false and q and r are both false, then p is ___.
Answer» If $(p \land \sim r) \Rightarrow (q \land r)$ is false and q and r are both false, then p is ___.

Discussion

9.	The polars drawn from (-1,2) to the circle sS1≡x2+y2+6y+7=0 and S2≡x2+y2+6x+1=0, are
Answer» The polars drawn from (-1,2) to the circle s $S_{1} \equiv x^{2} + y^{2} + 6 y + 7 = 0$ and $S_{2} \equiv x^{2} + y^{2} + 6 x + 1 = 0$ , are

Discussion

10.	If ar=(cos2rπ+isin2rπ)19 , then the value of ∣∣∣∣a1a2a3a4a5a6a7a8a9∣∣∣∣ is
Answer» If $a_{r} = (cos 2 r π + i sin 2 r π)^{\frac{1}{9}}$ , then the value of $∣ ∣∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} a_{4} & a_{5} & a_{6} a_{7} & a_{8} & a_{9} \end{matrix} ∣ ∣∣ ∣$ is

Discussion

11.	List - IList - II(I)Number of solutions of the equation(P)0ex+e−x=tanx ∀ x∈[0,π2)(II)Number of solutions of the equations(Q)1x+y=2π3 and cosx+cosy=32 is(III)Number of solutions of the equation(R)2cosx+2sinx=1, x∈[0,2π) is(IV)Number of solutions of the equation(S)Infinite(√3sinx+cosx)√√3sin2x−cos2x+2=4 is Which of the following is only INCORRECT combination?
Answer» $\begin{matrix} List - I & List - II (I) & Number of solutions of the equation & (P) & 0 e^{x} + e^{- x} = tan x \forall x \in [0, \frac{π}{2}) (II) & Number of solutions of the equations & (Q) & 1 x + y = \frac{2 π}{3} and cos x + cos y = \frac{3}{2} is (III) & Number of solutions of the equation & (R) & 2 cos x + 2 sin x = 1, x \in [0, 2 π) is (IV) & Number of solutions of the equation & (S) & Infinite (\sqrt{3} sin x + cos x)^{\sqrt{\sqrt{3} sin 2 x - cos 2 x + 2}} = 4 is \end{matrix}$ Which of the following is only INCORRECT combination?

Discussion

12.	In how many ways can a football team of 11 players be selected from 16 players ? How many of these will (i) include 2 particular players ? (ii) exclude 2 particular players ?
Answer» In how many ways can a football team of 11 players be selected from 16 players ? How many of these will (i) include 2 particular players ? (ii) exclude 2 particular players ?

12.

In how many ways can a football team of 11 players be selected from 16 players ? How many of these will (i) include 2 particular players ? (ii) exclude 2 particular players ?

Answer»

In how many ways can a football team of 11 players be selected from 16 players ?

How many of these will (i) include 2 particular players ? (ii) exclude 2 particular players ?

Discussion

13.	Equation of the plane containing the lines →r=^i+^j−^k+λ(^i+2^j−^k) and →r=^i+2^j−^k+μ(^i+^j+3^k) is
Answer» Equation of the plane containing the lines $\to r =^i +^j -^k + λ (^i + 2^j -^k) a n d \to r =^i + 2^j -^k + μ (^i +^j + 3^k)$ is

13.

Equation of the plane containing the lines →r=^i+^j−^k+λ(^i+2^j−^k) and →r=^i+2^j−^k+μ(^i+^j+3^k) is

Answer»

Equation of the plane containing the lines $\to r =^i +^j -^k + λ (^i + 2^j -^k) a n d \to r =^i + 2^j -^k + μ (^i +^j + 3^k)$ is

Discussion

14.	If a ball is dropped from a height of 40 m and bounce back upto 60% of the orginal height, then total distance travelled (in m) by the ball before coming to rest is
Answer» If a ball is dropped from a height of $40 m$ and bounce back upto $60 %$ of the orginal height, then total distance travelled (in $m$ ) by the ball before coming to rest is

Discussion

15.	If A(θ) and B(ϕ) are the parametric ends of a chord of hyperbola x216−y29=1 which passes through (4,0), then the value of tanθ2⋅tanϕ2is
Answer» If $A (θ)$ and $B (ϕ)$ are the parametric ends of a chord of hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ which passes through $(4, 0)$ , then the value of $tan \frac{θ}{2} \cdot tan \frac{ϕ}{2}$ is

