Explore topic-wise InterviewSolutions in Current Affairs.

If $\frac{{\sin }^{4}x}{3}+\frac{{\cos }^{4}x}{4}=\frac{1}{7},$ then the value of $\frac{{\sec }^{2}x}{3}+\frac{{\text{cosec}}^{2}x}{4}$ is

Write -1 + i $\sqrt{3}$ in polar form.

The differential equation of the family of curves $v=\frac{A}{r}+B$ where A and B are arbitrary constants, is

A value of $\theta$ such that $\frac{2+i\sin \theta }{1-2i\sin \theta }$ is purely real is

Find:

$\left(i\right){lim}_{x\to 2}\left[x\right]$

$\left(ii\right){lim}_{x\to \frac{5}{2}}\left[x\right]$

$\left(iii\right){lim}_{x\to 1}\left[x\right]$

Find the value of tan 3A - tan2A - tanA is equal to ________

If $f_n\left(x\right)=\ln \ln \ln \cdots \ln x(\ln$ is repeated $n$ -times), then $\int {\left[x{f}_1\right(x\left)f_2\right(x)\cdots f_n(x\left)\right]}^{-1}dx$ is equal to

(where $C$ is constant of integration)

Which of the following is or are correct statements for conditions of col-linearity of three points

$A(x_1,y_1),B(x_2,y_2)andC(x_3,y_3)?$
1.slope of line AB = slope of line BC = slope of line CA
2.Area of $△$ABC = 0
3. AC = AB + BC or AB ˜BC

If $f\left(x\right)=\frac{1}{(x-1)(x-2)}andg\left(x\right)=\frac{1}{x^2}$, then points of discontinuity of f(g(x)) are

Let $f_1\left(x\right)=\frac{x}{3}+10,\forall x\in R$ and $f_n\left(x\right)=f_1\left(f_{n-1}\right(x\left)\right)$ for $n\ge 2.$ Then $f_{40}\left(x\right)$ is equal to

if $p^{th}$,$q^{th}$,$r^{th}$ and $s^{th}$ terms of an A.P. be in G.P., then (p - q),(q - r),(r - s) will be in

If $y={\cos }^2({45}^{\circ }+x)+(\sin x-\cos x{)}^2$, where $x\in (0,\frac{\pi }{2}]$, then the possible value(s) of $y$ is/are

A circle has radius 3 units and its centre lies on the line y = x - 1. If it passes through the point (7, 3), find its equations.

The number of real roots of the equation

$(x+4)(x+6)(x+8)(x+12)=8x^2$ is

The value of $x$, if ${\log }_{\sqrt{2}}\left({\log }_2\right({\log }_4(x-15)\left)\right)=0$

The number of ways can $4$ men, $3$ boys, $2$ women be seated in a row so that the men, the boys and the women are not seperated is

If the sum of the n terms of G.P. is S product is P and sum of their inverse is R, than $P^2$ is equal to

Which of the following functions is concave down over the set of positive real numbers:

If P,Q and R are $n\times n$ matrix and

det(P) = 2, det(Q) = 3 and det(R) = 5,

then find the value of $\det \left(P^2{\mathrm{QR}}^{-1}\right).$

If $f(x+y)=f\left(x\right)f\left(y\right)$ and $\sum _{x=1}^{\infty }f\left(x\right)=2,x,y\in N,$ where $N$ is the set of all natural numbers, then the value of $\frac{f\left(4\right)}{f\left(2\right)}$ is:

If the tangent to the conic, $y–6=x^2$ at $(2,10)$ touches the circle, $x^2+y^2+8x–2y=k$ (for some fixed$\left(k\right)$ at a point $(\alpha ,\beta )$; then $(\alpha ,\beta )$ is :