Explore topic-wise InterviewSolutions in Current Affairs.

The interval in which $y=x^2{e}^{-x}$ is increasing with respect to x is

a) $(-\infty ,\infty )$
b) (-2, 0)
c) $(2,\infty )$
d) (0.2)

Find domain of

(Cos2x)^1/2 + (16 - x² )^1/2

Find the value of x, y and z from the following equations:
$\left(ii\right)\left[\begin{array}{cc}x+2& 2\\ 5+z& xy\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 5& 8\end{array}\right]$

A commitee of six is chosen from ten men and seven women so as to contain atleast three men and two women. If two particular women refuse to serve on the same committee, the number of ways of forming the committee is:

The points of discontinuity of the function $f\left(x\right)={lim}_{n\to \infty }\frac{(2\sin x{)}^{2n}}{3^n-(2\cos x{)}^{2n}}$ are given by

Let $I_1={\left(\frac{\pi }{4}\right)}^2+\sqrt{2},I_2={\left(ta{n}^{-1}\left(\frac{1}{e}\right)\right)}^2+\frac{2e}{\sqrt{e^2+1}},I_3=(ta{n}^{-1}e{)}^2+\frac{2}{\sqrt{e^2+1}}$, then which of the following is true?

Show that the given differential equation is homogeneous and then solve it.

$y^{\prime }=\frac{x+y}{x}$

The equation of chord of ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ whose sum and difference of eccentric angles are $\frac{\pi }{3}$ and $\frac{2\pi }{3}$ respectively is

Coefficient of $x^{11}$ in the expansion of $(1+x^2{)}^4(1+x^3{)}^7(1+x^4{)}^{12}$ is

Q1- Find the approximate value of f (3.02) where f (x) =3x²+5x+3

Q2- find the approximate value of(31.9)^1/5

In the plot of the function below. Which is the point at which the discontinuity is of removable type?

If $\frac{a}{|z_1-z_2|}=\frac{b}{|z_2-z_3|}=\frac{c}{|z_3-z_1|}\text{where}(a,b,c\in R),$ then value of $\frac{a^2}{z_1-z_2}+\frac{b^2}{z_2-z_3}+\frac{c^2}{z_3-z_1}$ is

$a^{2}sin(B-C)=(b^2-c^2)sinA$

Trigonometric series of the form
$\frac{\sin (A-B)}{\cos A\cdot \cos B}+\frac{\sin (B-C)}{\cos B\cdot \cos C}+\frac{\sin (C-D)}{\cos C\cdot \cos D}$
$=\tan A-\tan D$
As we know that,
$\frac{\sin (A-B)}{\cos A\cdot \cos B}=\tan A-\tan B$
Based on the above given information, find sum of the series
$\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x}+\cdots$ upto $n$ terms

We rotated vector A through an angle θ about its tail and we get a vector B. We rotated the same vector A through an angle θ about the centre of the vector and we get C as shown in the figure. Choose the correct option?

Let $f:R\to R$ be a function defined by $f\left(x\right)=x^3+x^2+x-1.$ If $g$ is the inverse of $f,$ then $g^{\prime }\left(2\right)$ is

If $A=\{x:x=2k,k\in N\text{and}k\le 100\}$, $B=\{x:x=2^k,k\in W\text{and}k<11\}$ and $C=\{x:x=k^3,k\in N\text{and}k<11\}$, then the value of $n\left(A△B\right)+n\left(B△C\right)+n\left(A△C\right)$ is

There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

Let A = {1, 2} and B = {3, 4}. Find the total number of relations from A into B.

Let $A=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$ be a $2\times 2$ real matrix with $detA=1$. If the equation det $(A-\lambda I_2)=0$ has imaginary roots $(I_2$ be the Identify matrix of order $2)$, then

The equation of reflection of the ellipse $\frac{(x-4{)}^2}{16}+\frac{(y-3{)}^2}{9}=1$ about the line $x-y-2=0$ is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

Find the slope of the tangent to the curve $y=\frac{x-1}{x-2},x\ne 2$ at x=10.

The equilateral $\Delta ABC$ has vertices $B(1,0)$ and $C(5,0).$ If $A$ lies in the fourth quadrant, then the equation of the incircle of $\Delta ABC$ is

Find the solution to the following system of linear equations:
x-2y=6
2x+y=17

Suppose the propositions p,q and r have the truth values F,F,T respectively, then the truth value of $\sim q\Lambda randp\to (\sim q\Lambda r)$are

The quotient obtained when $15x^6-9x^4+x^3+6x+12$ is divided by $3x^2$ is

Draw the graph of $y=\left[e^{\left[x\right]}\right]$

The co-ordinates of a point which is equidistant from the points (0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c) are given by [MP PET 1993]

If words are formed by taking only $4$ at a time out of the letters of the word "PHYSICAL", then the number of words in which 'Y' occur is

The locus of point of intersection of two normals drawn to the parabola $y^2=4ax$ which are at right angles is

The point of intersection of the tangents to the parabola $y^2=4x$ at the points where parameter 't' has value 3 and 5.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability. that
one of them is black and other is red

Find the local maxima and local minima, if any of the following function. Also, find the local maximum and the local minimum values, as the case may be as follows.

$f\left(x\right)=x^3-6x^2+9x+15$

Select the correct structure of the sentence.

N = noun phrase; V = verb phrase; Adj = adjective phrase; p = prepositional phrase

The crowd dispersed.

If a, b, c are positive real number, then minimum value of $\frac{a^3}{4b}+\frac{b}{8c^2}+\frac{1+c}{2a}$, is

There are four boxes $A_1,A_2,A_3$ and $A_4$. Box $A_i$ has i cards and on each card a number is printed, the numbers are from 1 to i. A box is selected randomly, the probability of selection of box $A_i$ is $\frac{i}{\sum i}$ and then a card is drawn. Let $E_i$ represents the event that a card with number 'i' is drawn.

$P\left(E_1\right)$ is equal to

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

Let $A=\{1,4,9,25\}$ and $B=\{-5,-3,-2,-1,1,2,3,5\}$, if relation from $A$ to $B$ is $R=\left\{\right(1,1),(1,-1),(4,2),(4,-2),(9,3),(9,-3),(25,5),(25,-5\left)\right\}$, then the set builder form of relation is

Find the equation of the perpendicular bisector of the line joining the points $(1,3)$ and $(3,1).$