Discussion

16.	Number of values of x, satisfying the equation √(x+8)+2√(x+7)+√(x+1)−√x+7=4, is
Answer» Number of values of $x$ , satisfying the equation $\sqrt{(x + 8) + 2 \sqrt{(x + 7)}} + \sqrt{(x + 1) - \sqrt{x + 7}} = 4,$ is

Discussion

17.	The range of function f(x)=sin−1[x2+12]+cos−1[x2−12], where [.] is the greatest integer function is
Answer» The range of function $f (x) = {sin}^{- 1} [x^{2} + \frac{1}{2}] + {cos}^{- 1} [x^{2} - \frac{1}{2}]$ , where [.] is the greatest integer function is

Discussion

18.	A box has 50 pens of which 20 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement, at most one is defective?
Answer» A box has 50 pens of which 20 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement, at most one is defective?

Discussion

19.	The minimum value of d so that there is a dark fringe at O is dmin. The distance at which the next bright fringe is formed is x. Then
Answer» The minimum value of d so that there is a dark fringe at O is $d_{m i n}$ . The distance at which the next bright fringe is formed is x. Then

Discussion

20.	The equation of one of the lines represented by the pair of lines 12x2−10xy+2y2+11x−5y+2=0 is/are
Answer» The equation of one of the lines represented by the pair of lines $12 x^{2} - 10 x y + 2 y^{2} + 11 x - 5 y + 2 = 0$ is/are

Discussion

21.	If the length of the tangent drawn at the point (1,3) on the curve y=3x3 is a, then find the value of 9a2 ___
Answer» If the length of the tangent drawn at the point $(1, 3)$ on the curve $y = 3 x^{3}$ is $a$ , then find the value of $9 a^{2}$ ___

21.

If the length of the tangent drawn at the point (1,3) on the curve y=3x3 is a, then find the value of 9a2 ___

Answer»

If the length of the tangent drawn at the point $(1, 3)$ on the curve $y = 3 x^{3}$ is $a$ , then find the value of $9 a^{2}$

___

Discussion

22.	A vector joining two points with coordinates (1,2,3) & (-1, 4 ,2) can be written as -
Answer» A vector joining two points with coordinates (1,2,3) & (-1, 4 ,2) can be written as -

Discussion

23.	The equation of the plane containing the lines 2x−y+z−3=0, 3x+y+z=5 and at a distance of 1√6 from the point (2,1,−1) is
Answer» The equation of the plane containing the lines $2 x - y + z - 3 = 0, 3 x + y + z = 5$ and at a distance of $\frac{1}{\sqrt{6}}$ from the point $(2, 1, - 1)$ is

Discussion

24.	limx→a√x+√ax+a
Answer» ${lim}_{x \to a} \frac{\sqrt{x} + \sqrt{a}}{x + a}$

Discussion

25.	The equations of a pair of opposite sides of a parallelogram are x2 -5x+6 = 0 and y2 -6y+5=0, then the equation of the diagonal having positive slope is
Answer» The equations of a pair of opposite sides of a parallelogram are $x^{2}$ -5x+6 = 0 and $y^{2}$ -6y+5=0, then the equation of the diagonal having positive slope is

Discussion

26.	Let f be a one-one continuous function such that f(2) = 3 and f(5) = 7. Given ∫52f(x)dx=17, then the value of the definite integral ∫73f−1(x)dx equals
Answer» Let f be a one-one continuous function such that f(2) = 3 and f(5) = 7. Given $\int_{2}^{5} f (x) d x = 17$ , then the value of the definite integral $\int_{3}^{7} f^{- 1} (x) d x$ equals

Discussion

27.	If Tn=3n−1 of an A.P., then
Answer» If $T_{n} = 3 n - 1$ of an A.P., then

Discussion

28.	If g={(1,1),(2,3),(3,5),(4,7)} is a function defined as g(x)=αx+β, then α−β=
Answer» If $g = {(1, 1), (2, 3), (3, 5), (4, 7)}$ is a function defined as $g (x) = α x + β$ , then $α - β =$

