Explore topic-wise InterviewSolutions in Current Affairs.

Rewrite each of the following statements in the form "p if and only if q"

(i) p : If you watch television, then your mind is free and if your mind is free, then you watch television.

(ii) q : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

(iii) r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

If ${}^{20}{C}_r$ is the co-efficient of $x^r$ in the expansion of $(1+x{)}^{20},$ then the value $\sum _{r=0}^{20}{r}^2{}^{20}{C}_r$ is equal to:

f(x) = 5^{sec x}
f'(x) =

The $f\left(x\right)=\sqrt{x},g\left(x\right)=e^x-1\forall x\in (0,\infty )$ and $\int fog\left(x\right)dx=Afog\left(x\right)+B{\tan }^{-1}\left(fog\right(x\left)\right)+C$, then $A+B$ is

The coefficient of $x^{50}$ in $(1+x{)}^{1000}+x(1+x{)}^{999}+x^2(1+x{)}^{998}+...+x^{1000}$ is

If the line

$(3x+14y+7)+k(5x+7y+6)=0$

is parallel to the y-axis, then the value of $k$ is

Let $f:R\to R$ be a function defined by $f\left(x\right)=max\{x,x^3\}.$ Then the set of all points where $f$ is not differentiable, is

If the normal from the origin to the line $x\cos \alpha +y\sin \alpha =p$ meets it at the point $P(-2,9)$, then $p$ is equal to

Show that the statement

p: “If x is a real number such that x³ + 4x = 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive

Prove the following:
$\frac{\text{cos 4x+ cos 3x + cos 2x}}{\text{sin 4x + sin 3x + sin 2x}}=\text{cot}3x$

Two circles are externally tangent. Lines PAB and PA’B’ are common tangents with A and A’ on the smaller circle B and B’ on the larger circle. If PA = AB = 4, then the area of the smaller circle is

If $A=\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right]$ then $A^{16}$ =

Solution of the sysytem of equations, $x+2y+z=7,x+3z=11,2x-3y=1$, is $(x,y,z)$ then $x+y-z$ is equal to:

If $S={\int }_1^{\infty }{x}^{-3}dx$, then $S$ has the value

Identify the finite verb in the sentence.

Whether I help you or not, your victory is in your hands.

A real value of x satisfies the equation $\frac{3-4ix}{3+4ix}=a-b(a,bϵR),\text{if}{a}^2+b^2$

Find the 20${}^{th}$ term and the sum of 20 terms of the series :

$2\times 4+4\times 6+6\times 8+....$

If the equation $x^2+px+q=0$ and $x^2+qx+p=0$, have a common root, then p + q + 1 =

If $z^2-z+1=0,$ then possible value(s) of $z^n-z^{-n},$ where $n$ is even number

If $I_n=\int {\sec }^{n}xdx,$ then $I_8-\frac{6I_6}{7}=$

The expression ${\tan }^{-1}\left(\frac{6x-8x^3}{1-12x^2}\right)-{\tan }^{-1}\left(\frac{4x}{1-4x^2}\right)$ in the interval $|2x|<\frac{1}{\sqrt{3}}$ simlifies to:

If $A$ be the $A.M.$ and $H$ be the $H.M.$ of two numbers $a$ and $b,$ then the value of $\left(\frac{a-A}{a-H}\right)\cdot \left(\frac{b-A}{b-H}\right)$ is

If $(1+x{)}^n=C_0+C_{1}x+C_2{x}^2+.......+C_n{x}^n$, then $\frac{C_1}{C_0}+\frac{2C_2}{C_1}+\frac{3C_3}{C_2}+........+\frac{n{C}_n}{C_{n-1}}=$

A solution of the differential equation $\frac{dy}{dx}=\frac{y+\sqrt{x^2-y^2}}{x},y\left(1\right)=0,$ is:

Find the complex number z satisfying the equations $\left|\frac{z-12}{z-8i}\right|$=$\frac{5}{3}$, $\left|\frac{z-4}{z-8}\right|$=1

For any quadratic equation $y=a{x}^2+bx+c,$ with roots as $\alpha ,\beta$ such that $\alpha <\beta$ if $a<0\&D>0,$ then select the correct statements.

The mean weight of $150$ students in a certain class is $60$kg. The mean weight of boys in the class is $70$kg and that of girls is $55$kg, then number of boys and girls respectively are