Explore topic-wise InterviewSolutions in Current Affairs.

If ${}^n{P}_r={}^n{P}_{r+1}$ and ${}^n{C}_r={}^n{C}_{r-1}$, then the value of $r$ is equal to

What is the condition for a conic $x^2+2xy+2y+kx+3y^2=0$ to represent a pair of straight lines.

The equation of a common tangent to $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\text{and}\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ is

Let $a>2$ be an integer. If there are just $18$ positive integers satisfying the inequality $(x-a)(x-2a)(x-a^2)<0,$ then the value of $a$ is

If $A=\{x:x$ is a prime number between $2$ and $16\},$ then number of subsets of $A$ with exactly two elements is

There are two circles in the xy- plane whose equations are $x^2+y^2-2y=0$ and $x^2+y^2-2y-3=0$. A point is chosen at random inside the larger circle. Then the probability that the point has been taken from outside the smaller circle is

The equation of plane passes through $(1,2,3)$ and perpendicular to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{1}$ is

Find the value of $\lambda$ if (3, 4) and (-4, 3) lie on the opposite side of x - y + $\lambda$ = 0

Which among the following graph(s) represents an odd function

If $f_n\left(\theta \right)=\sum _{r=0}^n\frac{1}{4^r}{\sin }^4\left(2^r\theta \right)$, then which of the following alternative(s) is/are correct?

The range of $f\left(x\right)={\log }_e(3x^2-4x+5)$ is

The angle between the lines xy = 0 is

If the line $x-2y=k$ cuts off a chord of length 2 from the circle $x^2+y^2=3$, then k =

Which of the following is the graph of the function $y=e^x-1$

If,
find P (A ∩ B) if A and B
are independent events.

PSP’ is a focal chord of the ellipse $16x^2+25y^2=400.$ If SP = 8 then SP’ =

If the $m^{th}$ term of an A.P. be $\frac{1}{n}$ and $n^{th}$ term be $\frac{1}{m}$, then show that its ${\left(mn\right)}^{th}$ term is 1.

Find the equation of the curve passing through the point $(0,\frac{\pi }{4})$ whose differential equation is $sinxcosydx+cosxsinydy=0$

Find
the inverse of each of the matrices, if it exists.

Maximum area of rectangle whose two vertices lies on the $x-$axis & two on the curve $y=3-|x|,\forall |x|<3$

Solve the inequality

If $f\left(x\right)=\sum _{n=1}^x{\tan }^{-1}\left\{\frac{\sqrt{3}}{n^2+n+3}\right\},$ then the value of $f^{\prime }\left(1\right)$ is

The equation of plane through $(1,1,1)$ and passing through the line of intersection of the planes $x+2y-z+1=0$ and $3x-y-4z+3=0$ is:

If $a_1,a_2,.......,a_n$are positive real numbers whose product is a fixed number c, then the minimum value of $a_1+a_2+.......+a_{n-1}+2a_n$ is

If $A,B$ and $C$ are matrices such that $AB=AC,$ then which of the following is true

If $A=\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]$ and $f\left(x\right)=\frac{1+x}{1-x}$, then $f\left(A\right)$ is

The number of subsets of the power set of a singleton set is