Discussion

29.	Let f:R+→R be a differentiable function satisfying f(x)=e+(1−x)ln(xe)+x∫1f(t) dt ∀ x∈R+. If the area enclosed by the curve g(x)=x(f(x)−ex) lying in the fourth quadrant is A, then the value of A−2 is
Answer» Let $f : R^{+} \to R$ be a differentiable function satisfying $f (x) = e + (1 - x) ln (\frac{x}{e}) + x \int 1 f (t) d t \forall x \in R^{+}$ . If the area enclosed by the curve $g (x) = x (f (x) - e^{x})$ lying in the fourth quadrant is $A$ , then the value of $A^{- 2}$ is

Discussion

30.	The H.C.F. and L.C.M. of two numbers are 8 and 96 respectively. If one number is 24, the other number is
Answer» The H.C.F. and L.C.M. of two numbers are $8$ and $96$ respectively. If one number is $24,$ the other number is

Discussion

31.	Write the set of value of n for which the statement P(n) : 2n < n! is true.
Answer» Write the set of value of n for which the statement P(n) : 2n < n! is true.

Discussion

32.	Let D1=∣∣∣∣xab−10xx21∣∣∣∣ and D2=∣∣∣∣cx22a−bx21−10x∣∣∣∣. If all the roots of the equation (x2−4x−7)(x2−2x−3)=0 satisfies the equation D1+D2=0, then the value of a+4b+c is
Answer» Let $D_{1} = ∣ ∣∣ ∣ \begin{matrix} x & a & b - 1 & 0 & x x & 2 & 1 \end{matrix} ∣ ∣∣ ∣$ and $D_{2} = ∣ ∣∣ ∣ \begin{matrix} c x^{2} & 2 a & - b x & 2 & 1 - 1 & 0 & x \end{matrix} ∣ ∣∣ ∣ .$ If all the roots of the equation $(x^{2} - 4 x - 7) (x^{2} - 2 x - 3) = 0$ satisfies the equation $D_{1} + D_{2} = 0,$ then the value of $a + 4 b + c$ is

Discussion

33.	If Cr= 25Cr and C0+5⋅C1+9⋅C2+⋯+101⋅C25=225⋅k k is equal to
Answer» If $C_{r} =^{25} C_{r}$ and $C_{0} + 5 \cdot C_{1} + 9 \cdot C_{2} + \dots + 101 \cdot C_{25} = 2^{25} \cdot k$ $k$ is equal to

Discussion

34.	Explain Rolles & mean value theorem in detail & also explain these graphicallyundefinedundefinedundefinedundefined
Answer» Explain Rolles & mean value theorem in detail & also explain these graphically undefined undefined undefined undefined

Discussion

35.	The equation ax2+bx+c = 0 does not have real roots and c < 0. Which of these is true?
Answer» The equation $a x^{2} + b x + c$ = 0 does not have real roots and c < 0. Which of these is true?

Discussion

36.	limx→0ex−1√1−cosx
Answer» ${lim}_{x \to 0} \frac{e^{x} - 1}{\sqrt{1 - c o s x}}$

Discussion

37.	The line 4x−3y+2=0 is rotated through an angle of π4 in clockwise direction about the point (1,2). The equation of the line in its new position is
Answer» The line $4 x - 3 y + 2 = 0$ is rotated through an angle of $\frac{π}{4}$ in clockwise direction about the point $(1, 2) .$ The equation of the line in its new position is

Discussion

38.	Let f(x)=ax2+bx+c, where a is positive and b and c are both negative, then the number of point in R where g(x)=f(\|x\|) is non-differentiable is/are
Answer» Let $f (x) = a x^{2} + b x + c,$ where $a$ is positive and $b$ and $c$ are both negative, then the number of point in $R$ where $g (x) = f (\| x \|)$ is non-differentiable is/are

Discussion

39.	If a,b,c are unequal and positive ,show that bc/(b+c ) +ac/(c+a) +ab/(a+b) is less than1/2(a+b+c)
Answer» If a,b,c are unequal and positive ,show that bc/(b+c ) +ac/(c+a) +ab/(a+b) is less than1/2(a+b+c)

Discussion

40.	If \|z+4\|≤3, then find the greatest and least values of \|z + 1\|.
Answer» If $\| z + 4 \| \leq 3$ , then find the greatest and least values of \|z + 1\|.

