Explore topic-wise InterviewSolutions in Current Affairs.

The ratio of the A.M
and G.M. of two positive numbers a and b, is m:
n. Show that
.

$sin{20}^{\circ }sin{40}^{\circ }sin{60}^{\circ }sin{80}^{\circ }$=

A biased coin (with probability of obtaining a head equal to $p>0$) is tossed repeatedly and independently until the first head is observed. The probability that the first head appears at an even numbered toss, is

Tangents are drawn from the origin to the curve y = sin x. Their points of contact lie on the curve

The solution of the differential equation

$\frac{dy}{dx}=\frac{y^2-2xy-x^2}{y^2+2xy-x^2}$ given $y=1$ at $x=1$ is:

Let $S_1$ be the sum of areas of the squares whose sides are parallel to coordinate axes.
Let $S_2$ be the sum of areas of the slanted squares as shown in the figure. Then $S_1/S_2$ is

Matrices $A$ and $B$ satisfy $AB=B^{-1},$ then the matrix $X$ satisfying $A^{-1}XA=B$ is equal to

Differentiate the following functions with respect to x.

$sin(x^2+5)$

There are 10 questions; each question is either true or false. Number of different sequences of incorrect answers is also equal to

A fair coin is tossed $99$ times. Let $X$ be the number of times heads occurs. Then $P(X=r)$ is maximum when $r$ is

If $\left|\begin{array}{cc}2x& 5\\ 8& x\end{array}\right|=\left|\begin{array}{cc}6& -2\\ 7& 3\end{array}\right|$, then the value of x is

(a) $3$
(b) $\pm 3$
(c) $\pm 6$
(d) $6$

Let $S$ be the sum of the first $9$ terms of the series: $\{x+ka\}+\{x^2+(k+2\left)a\right\}+\{x^3+(k+4\left)a\right\}+\{x^4+(k+6\left)a\right\}+...$ where $a\ne 0$ and $a\ne 1$. If $S=\frac{x^{10}-x+45a(x-1)}{x-1}$, then $k$ is equal to:

Let $x^2-(m-3)x+m=0,m\in R$ be a quadratic equation. Then the set of value(s) of $m$ for which roots are real and distinct is/are

If ${\Delta }_1=\left|\begin{array}{cc}a& -b\\ -c& d\end{array}\right|,{\Delta }_2=\left|\begin{array}{cc}-2& 1\\ 1& -2\end{array}\right|.$ Then which of the following is equal to the product ${\Delta }_1\cdot {\Delta }_2?$

Consider a sequence $\left\{a_n\right\}$ with $a_1=2$ and $a_n=\frac{a_{n-1}^2}{a_{n-2}}$for all $n\ge 3$, terms of the sequence being distinct. Given that $a_2$ and $a_5$ are positive integers and $a_5\le 162$ then the possible value(s) of $a_5$ can be

$\text{The value of}{lim}_{x\to 0}\frac{\sqrt[3]{31+sinx}-\sqrt[3]{31-sinx}}{x}is$

Find the value of $\lambda$ if ($\lambda$ - 5) ($\lambda$ + 3) < 0

Verify MVT if $f\left(x\right)=x^3-5x^2-3x$ iin the interval [a, b], where a = 1 and b = 3. Find all c$ϵ$(1, 3) for which f'(c) = 0.

If the power of point $(1,-2)$ with respect to $x^2+y^2=1$ is equal to the radius of a circle and $(3,2)$ is the centre of that circle, then the equation of that circle is

Show that
the normal at any point θ
to the curve

is at a constant distance from the origin.

Integrate the rational functions.
$\int \frac{(x^2+1)(x^2+2)}{(x^3+3)(x^2+4)}dx$

If $a>b,$ where $a,b<0,$ then $a^r<b^r$ when

The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below


Which of the following options is/are true for the graph?

Find the equation of the plane through the intersection of the planes 3x-y+2z-4=0 and x+y+z-2=0 and the point(2,2,1).

Fill
in the blanks in following table:

If $S_n={\sum }_{r=1}^n\frac{1+2+2^2+Sumtorterms}{2^r}$,then $S_n$ is equal to

Prove that

Cosα/(1+sinα)+sinα/(1+cosα)=2secα

The order and degree of differential equation $[1+{\left(\frac{dy}{dx}\right)}^2]=\frac{d^{2}y}{d{x}^2}$ are
a) $2,\frac{3}{2}$
b) 2, 3
c) 2, 1
d) 3, 4

$f\left(x\right)=\{\begin{array}{cc}{2}^{x+2}-16& ifx\ne 2\\ \begin{array}{c}{4}^x-16\\ k\end{array}& ifx=2\end{array}atx=2$

If f(x) is continuous at x=2, then find the value of k.