Explore topic-wise InterviewSolutions in Current Affairs.

The cubic polynomial $f\left(x\right)=x^3-8x^2+19x-12$ has distinct zeros.

If ${}^{35}{C}_{n+7}={}^{35}{C}_{4n-2}$, then write the values of n.

What is the value of( 1 + logx) when x<1/e

Let $f\left(x\right)=1+\underset{0}{\overset{1}{\int }}(x{e}^y+y{e}^x)f\left(y\right)dy$ where $x$ and $y$ are independent variables. If complete solution set of $x$ for which the function $h\left(x\right)=f\left(x\right)+3x$ is strictly increasing is $(-\infty ,k),$ and $[.]$ denotes the greatest integer function, then $\left[\frac{4}{3}{e}^k\right]$ equals to

The point of intersection of the line joining the points (3, 4, 1) and (5, 1, 6) and the xy-plane is

Let p be a prime number. If p divides $a^2$ then p divides a, where a is a positive integer. Which theorem is this statement previously based on?

The value of $\underset{x\to \infty }{lim}{x}^2\ln \left(x{\cot }^{-1}x\right)$ is

The product of all the factors of determinant

$\left|\begin{array}{ccc}x& y& 1\\ x^2& y^2& 1\\ x^3& y^3& 1\end{array}\right|$ is:

If $f\left(x\right)=\frac{\log (e^{x^2}+2\sqrt{x})}{\tan \sqrt{x}},x\ne 0,$ then the value of $f\left(0\right)$ so that $f$ is continuous at $x=0$ is

Prove that
cot 4x (sin 5x + sin 3x) = cot x (sin 5x
– sin 3x)

A box contains 24 identical balls of which 12 are white and 12 black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

The graphical representation of $y=e^{\sin x}$ is

If $P$ is the number of natural numbers whose logarithms to the base $10$ have the characteristic $p$ and $Q$ is the number of natural numbers, logarithms of whose reciprocals to the base $10$ have the characteristic $-q$, then the value of ${\log }_{10}P-{\log }_{10}Q$ is

A hyperbola has $y$-axis and $x$-axis as its conjugate axis and transverse axis respectively. If one of the points of intersection of $x$-axis with the hyperbola is $(4,0)$ and equation of one of the tangents is $x-y=\sqrt{7},$ then the equation of the hyperbola is

The number of distinct roots of the equation $(x-5)(x-7)(x+6)(x+4)=504$ is

If $\frac{\sin (\alpha +\beta )}{\sin (\alpha -\beta )}=\frac{a+b}{a-b}$, where $\alpha \ne \beta ,a\ne b,b\ne 0$, then $\frac{\tan \alpha }{\tan \beta }$ is

The sum of two numbers
is 6 times their geometric mean, show that numbers are in the ratio.

Let $ABC$ be a triangle and $D$ be the midpoint of $BC$. Suppose $\cot \left(\angle CAD\right):\cot \left(\angle BAD\right)=2:1$. If $G$ is the centroid of triangle $ABC$, then the measure of $\angle BGA$ is

If a root to the given equation a $a(b-c)x^2+b(c-a)x+c(a-b)=0$ is 1, then the other will be

Let $A$ and $B$ be two sets such that $n\left(A\right)=p,$ $n\left(B\right)=q$ and number of subsets of $A$ is $56$ more than that of $B.$ If $N$ is the number of relations from $A$ to $B,$ then the value of $m$ such that the sum of the binomial coefficients in $(x+y{)}^m$ is $N,$ is equal to

Find the value of $\theta ,ifcos2\theta =sin45^{0}cos45^0+sin30^0-$

A and B are two events such that P(A) = $\frac{1}{4}$ , P = $\left(\frac{A}{B}\right)$ = $\frac{1}{2}$ and P = $\left(\frac{B}{A}\right)=\frac{2}{3}$ then P $(A\cup B)$ =

Let $S_1:x^2+y^2=9$ and $S_2:{(x-2)}^2+y^2=1$. Then the locus of center of a variable circle $S$ which touches $S_1$ internally and $S_2$ externally always passes through the points:

The greatest integral value of $(\sqrt{5}+1{)}^7$ is

If $z=x+iy$ and $Re\left(z^2\right)=0$, then the locus of $z$ can be