Explore topic-wise InterviewSolutions in Current Affairs.

If $x=a{t}^2,y=2at,then\frac{dy}{dx}=$

If $\overrightarrow{b}$ and $\overrightarrow{c}$ are non-zero and non-collinear vectors, $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})+(\overrightarrow{a}\cdot \overrightarrow{b})\overrightarrow{b}$$=(4-2x-\sin y)\overrightarrow{b}+(x^2-1)\overrightarrow{c}$ and $(\overrightarrow{c}\cdot \overrightarrow{c})\overrightarrow{a}=\overrightarrow{c}$. Then,

Find the equation of pair of tangents drawn to the circle $x^2+y^2-4x+4y=0$ from the point (2, 2)

Let $L_1:2x+3y=5$ and $L_2$ be equal sides of a triangle. If $L:x+y=2$ is the perpendicular bisector of the third side, then the equation of $L_2$ is

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three non -zero vectors such that no two of these are collinear. If the vector $\overrightarrow{a}+2\overrightarrow{b}$ is collinear with $\overrightarrow{c}$ and $\overrightarrow{b}+3\overrightarrow{c}$ is collinear with $\overrightarrow{a}$ $(\lambda$ being some non -zero scalar) then $\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}$ equals

Integrate the following functions w.r.t. x.

$\int \frac{1}{x-x^3}dx$

In India, if $60\%$ population likes tea, $10\%$ likes coffee and $5\%$ likes both. A person is selected at random, then the probability that he(she) does not like both is

If $C_0,C_1,C_2,\dots ,C_n$ denote the binomial coefficients of the expansion $(1+x{)}^n$ and $\sum _{r=0}^n(-1{)}^r{}^n{C}_r[\frac{1}{2^r}+\frac{3^r}{2^{2r}}+\frac{7^r}{2^{3r}}+\dots \text{upto}m\text{terms}]$= \dfrac{a^{mn}-1}{b^{mn}(c^n-1)},$ then

Find the maximum
area of an isosceles triangle inscribed in the ellipse
with
its vertex at one end of the major axis.

Which of the following transformation reduces the differential equation $\frac{dz}{dx}+\frac{z}{x}\ln z=\frac{z}{x^2}(\ln z{)}^2$ into the form $\frac{du}{dx}+uP\left(x\right)=Q\left(x\right)$

The sum of direction cosines of the given vector $6\hat{i}+2\hat{j}-3\hat{k}$ is

Equation $12x^2-10xy+2y^2+11x-5y+2=0$ represent a pair of straight lines. Find the acute angle between them.

Find the area of triangle formed by joining the mid points of the sides of the triangle whose

Vertices are (0,-1), (2,1) and (0,3).

The general solution of differential equation $xy\frac{dy}{dx}=\frac{1+y^2}{1+x^2}(1+x+x^2),$ where $c$ is the constant of integration, is

Find the intercepts cut
off by the plane

Determine whether each of the following relations are reflexive, symmetric and transitive:
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}

Identify the rectangular prism.

The value of $\underset{x\to 0}{lim}\frac{\sqrt{x+1}-1}{x}$ is

Three pipes $X,$ $Y$ and $Z$ can fill a tank from empty to full in $10$ minutes, $20$ minutes, and $40$ minutes respectively. When the tank is empty, all the three pipes are opened. $X,$ $Y$ and $Z$ discharge chemical solutions $P,$ $Q$ and $R$ respectively. What is the proportion of the solution $Q$ in the liquid in the tank after $5$ minutes?

The value of $\int \left(\tan 3x\tan 6x\tan 9x\right)dx$ is

(where $C$ is constant of integration)

The value of $sin\left(2ta{n}^{-1}\frac{1}{3}\right)+cos\left(ta{n}^{-1}2\sqrt{2}\right)$ is

Repeat part (a) of problem 6 if the push is applied horizontally and not parallel to the incline.

Which of the following differential equations has $y=c_1{e}^x+c_2{e}^{-x}$ as the general solution?
(a) $\frac{d^{2}y}{d{x}^2}+y=0$
(b) $\frac{d^{2}y}{d{x}^2}-y=0$
(c) $\frac{d^{2}y}{d{x}^2}+1=0$
(d) $\frac{d^{2}y}{d{x}^2}-1=0$

If the line joining the points $A(3,0)$ and $B(5,2)$ is rotated about $A$ in the anticlockwise direction through an angle of ${15}^0$ such that $B$ goes to $C$ in the new position .Similarly the line joining $A$ and $C$ is rotated about $A$ in the anticlockwise direction through an angle of ${45}^{\circ }$ such that $C$ goes to $D$ in the new position, then the coordinates of $D$ are

When tan theta =-1 what is the value of theta .How to find that

For a positive integer n, let $f_n\left(\theta \right)=\left(tan\frac{\theta }{2}\right)(1+sec\theta )(1+sec2\theta )(1+sec4\theta )......(1+sec{2}^n\theta ).Then$

For the equation $x^2+bx+c=0,$ if $1+b+c=0$ for all $b,c\in R,$ then the roots are

The numbers P, Q and R for which the function
$f\left(x\right)=P{e}^{2x}+Q{e}^x+Rx$ satisfies the conditions
$f\left(0\right)=-1,f^{{}^{\prime }}\left(log2\right)=31$ and ${\int }_0^{log4}\left[f\right(x)-Rx]dx=\frac{39}{2}$ are
given by

Fill in the blanks
to make each of the following a true statement:

(i)

(ii) Φ′
∩
A = …

(iii)

(iv)