Discussion

41.	General solution of differential equation dydx+y=1 (y≠1) is
Answer» General solution of differential equation $\frac{d y}{d x} + y = 1 (y \neq 1)$ is

Discussion

42.	Find the values of a and b so that the polynomial (x3−10x2+ax+b) is exactly divisible by (x-1) as well as (x-2).
Answer» Find the values of a and b so that the polynomial $(x^{3} - 10 x^{2} + a x + b)$ is exactly divisible by (x-1) as well as (x-2).

Discussion

43.	If x+4x−2>0, then
Answer» If $\frac{x + 4}{x - 2} > 0,$ then

Discussion

44.	The number of ways of selecting two squares from a chess board so that they have exactly one common corner is
Answer» The number of ways of selecting two squares from a chess board so that they have exactly one common corner is

Discussion

45.	If f(x.y) = f(x) . f(y) for all real x, y and f(7) = 343. Then find f(9) ?
Answer» If f(x.y) = f(x) . f(y) for all real x, y and f(7) = 343. Then find f(9) ?

Discussion

46.	If A=[aij] is a matrix of order 2×2, such that \|A\| = - 15 and Cij represents the cofactor of aij, then find a21C21+a22 C22.
Answer» If $A = [a_{i j}]$ is a matrix of order $2 \times 2$ , such that \|A\| = - 15 and $C_{i j}$ represents the cofactor of $a_{i j}$ , then find $a_{21} C_{21} + a_{22} C_{22} .$

Discussion

47.	If (1, 2, 3) B=(3, 4), then the order of B is
Answer» If (1, 2, 3) B=(3, 4), then the order of B is

Discussion

48.	If f:R→R be given by f(x)=(3−x3)13, then fof (x)is (a)x13(b)x3 (c)x (d)3−x3
Answer» If $f : R \to R$ be given by $f (x) = (3 - x^{3})^{\frac{1}{3}}$ , then fof (x)is $(a) x^{\frac{1}{3}} (b) x^{3}$ $(c) x$ $(d) 3 - x^{3}$

Discussion

49.	in a triangle ABC,is obtuse, sina=3/5,sinb=5/13 then sinc equal to
Answer» in a triangle ABC,is obtuse, sina=3/5,sinb=5/13 then sinc equal to

Discussion

50.	If the straight lines 2x+3y-1=0,x+2y-1=0and ax+by-1=0 forms a triangle with origin as orthocenter then (a,b) is
Answer» If the straight lines 2x+3y-1=0,x+2y-1=0and ax+by-1=0 forms a triangle with origin as orthocenter then (a,b) is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

∫e√x√x(x+√x)dx equals

Read the following. Then Keq=?

The rank of the word SUCCESS, If all possible permutations of the word SUCCESS are arranged in dictionary order is

The value(s) of θ for which cosθ=−12 is/are

The plane containing the line x−11=y−22=z−33 and parallel to the line x1=y1=z4 is

Let f be a real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) and g(x)=fx+8x f(t) dt then :

If (p∧∼r)⇒(q ∧ r) is false and q and r are both false, then p is ___.

The polars drawn from (-1,2) to the circle sS1≡x2+y2+6y+7=0 and S2≡x2+y2+6x+1=0, are

If ar=(cos2rπ+isin2rπ)19 , then the value of ∣∣∣∣a1a2a3a4a5a6a7a8a9∣∣∣∣ is

In how many ways can a football team of 11 players be selected from 16 players ? How many of these will (i) include 2 particular players ? (ii) exclude 2 particular players ?

Equation of the plane containing the lines →r=^i+^j−^k+λ(^i+2^j−^k) and →r=^i+2^j−^k+μ(^i+^j+3^k) is

If a ball is dropped from a height of 40 m and bounce back upto 60% of the orginal height, then total distance travelled (in m) by the ball before coming to rest is

If A(θ) and B(ϕ) are the parametric ends of a chord of hyperbola x216−y29=1 which passes through (4,0), then the value of tanθ2⋅tanϕ2is

Number of values of x, satisfying the equation √(x+8)+2√(x+7)+√(x+1)−√x+7=4, is

The range of function f(x)=sin−1[x2+12]+cos−1[x2−12], where [.] is the greatest integer function is

A box has 50 pens of which 20 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement, at most one is defective?

