Explore topic-wise InterviewSolutions in Current Affairs.

The roots of the equation
$(a+\sqrt{b}{)}^{x^2-15}+(a-\sqrt{b}{)}^{x^2-15}=2a$, where $a^2-b=1$ are

An ellipse has OB as a semi minor axis. F and F’ are its foci, and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is

Differentiate given problems w.r.t.x.
$x^{x^2-3}+(x-3{)}^{x^2},forx>3$

If the normal at the point $P\left(\theta \right)$ to the ellipse $\frac{x^2}{14}+\frac{y^2}{5}=1$ intersects it again at the point $Q\left(2\theta \right)$, then

The value of $2{\tan }^{-1}\left[\sqrt{\frac{a-b}{a+b}}\tan \frac{\theta }{2}\right]$ is equal to

How many 9 - digit numbers of different digits can be formed?

Let A = {3, 5} and B = {7, 11}. Let $R=\left\{\right(a,b):aϵA,bϵB,a-b$ is odd}. Show that R is an empty relation from A into B.

Find the distance of the line 2x + y = 3 from the point (-1, -3) in the direction of the line whose slope is 1.

Two lines $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$ and $\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}$ intersect at the point $R$. The reflection of $R$ in the $xy$- plane has coordinates :

How many of the following are not properties of equivalence classes?

1. All elements of an equivalence class will be related to each other
2. No element of an equivalence class will be related to an element of another equivalence class
3. All the equivalence classes, which are sets, are disjoint
4. Union of all the equivalence classes of particular relation will give the set A on which we defined the relation

If $\alpha ,\beta$ are two different vlaues of $\theta$ lying between 0 and $2\pi$ which satisfy the equations 6 cos \theta + 8 sin\theta= 9, find the value of sin $(\alpha +\beta )$.

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

If $\int \frac{\mathrm{dx}}{4{\sin }^{2}x+6{\cos }^{2}x}$$=a{\tan }^{-1}\left(\frac{2\mathrm{tanx}}{\sqrt{6}}\right)+C$, then $a$ is

Show that $x^2+xy+y^2,z^2+zx+x^2$ and $y^2+yz+z^2$ are consecutive terms of an A.P., if $x,y$ and $z$ are in A.P.

$\frac{5x+8}{4-x}<2$

If both the roots of the quadratic equation $x^2-(2n+18)x-n-11=0,n\in Z$ are rational, then the value(s) of $n$ is/are

Let $z=x+iy$ be a complex number such that $|z|=1$, where $i=\sqrt{-1}$. Match List - I with List - II.

$\begin{array}{cccc}\text{List-I}& & \text{List - II}& \\ \text{(I)}& \text{Re}\left(\frac{iz}{1+z^2}\right)\text{is equal to}& \text{(P)}& 0\\ \text{(II)}& \text{Im}\left(\frac{iz}{1+z^2}\right)\text{can be equal to}& \text{(Q)}& 1\\ \text{(III)}& \text{Number of integers NOT in the}& \text{(R)}& \frac{1}{2}\\ & \text{range of}\text{Im}\left(\frac{iz}{1+z^2}\right)\text{is equal to}& & \\ \text{(IV)}& \frac{1}{2\pi }\arg \left(\frac{iz}{1+z^2}\right)\text{is equal to}& \text{(S)}& -\frac{1}{2}\\ & (\text{where}-\pi <\arg (z)\le \pi )& & \\ & & \text{(T)}& -\frac{1}{4}\\ & & \text{(U)}& \frac{1}{4}\end{array}$

Which of the following is only CORRECT combination?

If $b$ is the first term of an infinite $G.P.$ whose sum is five, then $b$ lies in the interval :

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?

Find the number of solutions of $5^x=x^2+x+1$.

