Explore topic-wise InterviewSolutions in Current Affairs.

Philately helps keep the past alive. Discuss other ways in which this is done. What do you think of the human tendency to constantly move between the past, the present and the future?

If x is parallel to y and z where $x=2\hat{i}+\hat{j}+\alpha k,y=\alpha \hat{i}+\hat{k}$ and $z=5\hat{i}-\hat{j},$ then $\alpha$ is equal to

If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are vectors such that $\overrightarrow{a}\cdot \overrightarrow{b}=0$ and $\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{c},$ then

Prove the following:
$\frac{\text{sin x - sin 3x}}{{\text{sin}}^{2}x-{\text{cos}}^{2}x}=2\text{sin}$ x.

Ravi
obtained 70 and 75 marks in first two unit test. Find the minimum
marks he should get in the third test to have an average of at least
60 marks.

If $z_1,z_2,z_3,z_4,z_5$ and $z_6$ are vertices in anticlockwise direction of a regular hexagon whose circumcentre is origin and vertex $z_1=2+6i,$ then

Let $r_1$ and $r_2$ be the radii of the largest and smallest circles, respectively, which pass through the point $(–4,1)$ and having their centres on the circumference of the circle $x^2+y^2+2x+4y-4=0.$ If

$\frac{r_1}{r_2}=a+b\sqrt{2,}$ then $a+b$ is equal to:

$\mathrm{If}A=\left(\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\mathrm{and}I=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\mathrm{then}\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{holds}\mathrm{for}\mathrm{all}n\in N?$

If $A$ is a skew symmetric matrix, then which of the following is/are true?

The equation of the plane through the line of intersection of $2x-y+3z+1=0,x+y+z+3=0$ and parallel to the line $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ is:

A set $A=\{b:b<5\&b\in I\}$, where $I$ denote integers, then tap on the correct bubbles.

The domain of $f\left(x\right)=\sqrt{{\log }_{2}x}-{\log }_2\sqrt{x}$ is

A player tosses a coin and scores one point for every head and two point for every tail that truns up. He plays on until his scores reaches or psses $n$. $P_n$ denotes the probability of getting a scores of exactly $n$
$$\begin{array}{cc}\text{List I}& \text{List II}\\ \begin{array}{cc}\text{(a)}& \text{the value of}{P}_n\text{is}\end{array}& \text{(p)}1\\ \begin{array}{c}\text{(b) the value of}{P}_n+\frac{1}{2}{P}_{n-1}\end{array}& \text{(q)}\frac{5}{4}\\ \begin{array}{c}\text{(c)}2P_{101}+P_{100}\end{array}& \text{(r)}2\\ \begin{array}{c}\text{(d)}{P}_1+P_2\end{array}& \text{(s)}\frac{1}{2}[P_{n-1}+P_{n-2}]\end{array}$$
$\text{Which of the following is the only}\text{correct option?}$

If 0 < a < b,then $\underset{n\to \infty }{lim}(b^n+a^n{)}^{1/n}$ is equal to

The instantaneous rate of change of f(x) =$e^x$ at x = a is given as $e^2$ Find the value of a.

If the lines $x+y=|a|$ and $ax-y=1$ intersect in the first quadrant then

For the following question verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

$y=xsin3x:\frac{d^{2}y}{d{x}^2}+9y-6cos3x=0.$

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3}+\frac{y^2}{4}=4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does NOT lie on it?

If $\int {\sin }^{2}x{\cos }^{3}xdx=\frac{\left[f\right(x){]}^3}{3}-\frac{\left[f\right(x){]}^5}{5}+C,$ then the value of $f\left(\frac{\pi }{3}\right)$ is

(where $C$ is integration constant)

The equation of the parabola with focus (3, 0) and the directirx x +x3 = 0 is

In $\Delta ABC,$ the value of $\sum a{\cos }^2\frac{A}{2}$ is:

The remainder when, ${10}^{10}({10}^{10}+1)({10}^{10}+2)$ is divided by 6 is

The value of ${\tan }^{-1}(-1)$ is

The order of the differential equation whose solution is , is

[MP PET 1995]

The number of ways in which $3$ scholarships of unequal value be awarded to $17$ candidates, such that no candidate gets more than one scholarship is

If $f\left(x\right)$ is a continuous function for all real values of $x$ and satisfises $\underset{n}{\overset{n+1}{\int }}f\left(x\right)dx=\frac{n^2}{2}\forall n\in I$, then $\underset{-3}{\overset{5}{\int }}f\left(|x|\right)dx$ is equal to

If the locus of mid point of the chords of the parabola $y^2=4ax$ which passes through a fixed point $(h,k)$ is also a parabola, then length of its latus rectum (in units) is

If the length of tangents from vertices to incircle are in $H.P.$ then $r_1,r_2,r_3$ are in: