Explore topic-wise InterviewSolutions in Current Affairs.

Let $A=\{1,3,5,7\},$ $B=\{2,4,6,8\}$ and $f:A\to B.$ Then number of functions $f$ such that $f\left(i\right)\ne i+1,\forall i=1,3,5,7$ is

A point on the curve $y=x^2+x$, where the tangent is parallel to the chord joining the points (0, 0) and (1, 2) is .

If $(x^2+x+1)+(x^2+2x+3)+(x^2+3x+5)+\cdots +(x^2+20x+39)=4500,$ then $x$ is equal to

The value of $\int \left(\ln \right(1+\sin x)+x\tan (\frac{\pi }{4}-\frac{x}{2}))dx$ is equal to

(where $C$ is integration constant)

The point of inflection for $y=f\left(x\right)=x{e}^x$ is:

A man is moving away from a tower 41.6m high at a rate of 2 m/s. If the eye level of the man is 1.6m above the ground, then the rate at which the angle of elevation of the top of the tower is changing when he is at a distance of 30 m from the foot of the tower is

For a quadratic expression $y=f\left(x\right)=a{x}^2+bx+c,$ if $f\left(\alpha \right)=0$ and for the rest of values of $x,f\left(x\right)<0.$

Then $a$ , and $D$ .

If $y={\cot }^{-1}\left(x^2\right)$, then $\frac{dy}{dx}$ is equal to

The value(s) of $x$ for which the value of $detA=0,$ where $A=\left[\begin{array}{ccc}x-1& 1& 1\\ 1& x-1& 1\\ 1& 1& x-1\end{array}\right]$

Which on eof the following is a closed expression for the generating function of the sequence {$a_n$} where $a_n$ = 2n + 3 for all n = 0, 1, 2, 3...?

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is:

Let ${\overrightarrow{c}}_1=(1,0,0),{\overrightarrow{c}}_2=(1,1,0),{\overrightarrow{c}}_3=(1,1,1),$ and $({\overrightarrow{c}}_1,{\overrightarrow{c}}_2,{\overrightarrow{c}}_3)$ forms a system, then reciprocal of ${\overrightarrow{c}}_1=$

If $\sqrt{y-\sqrt{y-\sqrt{y}\cdots \infty }}=\sqrt{x+\sqrt{x+\sqrt{x}\cdots \infty }},$ then $\frac{dy}{dx}$ is equal to

If A ={a,b,c,d} and the function f={(a,b),(b,d),(c,a),(d,c)}, write $f^{-1}$.

Let R be a relation defined by

R={(a, b):ab+2>0}. Verify the following

i) (a, b ) belongs to R and (b, c) belongs to R implies that (a, c) belongs to R

If $\left[\begin{array}{cc}xy& 4\\ z+6& x+y\end{array}\right]=\left[\begin{array}{cc}8& w\\ 0& 6\end{array}\right]$ then find the values of x, y, z and w.

Find the area enclosed between the parabola $y^2=4ax$ and the line y = mx.

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of the hill is

If the green triangle is translated to get the blue triangle in the following image, what is the rule applied for x coordinate and y coordinate respectively?

For $a\in (-1,1)$ and $b\in (-1,1)$ if ${\sin }^{-1}\left(\frac{2a}{1+a^2}\right)+{\sin }^{-1}\left(\frac{2b}{1+b^2}\right)=2{\tan }^{-1}x$, then the value of $x$ is

Find the ratio in which the sphere $x^2+y^2+z^2$ = 504 divides the line joining the points (12, -4, 8) and (27, -9, 18)

Log(3^x-8)to the base3=2-x solve the equation.

For three sets $A,B$ and $C,A\cap (B-C)=$

Normal at $(5,3)$ of rectangular hyperbola $xy-y-2x-2=0$ intersects it again at a point

Suppose $f$ and $g$ are differentiable functions on $(0,\infty )$ such that $f\text{'}\left(x\right)=-\frac{g\left(x\right)}{x}$ and $g\text{'}\left(x\right)=-\frac{f\left(x\right)}{x}$, for all $x>0$. Further, $f\left(1\right)=3$ and $g\left(1\right)=-1$.

$g\left(\frac{1}{10}\right)$ is equal to

Angle subtended by common tangents intercepted between two ellipses $4(x-4{)}^2+25y^2=100$ and $4(x+1{)}^2+y^2=4$ at origin is

The set of all points, where the function $f\left(x\right)=\frac{x}{1+\left|x\right|}$ is differentiable is

Solution of the system of the equations:$\left[\begin{array}{ccc}a& b& c\\ a^2& b^2& c^2\\ a^3& b^3& c^3\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}d\\ d^2\\ d^3\end{array}\right],a\ne b\ne c\ne 0,$ is

Factories x^{​​​​​​2 _-} 3x + 24

Find $\frac{dy}{dx}$in the following questions:

$x^2+xy+y^2=100$

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 $f\left(f^{-1}\right(5\left)\right)$.