Explore topic-wise InterviewSolutions in Current Affairs.

If $\alpha$ is a root of $25{\cos }^2\theta +5\cos \theta -12=0,\frac{\pi }{2}<\alpha <\pi .$ Then the value of $\sin 2\alpha$ is equal to

In $△ABC,DC=2BD,\angle ABC={45}^{\circ }$ and $\angle ADC={60}^{\circ }.$ Find $\angle ACB$ in degrees.
(correct answer + 3, wrong answer 0)

The probability that out of 10 persons, all born in April, at least two have the same birthday is

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this.
(i) On $Z^{+}$, defined $\ast$ by $a\ast b=a-b$

(ii) On $Z^{+}$, defined $\ast$ by $a\ast b=ab$

(iii) On R, defined $\ast$ by $a\ast b=a{b}^2$

(iv) On $Z^{+}$, defined $a\ast b=|a-b|$

(v) On $Z^{+}$, defined $\ast$ by $a\ast b=a$

Given that E and F are events such that P (E) = 0.6 P (F) = 0.3 and
P$(E\cap F)=0.2,find\left(\frac{E}{F}\right)andP\left(\frac{F}{E}\right).$

Integrate the following functions.
$\int ta{n}^2(2x-3)dx.$

If $\frac{{\sin }^3\theta -{\cos }^3\theta }{\sin \theta -\cos \theta }-\frac{\cos \theta }{\sqrt{\left(1+{\cot }^2\theta \right)}}-2\tan \theta \cot \theta =-1,\theta \in \left[0,2\pi \right]$, then

${lim}_{x\to 0}\frac{\sqrt{1+3x}-\sqrt{1-3x}}{x}$

Assume that the chances of a patient having a heart attack is$40\%$. It is also assumed that a meditation and yoga course reduces the risk of heart attack by $30\%$ and prescription of certain drug reduces its chances by $25\%$. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Evaluate the definite integrals.
${\int }_2^3\frac{1}{x^2-1}dx.$

Prove using slope of midpoints of quadrilateral in order forms parallogram

Integrate the function.
$\int xse{c}^{2}xdx.$

If the line joining the points (-2, 6) and (4,8) is perpendicular to another line joining the points (8, 12) and (x, 24), then the value of x is

The sum of infinite series

$\left|\begin{array}{cc}1& 2\\ 6& 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{2}& 2\\ 2& 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{4}& 2\\ \frac{2}{3}& 4\end{array}\right|+......$ is

If $\alpha$ and $\beta$ are solutions of $si{n}^{2}x$ + a sin x + b = 0 as well as that of $co{s}^{2}x$ + c cos x + d = 0, then sin($\alpha$ + $\beta$ ) is equal to

If V and S are respectively the vertex and focus of the parabola $y^2+6y+2x+5=0,$ then SV=

If the circle $x^2+y^2+2ax+8y+16=0$
touches x-axis, then the value of a is

Two unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are pependicular to each other. Another unit vector $\overrightarrow{c}$ is inclined at an angle $\alpha$ to both $\overrightarrow{a}$ and $\overrightarrow{b}$. If $\overrightarrow{c}=x\overrightarrow{a}+y\overrightarrow{b}+z(\overrightarrow{a}\times \overrightarrow{b})$, then

$\text{A point moves as so that the difference of its distances from (ae,0)and(-ae,0)is 2 a,}\text{Prove that the equation to its locus is}\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,where{b}^2=a^2(e^2-1).$

If $tan\theta =\frac{a}{b}$, then b $cos2\theta +asin2\theta$ is equal to

$se{c}^2\left(ta{n}^{-1}x\right)+cose{c}^2\left(co{t}^{-1}x\right)=$

$\text{Find a poind on the x-axis which is equadistant from the point}(7,6)and(3,4).$

If the function $f\left(x\right)=\{\begin{array}{cc}a|\pi -x|+1,& x\le 5\\ & \\ b|x-\pi |+3,& x>5\end{array}$

is continuous at $x=5$, then the value of $a-b$ is :

The point P is the intersection of the straight line joining the points Q (2, 3, 5) and R (1, -1, 4) with the plane 5x-4y -z = 1. If S is the foot of the perpendicular drawn from the point T (2, 1 , 4) to QR, then the length of the line segment PS is

A carpet of mass $M$ is rolled along its length in the form of a cylinder of radius $R$ and kept on a rough floor. The decrease in potential energy, if the carpet is unrolled without sliding to a radius $\frac{R}{2}$ is equal to

The coefficient of xⁿ in (1+x+2x²+3x³+.....+nxⁿ)² is ?

If $\left[\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right]$ and $|A^3|=27$, then $\alpha$....

The general solution of $\cos x+\sin x=\cos 2x+\sin 2x$ is

If n(A) + n(B) + n(C) = n(AUBUC) then what are the sets A, B, C are called?

If
$\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 2\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 0& 1\end{array}\right]\cdots \left[\begin{array}{cc}1& n-1\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1& 78\\ 0& 1\end{array}\right]$,
then the inverse of $\left[\begin{array}{cc}1& n\\ 0& 1\end{array}\right]$ will be:

Let z and $\omega$be two complex numbers. If Re(z) = $|z-2|,Re\left(\omega \right)=|\omega -2|$ and arg (z $-$ $\omega$) = $\frac{\pi }{3}$, then Im (z + $\omega$)=

When 5-boys and 5-girls sit around a table the probability that no two girls come together

If $z_1$ is rotated through an angle of ${120}^{\circ }$ anti-clockwise about $z_0$ to reach $z_2$ , then $\frac{z_2-z_0}{z_1-z_0}$ equal to

Three letters are written to three different persons and addresses on the three envelopes are written.Without looking at the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is

Transforming to parallel axes through a point $(p,q),$ the equation $2x^2+3xy+4y^2+x+18y+25=0$ becomes $2x^2+3xy+4y^2=1.$ Then

A pair of dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

In the expansion of $(1+x{)}^n(1+y{)}^n(1+z{)}^n$, the sum of the coefficients of the terms of degree r is

${lim}_{x\to 0}\frac{1-cos4\theta }{1-cos6\theta }$

If $cosy=xcos(a+y),cosa\ne 1$ prove that $\frac{dy}{dx}=\frac{co{s}^2(a+y)}{sina}$

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of

A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the coordinates of

the point C.

If 5 sin $\alpha =3sin(\alpha +2\beta )\ne 0$, then the $tan(\alpha +\beta )$ is equal to

Angle between the line joining the origin to the points of intersection of the curves $2x^2+3y^2+10x=0$ and $3x^2+5y^2+16x=0$ is