Explore topic-wise InterviewSolutions in Current Affairs.

For the set of all natural numbers the universal set can be

Check the injectivity and surjectivity of the following functions:
$\left(i\right)f:Z\to Z$ given by $f\left(x\right)=x^2$

Find the inverse of the given matrix
$\left[\begin{array}{cc}-1& 5\\ -3& 2\end{array}\right]$

If $A$ is a $3\times 3$ non singular matrix and $A^3+3A^2-2A=0$ then find $A^{-1}$.

An event A has the outcomes $w_1,w_2,w_3$ and $w_4$ with probabilities $\frac{1}{12},\frac{1}{12},\frac{1}{6}$ and $\frac{1}{3}$.If the

probability of event A is P(A),find 24 P(A).

The number of common tangents to the circles $x^2+y^2-4x-6y-3=0$ and $x^2+y^2+2x+2y+1=0$ is

(1/x-1)+(2/x+1)-(3/x)=0

If the normals at $(x_i,y_i),\text{where,}i=1,2,3,4$ on the rectangular hyperbola $xy=c^2$ meet at $(\alpha ,\beta ).$ and $x_1{x}_2{x}_3{x}_4=a$ and $y_1{y}_2{y}_3{y}_4=b$, then $a+b$ is

Sovle the differential equation: $(1+x^2)\frac{dy}{dx}+y=e^{ta{n}^{-1}x}$

Let the line $y=mx$ and the ellipse $2x^2+y^2=1$ intersect at point $P$ in the first quadrant. If the normal to this ellipse at $P$ meets the co-ordinate axes at $(-\frac{1}{3\sqrt{2}},0)$ and $(0,\beta )$, then $\beta$ is equal to:

Let a,b,c be positive real numbers. The following system of equations in x,y,z

$\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=1,-\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1,-\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

In a G.P. if the $(m+n{)}^{th}$ term is p and $(m-n{)}^{th}$ term is q, then its $m^{th}$ term is

Mean of $n$ observations $x_1,x_2,\cdots ,x_n$ is $\overline{x}$. If an observation $x_q$ is replaced by $x_q^{\prime }$ then the mean is

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\frac{\pi }{2}}\frac{co{s}^{5}x}{si{n}^{5}x+co{s}^{5}x}dx.$

Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\frac{dp\left(t\right)}{dt}=\frac{1}{2}p\left(t\right)-200$. If $p\left(0\right)=100$, then $p\left(t\right)$ equals:

If x^3 + pX + q =0 has two equal roots then find 4p^3+27q^2

In $△PQR,PQ=13,QR=14$ and $PR=15$. A altitude is drawn from $P$ and a parallel line is drawn as $LM$ which divides the triangle into two equal areas, then the length of $PL$ is

One card is drawn at random from a well- shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
E : the card drawn is black, F: the card drawn is a king

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is:

If p and q are simple statements, $p\iff \sim q$ is true when

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\frac{\pi }{2}}\frac{si{n}^{\frac{3}{2}}}{si{n}^{\frac{3}{2}}x+co{s}^{\frac{3}{2}}x}dx.$

Write minors and cofactors of elements of following determinants

$\left|\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right|$

$\left|\begin{array}{ccc}1& 0& 4\\ 3& 5& -1\\ 0& 1& 2\end{array}\right|$

Differentiate the following functions with respect to x :

$e^{x}loga+e^{a}logx+e^{a}loga$

Let $\overrightarrow{a}=\hat{i}-2\hat{j}+3\hat{k}$, if $\overrightarrow{b}$ is a vector such that $\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{b}{|}^2$ and $|\overrightarrow{a}-\overrightarrow{b}|=\sqrt{7}$, then $|\overrightarrow{b}|=$

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

$\int \frac{1}{(x^2+1)(x^2+4)}dx.$

If $tan\left(\frac{3\pi }{11}\right)+4sin\left(\frac{2\pi }{11}\right)=\lambda$ then the value of ${\lambda }^2-9$ is equal to ___

The parabola $y^2=4x+1$ divides the disc $x^2+y^2\le 1$ into two regions with areas $A_1$ and $A_2$. Then $|A_1-A_2|$ equals

${lim}_{x\to 3}(x^2-9)(\frac{1}{x+3}+\frac{1}{x-3})$

If the vertex of parabola y = $x^2$-8x + c lies on x - axis, then the value of c is

Write the argument of :

$(1+i\sqrt{3})(1+i)(cos\theta +sin\theta )$

Prove that:

$co{s}^2(\frac{\pi }{4}-\theta )-si{n}^2(\frac{\pi }{4}-\theta )=sin2\theta$

From the sets given below, pair the equivalent sets :

A = {1, 2, 3}, B = {t, p, q, r, s}, C = {$\alpha ,\beta ,\gamma$ }, D = {a, e, i, o,u}.

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the centre of the hyperbola, then eccentricity of the hyperbola is

Find the mirror image of the point $(1,2,2)$ on the line
$\frac{x-5}{2}=\frac{y-3}{2}=\frac{z-2}{1}$ .

Find the coordinates of the incentre and centroid of the triangle whose sides have the equations $3x-4y=0,12y+5x=0$ and $y-15=0.$

(a) Complete the following table.

$\begin{array}{ccc}\text{MPC}& \text{MPS}& \text{Multiplier}\\ 0& -& -\\ -& 0.5& -\\ -& -& 4\end{array}$

(b) Why rise in MPC leads to increase in Multiplier?

The lengths (in cm) of 10 rods in a shop are given below :

40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2

(i) Find mean deviation from median

(ii) Find mean deviation from the median also.

Let α and β be the roots of x²-6x-2 =0 with α>β. If a_n = α_n - β_n for n≥1, then the value of

Find the equation of a line making an angle of ${150}^{\circ }$ with the x-axis and cutting off an intercept 2 from y-axis.

The number of real solutions of the equation $(\sin x-x)(\cos x-x^2)=0$ is

${lim}_{x\to \frac{\pi }{3}}\frac{\sqrt{1-cos6x}}{2(\frac{\pi }{3}-x)}$

The owner of a milk store finds that he can sell 980 liters milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.