Explore topic-wise InterviewSolutions in Current Affairs.

If the direction cosines of a line $L$ are $(ab,b,b)$ and the angle between $L$ and $X$ axis is $\frac{\pi }{3}$. Then the value of $\frac{1}{a^2}+\frac{1}{b^2}$ is

cosA + cos (120° + A) + cos(120° - A) =

The solution of the differential equation $(x+y)dy-(x-y)dx=0$ is

(where $C$ is integration constant)

If A
is an invertible matrix of order 2, then det (A⁻¹)
is equal to

A. det
(A) B. C. 1 D. 0

Let $f\left(x\right)=\tan x-{\tan }^{3}x+{\tan }^{5}x-{\tan }^{7}x+...+\infty ,xϵ(0,\frac{\pi }{4})$, then

Sum of maximum and minimum value of the objective function $z=10x+7y$, subjected to the constraints $0\le x\le 60,0\le y\le 45,5x+6y\le 420$ is

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

$\frac{2sin\theta cos\theta -cos\theta }{1-sin\theta +si{n}^2\theta -co{s}^2\theta }=cot\theta$

Three numbers are chosen at random without replacement from $\{1,2,3,...,8\}$. The probability that their minimum is $3$, given that their maximum is $6$, is :

Show
that the function defined by f (x)
= cos (x²)
is a continuous function.

If the roots of the equation $a{x}^2+bx+a_1^2+b_1^2+c_1^2-a_1{b}_1-a_1{c}_1-b_1{c}_1=0$ are non real then

If
is
a differentiable function and if
does
not vanish anywhere, then prove that.

If $f:[-2,2]\to R$ is differentiable such that $f\left(0\right)=2,f^{\prime }\left(0\right)=-1$ and $h\left(x\right)=f\left(f\right(x{)}^2+f\left(x\right)-6),$ then the value of $h^{\prime }\left(0\right)$ is

Show that
each of the given three vectors is a unit vector:

Also, show
that they are mutually perpendicular to each other.

Let $x_1,x_2,\cdots ,x_n$ be n observations, and let $\overline{x}$ be their arithmetic mean and ${\sigma }^2$ be the variance.

Statement – 1: Variance of $2x_1,2x_2,\cdots ,2x_n\text{is}4{\sigma }^2$

Statement – 2: Arithmetic mean $2x_1,2x_2,\cdots ,2x_n\text{is}4\overline{x}$

The value of $\underset{x\to 0}{lim}\frac{1}{x^3}{\int }_0^x\frac{t\ln (1+t)}{t^4+4}dt$ is

The sixth term in the expansion of ${[\sqrt{\left\{2^{\log (10-3^x)}\right\}}+\sqrt[5]{5\left\{2^{(x-2)\log 3}\right\}}]}^m$is equal to $21$. If it is known that the binomial coefficient of the $2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ terms in the expansion represents respectively the first, third and fifth terms of an A.P. (the symbol log stands for logarithm to the base $10$) then the value of $m$ is

The number of solutions of the equation ${32}^{{\tan }^{2}x}+{32}^{{\sec }^{2}x}=81,$ $0\le x\le \frac{\pi }{4}$ is

If ${\sin }^3\theta \cos \theta -{\cos }^3\theta \sin \theta =\frac{1}{4},$ then the values of $\theta$ which satisfy the equation is

Given the function $f\left(x\right)=x^3-2x^2-x+1$. Then the value(s) of $c$ satisfying the conditions of the mean value theorem for the function on the interval $[-2,2]$, is

Let $\left\{y\right\}$ and $\left[y\right]$ denote fractional part function and greatest integer function respectively.

If $f\left(x\right)={\sin }^{-1}\{[3x+2]-\{3x+(x-\left\{2x\right\}\left)\right\}\}$ for $x\in (0,\frac{\pi }{12})$ and $(g\circ f)\left(x\right)=x$ for all $x\in (0,\frac{\pi }{12}),$ then $g^{\prime }\left(\frac{\pi }{6}\right)$ is equal to

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)

The value of integral $\underset{0}{\overset{{\pi }^2/4}{\int }}\cos \sqrt{x}dx$ is

Given non-empty set X, consider the binary operation $\ast :P\left(X\right)\times P\left(X\right)\to P\left(X\right)$ given by $A\ast B=A\cap B\forall A,B$ in P(X), where P(X)is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation.

The line $lx+my+n=0$ will be a tangent to the circle $x^2+y^2=a^2$ iff

Evaluate:
$\cos \left(\frac{\pi }{2}-{\sin }^{-1}\left(-\frac{1}{2}\right)\right\}.$

The solution(s) of ${\sin }^{-1}x-{\sin }^{-1}2x=\pm \frac{\pi }{3}$ is

Which of the following is true in the interval of $x\in (0,1)$

If $3^{2\sin 2\alpha -1}$, $14$ and $3^{4-2\sin 2\alpha }$ are the first three terms of an A.P. for some $\alpha$, then the sixth term of this A.P. is:

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{|[|x|-5]|-5}}$ is
(where [.] denotes the greatest integer function)