Explore topic-wise InterviewSolutions in Current Affairs.

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& f\left(x\right)={\sin }^{-1}\left(\frac{\sin x+\cos x}{2}\right)& \text{(P)}& \text{Domain is}R\\ \text{(B)}& g\left(x\right)={\sin }^{-1}\left(\frac{2}{\pi }{\tan }^{-1}x\right)& \text{(Q)}& \text{Range contains only one integer}\\ \text{(C)}& h\left(x\right)={\tan }^{-1}\left(\frac{2}{\pi }(2{\tan }^{-1}x-{\sin }^{-1}x+{\cot }^{-1}x-{\cos }^{-1}x)\right)& \text{(R)}& \text{Odd function}\\ \text{(D)}& j\left(x\right)={\tan }^{-1}(x^3+x)& \text{(S)}& \text{No vertical tangent}\end{array}$



Which of the following is a CORRECT combination?

If $ta{n}^{2}x+secx-a=0$ has alteast one solution, then $a\in$..........

${lim}_{n\to \infty }\frac{n^2}{1+2+3+....+n}$

If a tan $\theta$ = b, then a cos 2$\theta$ + b sin 2$\theta$ =

Integrate the rational functions.
$\int \frac{1}{e^x-1}dx$

1. 12.57

$\underset{x\to 0}{lim}\frac{e^{\alpha x}-e^{\beta x}}{x}=$

Find the sum total of 12 + 7.

If two functions f(x) and g(x) defined on R intersect each other at x = a & x =b then the area enclosed between these two functions will be -

Let $f\left(x\right)=\left|\begin{array}{ccc}{\cos }^2\theta & {\tan }^2\theta & 1\\ -{\sin }^2\theta & {\sec }^2\theta & 1\\ {\sin }^{2}x& {\tan }^{2}x& 16x\end{array}\right|,\theta \in (0,\frac{\pi }{2}).$ Then the value of $f^{\prime \prime }\left(\frac{\pi }{4}\right)$ is equal to

If $f\left(x\right)=\frac{{\log }_e(1+x^2\tan x)}{\sin x^3},x\ne 0$ is continuous at $x=0$, then the value of $f\left(0\right)$ is

Show that the function given by f(x)
= sin x is

(a) strictly
increasing in

(b) strictly decreasing in

(c) neither
increasing nor decreasing in (0, π)

If f(x) = -x + 2, what is f(-4)?

The image of the point $(3,8)$ in the line $x+3y=7$ is

If $A$ is a square matrix, then $(adjA{)}^{-1}=adj(A^{-1})=$

Integrate the function.
$\int 1.ta{n}^{-1}xdx$

If $\alpha =1+\frac{1}{2}+\frac{1}{3}+\cdots \cdots +\frac{1}{101}$ and $\beta =\sum _{r=1}^{99}\frac{r}{(102-r)(101-r)}$, then the value of $\alpha +\beta$ is

The coefficient of $x^4$ in the expansion of $(x^2-x-2{)}^6$ is

Find the critical points of the function $f\left(x\right)=2x^3+15x^2+36x.$

Volume of a cone is 150 cu. cm. Its height is 15 cm. Find the area of its base.

The area (in square units) bounded by the curves $x=-2y^{2}andx=1-3y^2$ is

Let $F\left(x\right)=\frac{x}{(1+x^n{)}^{1/n}}$ for $n\ge 2$ and $g\left(x\right)=\underset{\text{f occours n times}}{\underset{}{(f\circ f\circ ..\circ f)}}\left(x\right)$. Then $\int x^{x-2}g\left(x\right)dx$ equals.

Find the equation of the tangent and the normal to the curve $16x^2+9y^2=145$ at the point $(x_1,y_1)$, where $x_1=2$ and $y_1>0$.

OR

Find the intervals in which the function $f\left(x\right)=\frac{x^4}{4}-x^3-5x^2+24x+12$ is (a) strictly increasing, (b) strictly decreasing.

All real values of $x$ which satisfy $x^2-3x+2>0$ and $x^2-3x-4\le 0$ lie in the interval

If the tangent to the curve $y=x+\sin y$ at a point $(a,b)$ is parallel to the line joining $(0,\frac{3}{2})$ and $(\frac{1}{2},2)$ then:

The asymptote(s) of the curve $y=3x+\frac{2}{x}$ is/are:

Let P(x) = x^{​​​​​​6} + ax^{​​​​​5} + bx^{​​​​​4} + cx^​3 + dx^{​​​​​2} + ex + f be a polynomial such that P(1)=1; P(2)=2; P(3)=3; P(4)=4; P(5)=5; P(6)=6 then find the value of P(7).