If $k+|k+z^2|=|z{|}^2,(k\in R^{-})$, then possible argument of $z$ is

If $z_1,z_2,z_3$ are the vertices of a triangle in argand plane such that $|z_1-z_2|=|z_1-z_3|,$ then $\arg (\frac{2z_1-z_2-z_3}{z_3-z_2})$ is

${lim}_{x\to \infty }\sqrt{x^2+cx}-x$

The number of 6 digit numbers that can be made with the digits 1,2,3 and 4 and having exactly two pairs of digits, is

Assume X,Y,Z, W and P are matrices of orders $2\times n,3\times k,2\times p,n\times 3andp\times k$ respectivley. Choose the correct answer in Q.21 and Q.22.
If n = p, then the order of the matrix 7X-5Z is
$\left(a\right)p\times 2$
$\left(b\right)2\times 2$
$\left(c\right)n\times 3$
$\left(d\right)p\times n$

The value of $\underset{x\to 2}{lim}\frac{x^3-4x^2+4x}{x^2-4}$

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding / cutting machine and a sprayer. It takes 2 h on grinding / cutting machine and 3 h on the sprayer to manufacture a pedestal lamp. It takes 1 h on the grinding / cutting machine and 2 h on the sprayer to Manufacture a shade. On any day, the sprayer is available for at the most 20 h and the grinding / cutting machine for at most 12 h. The profit from the sale of a lamp is Rs. 5 and that from a shades is Rs. 3. Assuming that the manufacture can sell all the lamps and shades that he produce, how should he schedule his daily production in order to maximize his profit?

A wheel makes 360 revolutions in 1 minute, Through how many radians does it turn in 1 second ?

In the following exercises find the distance of each of the given points from the corresponding given plane:

$\begin{array}{cc}point& Plane\\ \left(a\right)(0,0,0)& 3x-4y+12z=3\end{array}$

$\begin{array}{cc}point& Plane\\ \left(b\right)(3,-2,1)& 2x-y+2z+3=0\end{array}$

$\begin{array}{cc}point& Plane\\ \left(c\right)(2,3,-5)& x+2y-2z=9\end{array}$

$\begin{array}{cc}point& Plane\\ \left(d\right)(-6,0,0)& 2x-3y+6z-2=0\end{array}$

Differentiate given problems w.r.t.x.

$si{n}^{-}1\left(x\sqrt{x}\right),0\le x\le 1$.

(P) If k be the number of common tangents to $4x^2+9y^2=36$ and $x^2+(y-1{)}^2=2$ then k is greater than or equal to.
(Q) If m be the number of points of intersection of $y^2=8x+3$ and $2x^2+y^2=4$ then m is less then or equal to-
(R) If $\lambda$ be the number of common normals of $y^2=4x$ & $(x-10{)}^2+(y-1{)}^2=1$ then $\lambda$ is greter than or equal to-
(S) If y = mx + 4 is tangent to the parabela $x^2+16y=0$ then |m| is less then or equal to.

What is the condition for the line y = mx + c to be a secant of the circle $x^2+y^2=a^2$

Solution set of the equation $\left|\frac{x}{x-1}\right|+|x|=\frac{x^2}{|x-1|}$ is :

In $△$ ABC, a sin (B - C) + b sin (C - A) + c sin (A-B) =
[ISM Dhanbad 1973]

A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?

For any vector $\overrightarrow{x}$, the value of $(\overrightarrow{x}\times \hat{i}{)}^2+(\overrightarrow{x}\times \hat{j}{)}^2+(\overrightarrow{x}\times \hat{k}{)}^2$ is equal to

If the polynomial $f\left(x\right)=\left|\begin{array}{ccc}(1+x{)}^a& (2+x{)}^b& 1\\ 1& (1+x{)}^a& (2+x{)}^b\\ (2+x{)}^b& 1& (1+x{)}^a\end{array}\right|,$ then the constant term of $f\left(x\right)$ is

If the line $y=x\sqrt{3}-3$ cuts the parabola $y^2=x+2$ at P and Q if A be the point $(\sqrt{3},0)$, then AP. AQ is

If $|x-{\log }_{\sqrt{3}/2}\left(\frac{64}{27}\right)|=1$, then the value of $x$ is/are

$\frac{(cos\theta +isin\theta {)}^4}{(sin\theta +icos\theta {)}^5}$ is equal to

The intergral $\int \frac{2x^{12}+5x^9}{(x^5+x^3+1{)}^3}$dx is equal to :