Explore topic-wise InterviewSolutions in Current Affairs.

If the straight line $x\cos \theta +y\sin \theta =2$ touches the circle $x^2+y^2-2x=0$ then

What is cosec(-585)

If A and B are two events such that A$\subset$ B and P(B) $\ne$ 0, then which of the following is correct?

$\left(a\right)P\left(\frac{A}{B}\right)=\frac{P\left(A\right)}{P\left(B\right)}\left(b\right)P\left(\frac{A}{B}\right)<P\left(A\right)\left(c\right)P\left(\frac{A}{B}\right)\ge P\left(A\right)\left(d\right)Noneofthese$

Given, A={2,3,4}, B ={2,5,6,7}. Construct an example of each of the following
(iii) a mapping from B to A.

The number of ways of distributing $20$ identical fruits among $5$ people, so that no one receives less than $3$ fruits is

Prove that the functions f(x) =5x-3 is continuous at x = 0, at x = -3 and at x=5.

Find the integrals of the functions.
$\int si{n}^2(2x+5)dx.$

If A and B be square matrices of the same order such that AB=BA, then show that (A+B)²=A²+2AB+B².

Find a particular solution of the differential equation $\frac{dy}{dx}+ycotx=4xcosecx(x\ne 0)$ given that y=0 when $x=\frac{\pi }{2}$

If P (n) is the statement "n(n + !) is even", then what is P (3) ?

The normal at any point q to the curve x = a (cos q + q sin q), y = a (sin q - q cos q)
is at distance from the origin that is equal to... .

If $\underset{x\to 0}{lim}\frac{a\tan 3x+(1-\cos 2x)}{x+\sin x+\tan x}=1$, then the value of $a$ is

Prove that:

cos x coss 2x cos 4x cos 8x = sin 16x/ 16sin x

Equation of the common tangent to the parabola $y^2=4ax$ and $x^2=4by$ is

The relation R = (x,$x^{\frac{1}{3}}$:x is a natural number less than 1000}. Find range such that all the elements of Range are integer.

Find the maximum value of $2x^3-24x+107$ in the interval [1,3]. Find the maximum value of the same function in [-3,-1].

Using elementary transformations, find the inverse of the followng matrix.

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

A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and $\frac{1}{2}$, respectively. If the probability that the student is successful, is $\frac{1}{2}$, then

(Sec ^2 A+cosec^2A^{​​​​​} )square root=tan A+cot A

IF,

1/3

(X+iy) ^ = a+ib SHOW THAT

X/a+Y/b= 4(a^2 - b^2)

​​

Find the term independent of x in the expansion of $(x^2+2x^4)(x+\frac{1}{x}{)}^{32}$

The equation of line perpendicular to $3x+5y=19$ and passing through $(3,2)$ is

Let $PAB$ be a triangle in which $PA=PB$ and the coordinates of $A$ and $B$ are $(-1,-6)$ and $(-5,-2)$ respectively. If the area of $△PAB$ is $8$ square units, then the coordinates of $P$ are

The point on the parabola which is nearest to directrix is

2. f:/R tends to R defined by f(x) {x, x<1

{x2, x is greater or equal to 1 then f inverse of (x) is

3. The domain of the function f(x) = 1/ square root of |x| - x is

${\sum }_{i=1}^{n}6i^2$ = a$n^3$ + b$n^2$ + cn + d.Then

If $A=\left[\begin{array}{ccc}1& 1& 2\\ a& 0& a\\ 1& 4& a\end{array}\right]$ is a singular matrix then the number of values of $a$ is:

The sixth term in the expansion of ${[\sqrt{\left\{2^{\log (10-3^x)}\right\}}+\sqrt[5]{5\left\{2^{(x-2)\log 3}\right\}}]}^m$ is equal to $21$. If it is known that the binomial coefficient of the $2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ terms in the expansion represents respectively the first, third and fifth terms of an A.P. (the symbol log stands for logarithm to the base $10$) then sum of possible values of $x$ is

The function f(x) = cos x is

Two rods of same length and cross-sectional area are joined in series. Thermal conductivity of the rods are in ratio of $2:1$.


The ends are maintained at temperatures ${\theta }_A$ and ${\theta }_B$ as shown with ${\theta }_A>{\theta }_B$ and sides are thermally insulated.
Which of the following graph represents temperature gradient $\left(\frac{dT}{dx}\right)$ against $x$ in steady state.

If

$[x4-1]\left[\begin{array}{ccc}2& 1& 0\\ 1& 0& 2\\ 0& 2& 4\end{array}\right]\left[\begin{array}{cc}x& \\ 4& \\ -1& \end{array}\right]=0,thenx=$

If y = $ta{n}^{-1}\sqrt{\left(\frac{1+sinx}{1-sinx}\right)},\frac{\pi }{2}<x<\pi$, then $\frac{dy}{dx}$ equals

If $f\left(x\right)=a{x}^2+bx+c$ $a,b,cϵR$ and the equation $f\left(x\right)-x=0$ has imaginary roots $\alpha$ and $\beta$ and $\gamma$ and $\delta$ be the roots of $f\left(f\right(x\left)\right)-x=0,then\left|\begin{array}{ccc}2& \alpha & \delta \\ \beta & 0& \alpha \\ \gamma & \beta & 1\end{array}\right|$ is

Let $f:R^{+}\to R^{+}$ be a function satisfying the relation \(f(x.f(y))=f(xy)+x~for~all~x,y \epsilon R^{+}\). Then $\underset{x\to 0}{lim}\left(\frac{\left(f\right(x){)}^{\frac{1}{3}}-1}{\left(f\right(x){)}^{\frac{1}{2}}-1}\right)$=

The equation of parabola whose latus rectum is the line segment joining the points (–3, 1), (1, 1) is

Polar form of $z=\frac{(1+7i)}{(2-i{)}^2}$ is

Let $f:R\to (0,1)$ be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval (0, 1)?

If $\alpha$ and $\beta (\alpha <\beta )$ are the roots of the equation $x^2+bx+c=0$, where $c<0<b,$ then

For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than $2\sqrt{2}$. Then

If $\theta =\frac{2\pi }{7}$, then the value of tan $\theta$ tan $2\theta +tan2\theta$ tan $4\theta +tan4\theta$ tan $\theta$ is