Explore topic-wise InterviewSolutions in Current Affairs.

If $\int 2^{2^x}{.2}^{x}dx=A{.2}^{2^x}+c$, then $A=$

For what value of $\lambda$ are the three lines $2x-5y+3=0,5x-9y+\lambda =0$ and $x-2y+1=0$ concurrent?

The parabola $x^2=py$ passes through (12, 16). Then the focal distance of the point is

If $\theta =ta{n}^{-1}\frac{d}{1+a_1{a}_2}+ta{n}^{-1}\frac{d}{1+a_2{a}_3}+\cdots +ta{n}^{-1}\frac{d}{1+a_{n-1}{a}_n}$, where $a_1,a_2,a_3,\cdots a_n$ are in A.P. with common difference d, then $tan\theta =$

Find the value of

$\frac{\left(}{{18}^3+7^3+3\cdot 18\cdot 7\cdot 25}$

A diet is
to contain at least 80 units of vitamin A and 100 units of minerals.
Two foods F₁and F₂ are available. Food F₁
costs Rs 4 per unit food and F₂ costs Rs 6 per unit. One
unit of food F₁ contains 3 units of vitamin A and 4 units
of minerals. One unit of food F₂ contains 6 units of
vitamin A and 3 units of minerals. Formulate this as a linear
programming problem. Find the minimum cost for diet that consists of
mixture of these two foods and also meets the minimal nutritional
requirements?

The derivative of ${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x=\frac{1}{2}$ is :

Find the middle term in the expansion of:

$\left(i\right){(3x-\frac{x^3}{6})}^9$

$\left(ii\right){(2x^2-\frac{1}{x})}^7$

$\left(iii\right){(3x-\frac{2}{x^2})}^{15}$

$\left(iv\right){(x^4-\frac{1}{x^3})}^{11}$

Let $x^2-ax+b=0$, where $a,b\in R$ be a quadratic equation such that the roots are opposite in sign and the magnitude of one root is twice the other. Then which of the following options is/are always true ?

The value of $\int e^x{\sin }^{-1}\left(x^2\right)+e^x{\cos }^{-1}\left(x^2\right)dx;x\in (0,1)$ is

(where $C$ is constant of integration)

By using
properties of determinants, show that:

Find the value of ${\int }_0^{\infty }x{e}^{-x}dx$

The length of the longest interval in which the function $f\left(x\right)=3\sin x-4{\sin }^{3}x$ is increasing, is

Find the derivative of $f\left(x\right)=x^2-2$ at x = 10

If the function $f:R\to A$ given by $f\left(x\right)=\frac{x^2}{x^2+1}$ is surjection, then $A=$

Let $a,b,x$ and $y$ be real numbers such that $a–b=1$ and $y\ne 0$. If the complex number $z=x+iy$ satisfies $lm\left(\frac{az+b}{z+1}\right)=y$ , then which of the following is(are) possible value(s) of $x$ ?

1. 2

sin⁻¹
(cos x)

The value of $2{\tan }^{-1}\frac{1}{3}+{\tan }^{-1}\frac{1}{2}=$

Let $\sin \alpha =\frac{12}{37}$ for $\alpha \in (\frac{\pi }{2},\pi )$ and $\cos \beta =\frac{20}{101}$ for $\beta \in (\frac{3\pi }{2},2\pi ).$ If $\text{cosec}(\alpha +\beta )=\frac{p}{q}$ where $p$ and $q$ are co-prime numbers, then the value of $p+q$ is

A person plays a game of tossing a coin thrice. For each head, he is given Rs $2$ by the organiser of the game and for each tail, he has to give Rs $1.50$ to the organiser. Let $X$ denotes the amount gained or lost by the person. Then range of $X$ is:

(Where minus sign shows the loss to the player and positive sign shows gain to the player)

Given that the two curves $\arg \left(z\right)=\frac{\pi }{6}$ and $|z-2\sqrt{3}i|=r$ intersect in two distinct points, then

([r] represents integaral part of $r$)

If $A=\{x:x\text{is a multiple of}3\}$ and $B=\{x:x\text{is a multiple of}5\}$, then $A-B=$

If the median of $\Delta ABC$ through $A$ is perpendicular to $AB$ then

Choose the correct answer in each of the question.
$\int \frac{dx}{x(x^2+1)}$ equals
$\left(a\right)log|x|-\frac{1}{2}log(x^2+1)+C\left(b\right)log|x|+\frac{1}{2}log(x^2+1)+C\left(c\right)-log|x|+\frac{1}{2}log(x^2+1)+C\left(d\right)\frac{1}{2}log|x|+log(x^2+1)+C$

If $I_n$ is the area of $n$ sided regular polygon inscribed in a circle of unit radius and $O_n$ be the area of polygon circumscribing the given circle, then the value of $\frac{O_n(1+\sqrt{1-{\left(\frac{2I_n}{n}\right)}^2})}{I_n}=$