Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\sum _{r=1}^{n}r\times r!$ is

The given graph shows a function representing the speed of a car with time. Find the domain where the speed is constant.

Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is

Which of the following can be treated as an Elementary Row transformation.

In a triangle $ABC$ we define
$x=tan\frac{B-C}{2}tan\frac{A}{2},y=tan\frac{C-A}{2}tan\frac{B}{2}$ and $z=tan\frac{AB}{2}tan\frac{C}{2}$
Then the value of $x+y+z$ (in terms of $x,y,z$) is

The value of $\underset{0}{\overset{\pi }{\int }}|\cos x{|}^{3}dx$ is :

The eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$whose latus rectum is half of its major axis, is .

If A and B are two matrices such that AB = B and BA = A, then

If $A=\left[\begin{array}{ccc}2& -3& 5\\ 3& 2& -4\\ 1& 1& -2\end{array}\right]$, find $A^{-1}$. Using $A^{-1}$ solve the system of equations $2x-3y+5z=11,3x+2y-4z=-5,x+y-2z=-3$

For a function, $f\left(x\right)$ satisfying the following conditions
$1\left)f\right(0)=6,f(2)=16$
$2)f$ has a minimum value at $x=-4$
$3)$ For all $x,$
$f^{\prime }\left(x\right)=\left|\begin{array}{ccc}2ax& 4ax-1& 3ax-b+3\\ b& 2b+1& 2ax+1\\ 2b-2ax& 4b-4ax+3& b+ax\end{array}\right|,$

the values of $a$ and $b$ are

${lim}_{x\to 0}\frac{3sinx-4si{n}^{3}x}{x}$

An instructor has a question bank consisting of $300$ easy True/False questions, $200$ difficult True/False questions, $500$ easy multiple choice questions and $400$ difficult multiple choice questions. If a question is selected at random from the question bank, then the probability that it will be an easy question given that it is a multiple choice question is:

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 bisector of the angles between the pairs of lines given by the equation
$a{x}^2+2hxy+b{y}^2=0$ and $a{x}^2+2hxy+b{y}^2+\lambda (x^2+y^2)=0$
be coincident, then $\lambda$ =

If $\frac{2\sin \alpha }{1+\cos \alpha +\sin \alpha }=\frac{3}{4},$ then the value of $\frac{1-\cos \alpha +\sin \alpha }{1+\sin \alpha }$ is

If A is an idempotent matrix and A + B =I, then which of the following is true?

If $g$ is the inverse of a function $f$ and $f\text{'}\left(x\right)=\frac{1}{1+x^5}$, then $g\text{'}\left(x\right)$ is equal to:

If $I_1=\underset{0}{\overset{1}{\int }}\sqrt[9]{91-x^5}dx,I_2=\underset{0}{\overset{1}{\int }}\sqrt[5]{51-x^9}dx,$

then $\frac{I_1}{I_2}$ is equal to

In an A.P if the common difference is twice the first term of the progression, then the sum of first n terms of the progression is

Total number of solutions for the equation ${\sin }^{4}x+{\cos }^{4}x=\sin x\cos x,x\in [0,2\pi ]$ is

The points A, B and C with position vectors $\overrightarrow{a},\overrightarrow{b}and\overrightarrow{c}$, and respectively lie on a circle centred at origin O. Let G and E be the centroid of $\Delta$ ABC and $\Delta$ ACD respectively where D is midpoint of AB.
If GE and OC are mutually perpendicular then orthocentre of $\Delta ABC$ must lie on

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:

6 times q is subtracted from the smallest two-digit number.

If $y=mx+4$ is a tangent to both the parabolas, $y^2=4x$ and $x^2=2by,$ then $b$ is equal to

The circle passing through the intersection of the circles, $x^2+y^2-6x=0$ and $x^2+y^2-4y=0$, having its centre on the line, $2x-3y+12=0$, also passes through the point

If $x=2cost-cot2t,y=2sint-sin2t$, then $\frac{d^{2}y}{d{x}^2}$ at t = $\frac{\pi }{2}$ is

The first term of a harmonic is $\frac{1}{7}$ and the second term is $\frac{1}{9}$. The ${12}^{th}$ term is