Explore topic-wise InterviewSolutions in Current Affairs.

If $△=\left|\begin{array}{ccc}a-b& b-c& c-a\\ b-c& c-a& a-b\\ c-a& a-b& b-c\end{array}\right|,$ then which of the following is correct?

If $A,B,C,D$ are the angles of a cyclic quadrilateral, then $\cos A+\cos B+\cos C+\cos D$ is equal to

Which among the following is/are skew hermitian matrix.

The first term of a G.P. is $1$. If the sum of the third and fifth terms of the G.P. is $90$, then the common ratio of the G.P. is

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4

Let ${(1-x+x^4)}^{10}=a_0+a_{1}x+a_2{x}^2+\cdots +a_{40}{x}^{40}.$ Then the correct option(s) is (are)

The number of positive integral triplets (x, y, z) satisfying the equation $\left|\begin{array}{ccc}{y}^3+1& y^{2}z& y^{2}x\\ y{z}^2& z^3+1& z^{2}x\\ y{x}^2& x^{2}z& x^3+1\end{array}\right|=11$ is

Let $I_n={\int }_0^{\frac{\pi }{2}}\frac{sin(2n-1)x}{sinx}dx,J_n={\int }_0^{\frac{\pi }{2}}\frac{si{n}^{2}nx}{si{n}^{2}x}dx,n\in N$, then

The range of ${\sin }^{-1}\left(2^x\right)$ is

The argument of the complex number $\frac{2+3i}{(3+i){(1+2i)}^2}$ is equal to

If $h\left(x\right)=\left(fog\right)\left(x\right)+k$ where $k$ is any constant. If $\frac{d}{dx}\left(h\right(x\left)\right)=-\frac{\sin x}{{\cos }^2\left(\cos x\right)},$ then compute the value of $j\left(0\right)$,

where $j\left(x\right)=\underset{g\left(x\right)}{\overset{f\left(x\right)}{\int }}\frac{f\left(t\right)}{g\left(t\right)}dt,$ $f$ and $g$ are trigonometric functions

Show that ${\tan }^{-1}\left(\frac{1}{2}\right)+{\tan }^{-1}\left(\frac{2}{11}\right)={\tan }^{-1}\left(\frac{3}{4}\right)$

The area(in sq.units) bounded by the curve $y=x^3,x-$ axis and the two ordinates $x=-2,x=1$ is

The value of the integral $\int \frac{x^2}{(x^2+1)(x^2+4)}dx$

(where $C$ is integration constant)

Determine order and degree(if defined)
of differential equation

If the $p^{th}$ and $q^{th}$ terms of a G.P. are q and p respectively, show that $(p+a{)}^{th}$ term is ${\left(\frac{q^p}{p^q}\right)}^{\frac{1}{p-q}}$.

If $A$ is an $3\times 3$ non–singular matrix such that $AA\text{'}=A\text{'}A$ and $B=A^{-1}A\text{'}$, then $BB\text{'}$ equals:

Let D, E, F be the mid points of the sides BC, CA, AB respectively of a $\Delta ABC$. Then,$\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}$ equals

The complete set of values of $\lambda$ for which the function

$f\left(x\right)=\{\begin{array}{cc}2x+1,& x<1\\ \lambda ,& x=1\\ 2x^2-x+3,& x>1\end{array}$

is strictly increasing at $x=1$

If,
then show that a, b, c and d are in G.P.

Let $z_1$ and $z_2$ be any two non-zero complex numbers such that $3|z_1|=4|z_2|$. If $z=\frac{3z_1}{2z_2}+\frac{2z_2}{3z_1}$ then :

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P(A and B)

If $(1+x)(1+x+x^2).....(1+x+.....+x^n)=a_0+a_{1}x+a_2{x}^2+a_3{x}^3+.....$, then the value of $a_0+a_2+a_4+.....$ is

The harmonic conjugate of $(2,3,4)$ w.r.t the points $(3,-2,2)$ and $(6,-17,-4)$ is:

What are the conditions for $a{x}^2+bx+c$> $0\forall$ x $ϵ$ R

Evaluate the definite integrals.
${\int }_{-1}^1(x+1)dx.$

Sum of first n terms in the following series

${cot}^{-1}$3 + ${cot}^{-1}$7 + ${cot}^{-1}$13 + ${cot}^{-1}$21 + .........n terms.is given by