Explore topic-wise InterviewSolutions in Current Affairs.

In each of the questions choose the correct answer.
If A and B are events such that $P\left(\frac{A}{B}\right)=P\frac{B}{A},$ then
(a) $A\subset BbutA\ne B$

(b) A = B

(c)$A\cap B=\varphi$

(d) P(A) = P(B)

$\underset{x\to 0}{lim}\frac{sinx+log(1-x)}{x^2}$

express the magnitude of a*b in terms of scalar product

Choose the correct answer,
Two events A and B are said to be independent, if
(a) A and B are mutually exclusive
(b) $P(A^{\prime }\cap B^{\prime })=[I-P(A\left)\right][1-P(B\left)\right]$
(c) $P\left(A\right)=P\left(B\right)$
(d) $P\left(A\right)+P\left(B\right)=1$

Find all the roots of the equation $x^7$ = 1

Is the value of the determinant different along different r o w s and columns can we evaluate one's column in the area of the triangle and get the same answer?

$\frac{sin5\theta +sin2\theta -sin\theta }{cos5\theta +2cos3\theta +2co{s}^2\theta +cos\theta }$ is equal to

If $|2x-1|+|3x-4|=|5x-5|$, then complete set of values of $x$ is

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

consider the function
$f\left(x\right)=\{\begin{array}{ccc}a+bx,x<1& & \\ 4,x=1& & \\ b-ax,x>1& & \end{array}$
If ${lim}_{x\to 1}f\left(x\right)=f\left(1\right)$, then the values of a and b are

If the eccentricity of an ellipse be $\frac{5}{8}$ and the distance between its foci be 10, then its latus rectum is

The coordinates of a point at unit distance from the lines 3x - 4y + 1 = 0 and 3x + 6y + 1 = 0 are

Acute angle bwtween the lines $ax+by+c=0$ and $x\cos \theta +y\sin \theta =c(c\ne 0)$ is ${45}^{\circ }.$ If both the lines meet with the line $y\cos \theta =x\sin \theta$ at same point, then the value of $a^2+b^2$ is

Five different games are to be distributed among 4 children randomly. The probability that each child get at least one game is

If the line $m(x-1)-m^2(y-1)+1=0$ is a tangent to a parabola for any real value of m, then the equation of the parabola is

$CsBr$ has a BCC structure where the edge length is 4.3. The shortest inter ionic distance between $C{s}^{+}$ and $B{r}^{-}$ is:

If the focus of a parabola divides a focal chord of the parabola in segments of length 3 and 2, the length of the latus rectum of the parabola is-

The least value of $\alpha ϵR$ for which $4\alpha x^2+\frac{1}{x}\ge 1$, for all x > 0, is

If A = {1, 2, 3} and B = {3, 8} then (A $\cup$ B) $\times$ (A $\cap$ B) is equal to

Number of real roots of the equation $(x^2+2{)}^2+8x^2$ = $6x(x^2+2)$ is :

Negation of "2+3 =5 and 8 is less than 10 " is

If ${}^{15}{C}_{3r}{=}^{15}{C}_{r+3},$ then r is equal to

If ${lim}_{x\to 3}\frac{x^n-3^n}{x-3}=108$, find the value of n.

If $A,B$ and $C$ represents the angles of a triangle, then $\cos A+\cos B+\cos C-1$ equal to

If $\overrightarrow{a},\overrightarrow{b}\&\overrightarrow{c}$ are 3 non-coplanar vectors and $\overrightarrow{p},\overrightarrow{q}\&\overrightarrow{r}$ are vectors defined by $\overrightarrow{p}\frac{\overrightarrow{b}\times \overrightarrow{a}}{\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]},\overrightarrow{q}=\frac{\overrightarrow{c}\times \overrightarrow{a}}{\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]}and\overrightarrow{r}=\frac{\overrightarrow{a}\times \overrightarrow{b}}{\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]}$, and, then the value of $(\overrightarrow{a}+\overrightarrow{b}).\overrightarrow{p}+(\overrightarrow{b}+\overrightarrow{c}).\overrightarrow{q}+(\overrightarrow{c}+\overrightarrow{a}).\overrightarrow{r}=$

If $\left|co{s}^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right|<\frac{\pi }{3}$ then

If $\theta$ is the exterior angle of a regular polygon of n sides and $\alpha$ is constant, then find the value of sin $\alpha$ + sin $(\alpha +\theta )$ + sin $(\alpha +2\theta )$ . . . . . up to n terms

If $f\left(x\right)=\{\begin{array}{c}{x}^2,whenx<0\\ x,when0\le x<1\\ \frac{1}{x},whenx>1\end{array}$
Find: (i) $f\left(\frac{1}{2}\right)$
(ii) $f(-2)$
(iii) $f\left(1\right)$
(iv) $f\left(\sqrt{3}\right)$
(v) $f\left(\sqrt{-3}\right)$

If the line y = 2x touches the curve y = ax^2 + bx + c at the point where x = 1 and the curve passes through the point (-1, 0), then the values of a, b, c are

The minimum value of the expression $y=|x-2|+|x+4|+|x-6|$ is

When a force of 6.0 N is exerted at 30${}^{\circ }$ to a wrench at a distance of 8 cm from the nut, it is just able to loosen the nut. What force F would be sufficient to loosen it if it acts perpendicularly to the wrench at 16 cm from the nut ?

If $A_i$ is the area bounded by $|x-a_i|+|y|=b_i,$ where $a_{i+1}=a_i+\frac{3}{2}{b}_i$ and $b_{i+1}=\frac{b_i}{2};$ $a_1=0,b_1=32,$ then

The sum of numbers between 100 and 500, which are divisible by 6, is:

The middle term in the expansion of ${(\frac{2x}{3}-\frac{3}{2x^2})}^{2n}$ is

The chord of contact of tangents drawn from any point on $x-1=0$ to $y^2-6y+4x+9=0$ passes through the point.

${lim}_{\pi \to \infty }\frac{1}{n}{\sum }_{r=1}^{2n}\frac{r}{\sqrt{n^2+r^2}}=$

From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer (ii) to include at least one officer ?

The degree of the differential equation is

[MP PET 1994, 95]

$\int e^{3logx}(x^4+1{)}^{-1}dx.$

$\frac{\sin 2A}{1+\cos 2A}$ =

If $x_r=cos\left(\frac{\pi }{3^r}\right)+isin\left(\frac{\pi }{3^r}\right)$, then $x_1{x}_2{x}_3.......to\infty is$:

The minimum value of the expression is $y=|x+1|+|x-3|$ is

A straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of ${60}^{\circ }$ with the line $x+y=0.$ Then an equation of the line $L$ is :

If 5^2×-1-25^×-1=2500,find x

The tangent to the curve, $y=x{e}^{x^2}$ passing through the point $(1,e)$ also passes through the point :

If $S_n={\sum }_{r=1}^n{t}_r=\frac{1}{6}n(2n^2+9n+13)$, then ${\sum }_{r=1}^n\sqrt{t_r}$ equals

Equation of a plane passing through the points $(2,-1,0)$ & $(3,-4,5)$ and parallel to the line $2x=3y=4z$ is