Explore topic-wise InterviewSolutions in Current Affairs.

Solution of the equation $xdy=(y+x\frac{f\left(\frac{y}{x}\right)}{f^{\prime }\left(\frac{y}{x}\right)})dx$

Out of $20$ consecutive integers, two are chosen at random. The probability that their sum is odd is

If $x-2y=11$ and $xy=8$ find the value of $x^3-8y^3$.

If $f\left(x\right)=\{\begin{array}{cc}x,& when0<1/2\\ 1,& whenx=1/2\\ 1-x& when1/2<x<1\end{array}$ , then

Six-digit odd numbers, greater than $6,00,000$ that can be formed using the digits $5,6,7,8,9$ and $0$ if repetition of digits is not allowed is :

How many equivalence classes can be formed on a deck of cards, with respect to the relation "Belongs to the same suit"

How many three -digit odd numbers are there ?

Show that the greatest integer function f(x) =[x] is continuous at all points except at integer points

Let $\theta \in (0,\frac{\pi }{4})and{t}_1=(tan\theta {)}^{tan\theta },t_2(tan\theta {)}^{cot}{t}_3=\left(cot\theta {)}^{tan\theta }and{t}_4\right(cot\theta {)}^{tan\theta }$ , then

If A $\ge 0,B\ge 0,A+B=\frac{\pi }{3}andy=tanAtanB$ then

If ${}^{n^2-n}{C}_2{=}^{n^2-n}{C}_{10}$, then

Find the equation of the line passing through the point of intersection of $2x-7y+11=0$ and $x+3y-8=0$ and is parallel to (i) x-axis (ii) y-axis.

If |Z-2+1| ≤2, the greatest and least values of |z + 4| are

If 1 + ${\sum }_{r=0}^{18}$ (r(r + 2) + 1) r! = n!, then n is not divisible by

If the roots of the equation a$x^2$ + bx + c = 0 are real and of the form$\frac{(\propto -1)}{\propto }$ and $\frac{(\propto +1)}{\propto }$, then value of ${(a+b+c)}^2$ is

What is the period of f(x) = sin (2x) ?

If $co{s}^{-1}\sqrt{p}+co{s}^{-1}\sqrt{1-p}+co{s}^{-1}\sqrt{1-q}=\frac{3\pi }{4}$, then the value of q is

If $\theta +\pi$ is the eccentric angle of a point on the ellipse $16x^2+25y^2=400,$ then the corresponding point on the auxilary circle is

Parametric coordinates of a point on ellipse, whose foci are $(-1,0)$ and $(7,0)$ and eccentricity is $\frac{1}{2},$ is

Find the equation of tangent to the curve y = (x-1)² which is parallel to the chord joining (1, 0) and (3, 4)

If $\frac{cos(x-y)}{cos(x+y)}+\frac{cos\left(7_t\right)}{cos(7-t)}=0$ then tan x tan y tan 7 tan t=

A point on the curve $\frac{x^2}{A^2}-\frac{y^2}{B^2}=1$ is

Area under the curve $y=\sqrt{3x+4}$ between x=0 and x=4 is

A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 on the die is:

The straight lines represented by the equation $a{x}^2+2bxy+b{y}^2=0$ are perpendicular if

If there exist three values of ${\alpha }_i,$ $-\frac{\pi }{2}\le {\alpha }_i\le \pi$, such that $\sum _{i=1}^3\sin {\alpha }_i=\sum _{i=1}^3\cos {\alpha }_i=0,$ then which of the following is/are correct?

In a rational number , twice the numerator is 2 more than the denominator . If 3 is added to each, numerator and the denominator, the new fraction is 2/3 . Find the original number .

Consider the following statements

P : Suman is brilliant

Q: Suman is rich

R: Suman is honest

The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

Total number of real values of x such that $\frac{(12+x{)}^{\frac{1}{7}}}{x}+\frac{(12+x{)}^{\frac{1}{7}}}{12}=\frac{64}{3}{x}^{\frac{1}{7}}$ is/are

If the term independent of $x$ in the ${(\sqrt{x}-\frac{k}{x^2})}^{10}$ is $405$, then the value(s) of $k$ can be

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2$ =4 with x+y=a. The set containg the value of 'a' is

What does the author mean by the terms 'infinite regress' or 'vicious circle' in this passage?

There are $6$ boxes labelled $B_1,B_2,....,B_6.$ In each trial, two fair dice $D_1,D_2$ are thrown. If $D_1$ shows $j$ and $D_2$ shows $k$, then $j$ balls are put into the box $B_k$. After $n$ trials, what is the probability that $B_1$ contains at most one ball?

The least positive integer $n$ such that ${\left(\begin{array}{cc}\cos \frac{\pi }{4}& \sin \frac{\pi }{4}\\ -\sin \frac{\pi }{4}& \cos \frac{\pi }{4}\end{array}\right)}^n$ is an identity matrix of order $2$ is

If A is a skew-symmetric matrix of order 3, then the matrix $A^4$ is

Let $x,y,z$ coordinates of each vertex of a triangle are in A.P. If $G(1,3,\lambda )$ is the centroid, then the distance of $G$ form origin is

The vertices of $△ABC$ lie on a rectangular hyperbola such that the orthocentre of the triangle is $(0,-1)$ and the asymptotes of the rectangular hyperbola are parallel to the co-ordinate axes. The two perpendicular tangents of the hyperbola intersect at the point $(2,3)$. Then which of the following point(s) lie on the hyperbola?

If f(x) = sin log $\left(\frac{\sqrt{4-x^2}}{1-x}\right)$, then the domain of f(x) is ___

Equation of the pair of tangents drawn from the origin to the circle $x^2+y^2+2gx+2fy+c=0$ is

If $lo{g}_{12}27=a,thenlo{g}_{6}16=$

f(x) and f’(x) are differentiable at x = c. Which of the following is the condition for f(x) to have a local maximum at x = c, if f’(c) = 0

The value of x in the expression $[x+x^{lo{g}_{10}\left(x\right)}{]}^5$, if the third term in the expansion is 10,00,000