Explore topic-wise InterviewSolutions in Current Affairs.

If z is the complex number. Which of the following is/are true?

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ , then $A^2$ equal to …….

Choose the word which is most OPPOSITE in meaning to the word as used in the passage:

Sophisticated

If coordinates of the centre and one end of a diameter of a circle are $(7,3)$ and $(5,-7)$ respectively, then the coordinates of the other end of the diameter are

For a positive integer n, if the mean of the binomial coefficients in the expansion of $(a+b{)}^{2n-3}$ is 16, then n is equal to

If the equations of four circles are $(x\pm 4{)}^2+(y\pm 4{)}^2=4^2$ then the radius of the smallest circle touching all the four circles is

12 persons are to be arranged around two round table such that one table can accommodate seven persons and another five persons only.

Number of ways of arrangement if 2 particular persons A and B do not want to be on the same table is

If $A=\left(\begin{array}{cc}i& -i\\ -i& i\end{array}\right)$ and $B=\left(\begin{array}{cc}1& -1\\ -1& 1\end{array}\right),$ then $A^8$ equals

If log₁₀ x = p, then 10^{2p - 3} in terms of x is

The expression $\sim (p\vee q)\vee (\sim p\wedge q)$ is logically equivalent to

If the equation asinx + cos2x = 2a–7 possesses a solution then a $ϵ$

A hyperbola has centre C and one focus at P(6, 8). If its two directrices are 3x + 4y + 10 = 0 and 3x + 4y – 10 = 0 then CP =

Three identical bodies are at temperature $T_1,T_2$ and $T_3$ having $e_1,e_2$ and $e_3$ as their respective emissivities. The thermal spectrum obtained for them is as shown in the diagram. Choose the correct order of temperatures and emissivities.

Through a point P(f, g, h) a plane is drawn at right angles to OP, to meet the axes in A, B, C. If OP = r, the
centroid of the triangle ABC is

If x = cy + bz, y = az + cx, z = bx + ay where x, y, z are not all zeros, then the value of $a^2+b^2+c^2+2abc$ is

In a single throw of two dice, the probability of getting more than 7 is

[MP PET 1991]

If centroid of the tetrahedron OABC, where A,B,C are given by (a, 2, 3),(1, b, 2) and (2, 1, c) respectively be (1, 2, -1), then distance of P(a,b,c) from origin is equal to

${\int }_0^{\frac{x}{2}}\frac{x+sinx}{1+cosx}dx=$ [Roorkee 1978]

Which of the following is/are true?

The equation of a tangent to the parabola, $x^2=8y$, which makes an angle $\theta$ with the positive direction of $x$-axis, is :

The value of $\sum _{r=1}^{n}r\times r!$ is

If the lines $x+y=|a|$ and $ax-y=1$ intersect each other in the first quadrant, then the range of $a$ is

${lim}_{x\to 3}\frac{x^2-4x+3}{x^2-2x-3}$

A sequence $a_1,a_2,a_3,.......$ is defined by letting $a_1=3$ and $a_k=7$ $a_{k-1}$ for all natural numbers $k\ge 2$. Show that $a_n={3.7}^{n-1}$ for all $nϵN$.

The amplitude of $\frac{1+i\sqrt{3}}{\sqrt{3}+i}$ is

If $I_1=\underset{0}{\overset{\pi }{\int }}\frac{\cos x}{(x+2{)}^2}dx,$ $I_2=\underset{0}{\overset{\pi /2}{\int }}\frac{\cos x\sin x}{(x+1)}dx$ and $\lambda I_2=\frac{2}{\mu +\pi }+k-\gamma I_1,$ then

If it is agreed that the capital of all the partners be proportionate to the new profit sharing ratio at the time of admission of new partner. How will you work out the new Partner's capital?

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4.

One kind of cake requires 200 g of flour and 25 g of fat and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.

Ravi and Rashmi are each holding $2$ red cards and $2$ black cards (all four red and all four black cards are identical). Ravi picks a card at random from Rashmi, and then Rashmi picks a card at random from Ravi. This process is repeated a second time. Let $p$ be the probability that both have all $4$ cards of the same colour. Then $p$ satisfies

If $\tan {40}^{\circ }+2\tan {10}^{\circ }=\cot x$, where $x\in (0,\pi /2)$, then the possible value of $x$ is

The velocity-time graph is given as


The most probable acceleration-time graph is

The graph of $|x|+|y|=1$ is

Find the second order derivative of the given functions.

x cos x

Integrate the following functions.
$\int \sqrt{ax+b}$ dx.

If $PSQ$ is the focal chord of a parabola such that $SP=2$ and $SQ=4$ then the length of the latus rectum is

Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of $x+2y=5$ and $x-3y=7$.