Explore topic-wise InterviewSolutions in Current Affairs.

The general solution of $\tan \alpha +2\tan 2\alpha +4\tan 4\alpha +8\cot 8\alpha =\sqrt{3}$ is
$(\text{where}n\in Z)$

Find the sum of n terms of the series whose general term is

n⁴+6n³+5n².

The shortest distance between the point $(2,1)$ and the curve $y^2=4x$ is

If x³-1/x³=14, then x-1/x=

The equation of a plane passing through $\overline{r}.(\hat{i}+\hat{j}+\hat{k})=1$ and $\overline{r}.(2\hat{i}+\hat{k})=2$ can be given by

The value of the expression ${\left({\int }_0^{14}{\sin }^2\pi xdx\right)}^2\times [{\left(\sum _{k=0}^{\infty }\frac{k}{7^k}\right)}^{-1}+13]$ is

The three lines 3x + 4y + 6 = 0, $\sqrt{2}x+\sqrt{3}y+2\sqrt{2}=0$ and 4x + 7y + 8 = 0 are

A wire of length 28 cm is to be into two pieces. One of the pieces to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

Prove that
the curves x = y² and xy = k cut at
right angles if 8k² = 1. [Hint: Two
curves intersect at right angle if the tangents to the curves at the
point of intersection are perpendicular to each other.]

The equation of a plane bisecting the angle between the plane $2x-y+2z+3=0$ and $3x-2y+6z+8=0$ is/are:

[Hint:
Put e^x = t]

In a game, winning is defined by the outcome $6$ on a die. Three players $A,B,C$ play this game. The die is first thrown by $C,$ followed by $A,$ and then $B.$ If the order of throwing the die is same for all rounds, then the probability that $A$ wins the game, is

The range of $f\left(x\right)={\log }_{11}(3\sin x+4\cos x+6)$ is

Total number less than $3\times {10}^8$ and can be formed using the digits $1,2,3$ is equal to $\frac{a}{b}\left(\right[a+2b]\cdot a^7-1)$, then

Number of $4$ digit numbers using digits $0,1,2,3,4,5$ which are divisble by $11$, when each digit is used at most once is

A={1, 2, 3, 4, …, 14}. Let R be a relation from A to A defined by
R = {(a, b):3a – b = 0, a, b∈ A} then domain of R is

A die is thrown 6 times. If getting an odd number is a success, What is the probability of

(ii) atleast 5 sucesses?

The value of $\frac{1}{2}+\frac{1}{3^2}+\frac{1}{2^3}+\frac{1}{3^4}+\frac{1}{2^5}+\frac{1}{3^6}+\cdots \cdots \infty$ is

If the roots of the equation $4x^2+ax+3=0$ are in ratio of $1:2$, then value(s) of $a$ is/are

Match the following

$x+y+z=2$

$x+y+\lambda z=1$

$x+\mu y+2y=3$

(a) $\mu =1,\lambda =1$ (i) No solution

(b) $\mu =2,\lambda =3$ (ii) Unique Solution

(c) $\mu =1,\lambda =0$ (iii) Infinite Solutions

For any two sets $A\&B,$ if $n(A\cup B)=100;n\left(A\right)=45,n\left(B\right)=60,$ then $n(A\cap B)=$

The equation of the tangents to the ellipse $3x^2+4y^2=12,$ which are perpendicular to the line $y+2x=4,$ are

The solution of the equation $(x^{2}y+x^2)dx+y^2(x-1)dy=0$ is (where $c$ is constant of integration)

Let p be a prime number. If p divides $a^2$ then p divides a, where a is a positive integer. Which theorem is this statement previously based on?

Minimise
and Maximise Z = x + 2y

subject
to.

Differentiate the following functions with respect to x :

$\frac{e^x+sinx}{1+logx}$

The angle between the pair of tangents of the parabola $y^2+12x=0$ which are normal to $x^2+y^2-6x-7y-4=0$ is

If x = 9 is the chord of contact of the hyperbola $x^2-y^2=9$, then the equation of the corresponding pair of tangents is

Sum of the real roots in the equation $x^2|x|-17x^2+95|x|-175$ = 0 is:

If the sides of a right angle triangle forms an AP, then 'sin' of the acute angles are

If the mean and variance of six observations $7,10,11,15,a,b$ are $10$ and $\frac{20}{3},$ respectively, then the value of $|a-b|$ is equal to:

If geometric mean between x and y is G, then value of $\frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}$ is equal to

The value of $k$ for which the lines $\frac{x+1}{-3}=\frac{y+2}{2k}=\frac{z-3}{2}\text{and}\frac{x-1}{3k}=\frac{y+5}{1}=\frac{z+6}{7}$ may be perpendicular is:

Let $f$ and $g$ be two functions defined as $f\left(x\right)=f(a-x)$ and $g\left(x\right)+g(a-x)=4,$ then the value of $\underset{0}{\overset{a}{\int }}f\left(x\right)g\left(x\right)dx$ is