Explore topic-wise InterviewSolutions in Current Affairs.

If $\underset{1}{\overset{2}{\int }}{e}^{x^2}dx=a$, then $\underset{e}{\overset{e^4}{\int }}\sqrt{\ln x}dx$ is equal to

If the average rate of change of f(x) with respect to x over the interval [a, b] is m, then find the value of $\frac{1}{m^2}$

If ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ are the greatest and least values of the function $f\left(x\right)=\cos x+\frac{1}{2}\cos 2x-\frac{1}{3}\cos 3x,x\in [0,2\pi ],$ then

The missing number in the second figure is

If $f\left(x\right)=\left[\sin \right[x\left]\right]$ in $(0,2\pi )$ where $[.]$ denotes greatest integer function, then $f\left(x\right)$ will be discontinuous at $x=$

The equation of common tangent to the curves $y^2=16x$ and $xy=–4$, is :

For $0<\theta <\frac{\pi }{2},$ the solution (s) of
${\sum }_{m=1}^{6}cosec(\theta +\frac{(m-1)\pi }{4})cosec(\theta +\frac{m\pi }{4})=4\sqrt{2}$ is/are

Rules of differentiation with example

If $p\to (q\vee r)$ is false, then the truth values of $p,q,r$ are respectively (where $T$ is true and $F$ is false)

The number of real values of $\lambda$ for which the lines $x-2y+3=0,\lambda x+3y+1=0$ and $4x-\lambda y+2=0$ are concurrent is

If $(1+x+x^2{)}^{20}=a_0+a_{1}x+a_2{x}^2+\cdots +a_{40}{x}^{40},$ then the value of $a_0+a_1+a_2+\cdots +a_{19}$ is

The value of $\underset{x\to 1}{lim}\frac{x-1}{x^3-x^2+x-1}$ is

Solution of the differential equation $\frac{dy}{dx}+2y=\cos x$ is:

(where $C$ is integration constant)

If X = $\{8^n-7n-1:n\in N\}andY=\left\{49\right(n-1):n\in N\}$ , then

1. -1.07

1. 943.594

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\pi }\frac{x}{1+sinx}dx.$

A steamer moves with a velocity 3 kmph in and against the direction of river water whose velocity is 2 kmph. Total time for total journey if the boat travels 2 km in direction of stream and then back to its place will be (in hour)

The solution of the differential equation

$\frac{dy}{dx}=\frac{y{f}^{\prime }\left(x\right)-y^2}{f\left(x\right)}$

(where $c$ is integration constant)

The value of the expression ${\tan }^{-1}\left(\frac{\sqrt{2}}{2}\right)+{\sin }^{-1}\left(\frac{\sqrt{5}}{5}\right)-{\cos }^{-1}\left(\frac{\sqrt{10}}{10}\right)$ is

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing 50 coins is equal to that head showing 51 coins, then the value of p is

Express the following matrices as the sum of a symmetric and a
skew symmetric matrix:

(i)

(ii)

(iii)

(iv)

If $p$ is true, $q$ is false and $r$ is false, then which of the following is true?

Any ordinate $MP$ of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ meets the auxiliary circle at $Q$, then locus of the point of intersection of normals at $P$ and $Q$ to the respective curves is

The value of the integral $\underset{0}{\overset{1}{\int }}\frac{dx}{x^2+2x\cos \alpha +1},\alpha \in (0,\frac{\pi }{2})$ is equal to

$\sqrt{lo{g}_{2}x}-0.5=lo{g}_2\sqrt{x}$, then x equals

The image of the interval $[-1,3]$ under the mapping $f\left(x\right)=4x^3-12x$ is

Solve the following system of inequalities graphically: 5x + 4y ≤ 20, x ≥ 1, y ≥ 2