Explore topic-wise InterviewSolutions in Current Affairs.

The value of
$1^2.{}^n{C}_1+2^2.{}^n{C}_2+3^2.{}^n{C}_3+...+n^2.{}^n{C}_n$ is

If $\frac{sinx}{siny}=\frac{1}{2},\frac{cosx}{cosy}=\frac{3}{2},x,yϵ(0,\frac{\pi }{2})$, then tan (x+y)=___

By using
properties of determinants, show that:

(i)

(ii)

44 seeds are equally divided into 2 groups. Each group will have number of seeds.

Find the differential equation of the family of lines passing through the origin.

If $f\left(x\right)=2x$ and $g\left(x\right)=\frac{x^2}{2}+1$ , then which of the following can be a discontinuous function

Let $\overrightarrow{a}=-\hat{i}+\hat{j}$ and $\overrightarrow{b}=\hat{i}+3\hat{j}.$ Then angle between the vectors $4\overrightarrow{a}+\overrightarrow{b}$ and $\frac{1}{4}(7\overrightarrow{b}-\overrightarrow{a})$ is

Differentiate between formal and informal communication.

There are five physics and ten maths books, then in how many ways one can select-

Axis of a parabola lies along $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin, on the positive $x$-axis then which of the following points does not lie on it?

If $(a-b{)}^2+(b-c{)}^2+(c-a{)}^2=0$, a,b,c ∈ R and a:b:c = 1:m:n, find m+n

Let $f\left(x\right)$ and $g\left(x\right)$ be two continuous functions defined from $R\to R$ such that $f\left(x_1\right)>f\left(x_2\right)$ and $g\left(x_1\right)<g\left(x_2\right),\forall x_1>x_2.$ Then the solution set of $f\left(g\right({\alpha }^2-2\alpha \left)\right)>f\left(g\right(3\alpha -4\left)\right)$ is

1. 12

If $\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{\cot x}{\cot x+\text{cosec}x}dx=m(\pi +n),$ then $m.n$ is equal to :

If $\int \frac{1}{5+4\cos 2\theta }d\theta =A{\tan }^{-1}\left(B\tan \theta \right)+C,$ then $(A,B)=$

(where $A,B$ are fixed constants and $C$ is integration constant)

is
a square matrix, if

(A)
m < n

(B) m
> n

(C) m
= n

(D) None
of these

Root 3 cosec 20 minus sec 20

1. 0.51

Find the total number of arrangements of the letters in the expression $a^3{b}^2{c}^4$ when written at full length.

The function $f\left(x\right)=2\left|x\right|+|x+2|-||x+2|-2\left|x\right||$

has a local minimum or a local maximum at x=

The set of values of ${\alpha }^2$, if there exists a tangent to the ellipse $\frac{x^2}{{\alpha }^2}+y^2=1$ such that the portion of the tangent intercepted by the hyperbola ${\alpha }^2{x}^2-y^2=1$ subtends a right angle at the centre of the curves, is

The shortest distance between the line $y=x$ and the curve $y^2=x-2$ is:

(2x+5) (3x-7)

for the function $f\left(x\right)=x^2{e}^{-x},$, the maximum occurs when $x$ is equal to

If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in G.P. with the same common ratio, then the points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃)

The range of $x$ satisfying ${\sin }^4\left(\frac{x}{3}\right)+{\cos }^4\left(\frac{x}{3}\right)>\frac{1}{2}$ is (where $n\in Z$)

If tan(α+θ) =n tan(α-θ) show that : (n+1)sin 2θ =(n-1)sin2α