Explore topic-wise InterviewSolutions in Current Affairs.

If $si{n}^{-1}(a-\frac{a^2}{3}+\frac{a^3}{9}-......\infty )+co{s}^{-1}(1+b+b^2+....\infty )=\frac{\pi }{2}$ then

An unbalanced dice (with six faces numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even, given that it is greater than $3$ is $0.75,$ then the probability that the face value exceeds $3,$ is

Write the coordinates of the imeage of the point (3,8) in the line $x+3y-7=0$.

The value of $\int \frac{e^x+e^{-x}}{1+e^{2x}}dx$ is

(where $C$ is constant of integration)

Let $C$ be the circle with centre $(0,0)$ and radius $3$ units. Locus of the point $P$ from which the chord of contact subtends an angle of ${60}^{\circ }$ at any point on the circumference of $C$ is

Evaluate $\underset{-\frac{1}{2}}{\overset{0}{\int }}|x\cos \left(\pi x\right)|dx$

The number of integral terms in the expansion of $(5^{\frac{1}{2}}+7^{\frac{1}{6}}{)}^{642}$ is

A
homogeneous differential equation of the form
can
be solved by making the substitution

A. y
= vx

B. v
= yx

C. x
= vy

D. x
= v

The equation of the circle passing through points of intersection of the circle $x^2+y^2-2x-4y+4=0$ and the line $x+2y=4$ and touches the line $x+2y=0$, is

Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3x + y = 12 which is intercepted between the axes of coordinates.

The dimensions of length are expessed as $G^x{c}^y{h}^z$, where $G$, $c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then

A function $f\left(x\right)$ satisfies $f\left(x\right)=\sin x+{\int }_0^x{f}^{\prime }\left(t\right)(2\sin t-{\sin }^{2}t)dt$, then $f\left(x\right)$ is

Which of the following is true about [x], greatest integer function ?

The acute angle between the curves $x^2+y^2=50$ and $x^2=5y$ is

If the coefficients of $x^7$ and $x^8$ in the expansion of ${(2+\frac{x}{3})}^n$ are equal, then the value of $n$ is

If for all real triplets $(a,b,c)$, $f\left(x\right)=a+bx+c{x}^2$; then $\underset{0}{\overset{1}{\int }}f\left(x\right)dx$ is equal to :

If A={a,b,c} , then the relation R={(b,c)}on A is

a reflexive only

b symmetric only

c transitive only

d reflexive and transitive only

$ta{n}^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)=\frac{\pi }{4}-\frac{1}{2}co{s}^{-1}x$

The solution set of $x\ge \frac{1}{x}$ is

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 16x² + y² = 16

Out of $100$ students, two sections of $40$ and $60$ are formed. Assume that you and your friend are among the $100$ students. Let $P\left(A\right)$ be the probability that you both enter in same section and $P\left(B\right)$ be the probability that you both enter in different sections. Then which of the following is/are true?

Which of the following sets are equal ?

(i) A = {1, 2, 3}

(ii) B = {$xϵR:x^2-2x+1=0$}

(iii) C = {1, 2, 2, 3}

(iv) D = {$xϵR:x^3-6x^2+11x-6=0$}.

The equation x- y = 4 and $x^2+4xy+y^2=0$ represent the sides of

If m is a positive integer, then $\left[\right(\sqrt{3}+1{)}^{2m}]+1$, where [x] denotes greatest integer $\le x$, is divisible by

If a and b are coefficients of $x^n$ in the expansion of $(1+x{)}^{2n}$ and $(1+x{)}^{2n-1}$ respectively, then write the relation between a and b.

The value of integral $\underset{0}{\overset{10\pi }{\int }}\frac{\cos 6x\cos 7x\cos 8x\cos 9x}{1+e^{{\sin }^{3}4x}}dx$ is equal to

For the question given below verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

$y=a{e}^x+b{e}^{-x}+x^2;x\frac{d^{2}y}{d{x}^2}+2\frac{dy}{dx}-xy+x^2-2=0$