Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\underset{0}{\overset{1}{\int }}\frac{xdx}{x^3+16}$ lies in the interval

For a particle displacement x at time t is given by $x^2=a{t}^2+b$ where a and b are constants. Its acceleration at time t is proportional to

If $z_1$ and $z_2$ lie on a circle having centre at the origin, then point of intersection of the tangents at $z_1$ and $z_2$ is

In a $△ABC,cosA=\frac{3}{5}andcosB=\frac{5}{13}$ The value of cot C can be

Scientific notation and significant figures

Solve the given inequality for real x: 3(2 – x) ≥ 2(1 – x)

If $f:R\to R$ defined by $f\left(x\right)=\{\begin{array}{cc}x,& x<1\\ x^2,& 1\le x\le 4\\ 8\sqrt{x},& x>4\end{array}$

, then $f^{-1}\left(x\right)$ is

Which of the following points are extrema for f(x) = sin(x) ?

Let $A$ be the set of first ten natural numbers and let $R$ be a relation on $A\times A$ defined by $R=\left\{\right(x,y):x+2y=10;x,y\in A\}.$ Then range of $R^{-1}$ is

If $x^3+y^3=\sin x+y,$ then $\frac{dy}{dx}=$

If $\frac{\pi }{3}\le \arg \left[\frac{(z+1)}{(z-1)}\right]\le \frac{2\pi }{3}$, represented by



then $z$ lies in

If $ta{n}^{-1}x+ta{n}^{-1}y=\frac{\pi }{4},xy<1$. then write the value of $x+y+xy$.

A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random?

If $\alpha ,\beta$ are the roots of the equation $2x^2+5x+6=0$, then find the equation whose roots are $\frac{1}{\alpha }and\frac{1}{\beta }$.

Find the
distance between
and
when:
(i) PQ is parallel to the y-axis, (ii) PQ is parallel to the
x-axis.

Question 1

Points A(5, 3) B(-2, 3) and D(5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and hence, find the coordinates of the vertex C.

If ${\Delta }_r=\left|\begin{array}{ccc}2r-1& {}^m{C}_r& 1\\ m^2-1& 2^m& m+1\\ {\sin }^2\left(m^2\right)& {\sin }^2\left(m\right)& {\sin }^2(m+1)\end{array}\right|,(0\le r\le m),$

then value of $\sum _{r=0}^m{\Delta }_r$ is

If $A=\left[\begin{array}{ccc}1& 2& -1\\ -1& 1& 2\\ 2& -1& 1\end{array}\right],$ then the value of $\text{det(adj(adj}A\left)\right)$ is

Find the value of $\underset{x\to \frac{\pi }{2}}{lim}\frac{\sin x}{x}$

Find the area of the region bounded by line x = 2 and parabola $y^2=8x$.

A straight line $L$ through the point $(3,-2)$ is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1.$ If $L$ also intersects the $x$-axis, then the equation of line $L$ is

A variable plane passes through a fixed point $(a,b,c)$ and cuts the coordinate axes at $A,B$ and $C.$ Then the locus of the centre of the sphere $OABC$ is

Let $I=\int \frac{{\sin }^{2}x+\sin x}{1+\sin x+\cos x}dx$, $J=\int \frac{{\cos }^{2}x+\cos x}{1+\sin x+\cos x}dx$ and $c$ is the constant of integration.



$$\begin{array}{cc}\text{Function}& \text{Integral}\\ \begin{array}{c}\text{(a) I}\end{array}& \text{(p)}\frac{1}{2}(x-\sin x-\cos x)+c\\ \begin{array}{c}\text{(b) J}\end{array}& \text{(q)}\frac{1}{2}(x+\sin x+\cos x)+c\\ \begin{array}{c}\text{(c) I + J}\end{array}& \text{(r)}x+c\\ \begin{array}{c}\text{(d) I - J}\end{array}& \text{(s)}c-\cos x-\sin x\\ \begin{array}{}\end{array}& \text{(t)}c+\cos x+\sin x\\ \begin{array}{}\end{array}& \text{(u)}-\frac{1}{2}(x+\sin x+\cos x+c)\end{array}$$



Then the value of $\frac{d(I+J)}{dx}$ at $x=\sqrt{2}$ is

If A $(\alpha ,\beta )=\left[\begin{array}{ccc}cos\alpha & sin\alpha & 0\\ -sin\alpha & cos\alpha & 0\\ 0& 0& e^{\beta }\end{array}\right],then$