The minimum value of d so that there is a dark fringe at O is dmin. The distance at which the next bright fringe is formed is x. Then

The equation of one of the lines represented by the pair of lines 12x2−10xy+2y2+11x−5y+2=0 is/are

If the length of the tangent drawn at the point (1,3) on the curve y=3x3 is a, then find the value of 9a2 ___

A vector joining two points with coordinates (1,2,3) &amp; (-1, 4 ,2) can be written as -

The equation of the plane containing the lines 2x−y+z−3=0, 3x+y+z=5 and at a distance of 1√6 from the point (2,1,−1) is

limx→a√x+√ax+a

The equations of a pair of opposite sides of a parallelogram are x2 -5x+6 = 0 and y2 -6y+5=0, then the equation of the diagonal having positive slope is

Let f be a one-one continuous function such that f(2) = 3 and f(5) = 7. Given ∫52f(x)dx=17, then the value of the definite integral ∫73f−1(x)dx equals

If Tn=3n−1 of an A.P., then

If g={(1,1),(2,3),(3,5),(4,7)} is a function defined as g(x)=αx+β, then α−β=

Let f:R+→R be a differentiable function satisfying f(x)=e+(1−x)ln(xe)+x∫1f(t) dt ∀ x∈R+. If the area enclosed by the curve g(x)=x(f(x)−ex) lying in the fourth quadrant is A, then the value of A−2 is

The H.C.F. and L.C.M. of two numbers are 8 and 96 respectively. If one number is 24, the other number is

Write the set of value of n for which the statement P(n) : 2n &lt; n! is true.

Let D1=∣∣∣∣xab−10xx21∣∣∣∣ and D2=∣∣∣∣cx22a−bx21−10x∣∣∣∣. If all the roots of the equation (x2−4x−7)(x2−2x−3)=0 satisfies the equation D1+D2=0, then the value of a+4b+c is

If Cr= 25Cr and C0+5⋅C1+9⋅C2+⋯+101⋅C25=225⋅k k is equal to

Explain Rolles & mean value theorem in detail & also explain these graphicallyundefinedundefinedundefinedundefined

The equation ax2+bx+c = 0 does not have real roots and c &lt; 0. Which of these is true?

limx→0ex−1√1−cosx

The line 4x−3y+2=0 is rotated through an angle of π4 in clockwise direction about the point (1,2). The equation of the line in its new position is

Let f(x)=ax2+bx+c, where a is positive and b and c are both negative, then the number of point in R where g(x)=f(|x|) is non-differentiable is/are

If a,b,c are unequal and positive ,show that bc/(b+c ) +ac/(c+a) +ab/(a+b) is less than1/2(a+b+c)

If |z+4|≤3, then find the greatest and least values of |z + 1|.

General solution of differential equation dydx+y=1 (y≠1) is

Find the values of a and b so that the polynomial (x3−10x2+ax+b) is exactly divisible by (x-1) as well as (x-2).

If x+4x−2&gt;0, then

The number of ways of selecting two squares from a chess board so that they have exactly one common corner is

If f(x.y) = f(x) . f(y) for all real x, y and f(7) = 343. Then find f(9) ?

If A=[aij] is a matrix of order 2×2, such that |A| = - 15 and Cij represents the cofactor of aij, then find a21C21+a22 C22.

If (1, 2, 3) B=(3, 4), then the order of B is

If f:R→R be given by f(x)=(3−x3)13, then fof (x)is (a)x13(b)x3 (c)x (d)3−x3

in a triangle ABC,is obtuse, sina=3/5,sinb=5/13 then sinc equal to

If the straight lines 2x+3y-1=0,x+2y-1=0and ax+by-1=0 forms a triangle with origin as orthocenter then (a,b) is

A vector joining two points with coordinates (1,2,3) & (-1, 4 ,2) can be written as -

Write the set of value of n for which the statement P(n) : 2n < n! is true.

The equation ax2+bx+c = 0 does not have real roots and c < 0. Which of these is true?

If x+4x−2>0, then