Explore topic-wise InterviewSolutions in Current Affairs.

If $\alpha$ is the value of $xϵ[0,2\pi ]$ which is a solution of the equation

$2co{s}^2$ $\frac{x^2+x}{6}=2^x$ + $2^{-x}$, then find the value of $\frac{2\alpha }{3\pi }$ .

Let $A$ and $B$ be two smallest sets such that $A\cup \left\{1\right\}=\{1,2,3,4\}$ and $B\cup \left\{5\right\}=\{4,5,6,7,8\}.$ If $P=A-B$ and $Q=B-A,$ then the number of relations from $P$ to $Q$ is

Let $b_i>1fori=1,2,...,101.$ Suppose $lo{g}_e{b}_1.lo{g}_e{b}_2,......,lo{g}_e{b}_{101}$ are in Arithmetic Progression (A.P) with the common diffrence $lo{g}_{e}2.$ Suppose $a_1,a_2,.....,a_{101}$ are in A.P. such that $a_1=b_1$ and $a_{51}=b_{51}.$ If $t=b_1+b_2+...+b_{51}$ and $s=a_1+a_2+......+a{5}_3.$ then

Find the equations of tangents to the ellipse

$\frac{x^2}{25}+\frac{y^2}{16}=1$

which are parallel to $3x+2y=25$

Given an isosceles triangle with equal sides of length $b$, base angle $\alpha <\frac{\pi }{4}$ and $R,r$ are the radii of circumcircle and incircle and $O,I$ are the centres of circumcircle and incircle respectively. Then:

If $\frac{(1-3x{)}^{\frac{1}{2}}+(1-x{)}^{\frac{5}{3}}}{\sqrt{4-x}}$ is approximately equal to a + bx for small values of x, then (a, b) =

If two lines are intersecting at $(4,3)$ and angle between them is ${45}^{\circ }$. If the slope of one line is $2$, then the equation(s) of other line is/are

The probability that a teacher will give a surprise test during any class meeting is $\frac{3}{5}$. If a student is absent on two days, then the probability that he will miss at least one test is

What is the value of $x$ if ${\tan }^4\theta +\frac{(1-{\cos }^2\theta )}{{\cos }^2\theta }=x{\sin }^2\theta$ ?

1. 0.66

Find
the values of k
so
that the function f
is continuous at the indicated point.

In $x\in (0,1),$ the value of $\sin [{\tan }^{-1}\left(\frac{1-x^2}{2x}\right)+{\cos }^{-1}\left(\frac{1-x^2}{1+x^2}\right)]$ is equal to

From the point (1,-2,3) lines are drawn to meet the sphere $x^2+y^2+z^2=4$ and they are divided internally in the ratio 2:3. The locus of the point of division is-

1. 20

$\text{The value of}\underset{x\to \infty }{lim}\frac{x+cosx}{x+sinx}is$

The angle between the $x-$axis and the line joining the points $(3,-1)$ and $(4,-2)$ is

A body is moving from rest under constant acceleration and let S₁ be the displacement in the first $(p-1)$ sec and S₂ be the displacement in the first p sec. The displacement in $(p^2-p+1{)}^{th}$ sec. will be

If p(x)=x²-2√2x+1then find p(2√2)

Choose the correct pair of an angle in centesimal system and sexagesimal system.

The angle between vectors $2\hat{i}+\hat{j}+2\hat{k}$ and $2\hat{i}+2\hat{j}-\hat{k}$ is

Let $A=\left[a_{ij}\right]$ be a real matrix of order $3\times 3$, such that $a_{i1}+a_{i2}+a_{i3}=1$, for $i=1,2,3.$ Then, the sum of all the entries of the matrix $A^3$ is equal to:

If a function f(x) is defined on [1,4] $\to$ [1,7] and given that f(3) = 5 and its inverse exists then find $f^{-1}$ ( f (5) ).

Let $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100$,

Then $n(A^c\cap B^c)=$