Explore topic-wise InterviewSolutions in Current Affairs.

Find the 8th term in the expansion of $(x^{3/2}{y}^{1/2}-x^{1/2}{y}^{3/2}{)}^{10}.$

The number of non negative integral solutions of the equation $x+y+3z=33$ is

Two rods whose lengths are $10\text{units}$ and $6\text{units}$ slides along $X$ and $Y$ axes respectively in such a way that their extremities are always concyclic, then the locus of the centre of the circle is

If the last term in the binomial expansion of ${(2^{1/3}-\frac{1}{\sqrt{2}})}^n$ is ${\left(\frac{1}{3^{5/3}}\right)}^{{\log }_{3}8},$ then the $5^{\text{th}}$ term from the beginning is

Let $S$ be the set of all non-zero real number $\alpha$ such that the quadratic equation $\alpha x^2-x+\alpha =0$ has two distinct real roots $x_1$ and $x_2$ satisfying the inequality $|x_1-x_2|<1.$ Which of the following interval is(are) a subset(s) of $S?$

If $\sum _{k=1}^n\sum _{m=1}^k{m}^2=a{n}^4+b{n}^3+c{n}^2+dn+e,\text{then}$

Find the integrals of the functions.
$\int si{n}^{4}xdx.$

A four digit number (numbered from 0000 to 9999) is said to be lucky if the sum of first two digits is equal to the sum of its last two digits. If a four digit number is picked up at random, then the probability that it is lucky is

If set $A=\left\{\right(r,s)|r,s\in W\}$, then the number of element(s) in set $A$ such that ${}^5{C}_r\cdot {}^6{C}_s=1$ is

Let $\overrightarrow{p},\overrightarrow{q}$ and $\overrightarrow{r}$ be three non-coplanar unit vectors equally inclined to each other at an acute angle $\theta$. The value of $|\overrightarrow{p}\times (\overrightarrow{q}\times \overrightarrow{r})|$ is -

If the pairs of lines $x^2+2xy+a{y}^2=0$ and $a{x}^2+2xy+y^2=0$ have exactly one line in common then the joint equation of the other two lines is given by

Prove it:

Cos²A-cos²A=sin²A-sin²A

Let $n\left(A\right)=m,n\left(B\right)=n$, then the total number of non-empty relations that can be defined from $A$ to $B$ is

F(x) = tan (log x)

F'(x) =

Let A and B be two finite sets having m and n elements respectively. If m $\le$ n, the total number of injective functions from A to B is

The perimeter of the locus represented by $\arg \left(\frac{z+i}{z-i}\right)=\frac{\pi }{4}$ is equal to

The locus of the point of intersection of perpendicular tangent drawn to each one of the parabola $y^2=4x+4$ and $y^2=8x+16$ is

Statement 1: If a line $L=0$ is tangent to the circle $S=0$, then it will also be a tangent to the circle $S+\lambda L=0$

Statement 2: If a line touches a circle, then perpendicular distance of the line from the centre of the circle is equal to the radius of the circle.

The numerically greatest term in the expansion of $(2x-3y{)}^{12}$) when $x=1,y=\frac{5}{3}$, is

If for a complex number $z_1$ and $z_2$, $\arg \left(z_1\right)-\arg \left(z_2\right)=0$, then $|z_1-z_2|$ is equal to

Find the number of solutions for $y=-2x+2$ and $y=-8x+8$.

If x is so small that $x^3$ and higher powers of x may be neglected, the $\frac{(1+x{)}^{\frac{3}{2}}-(1+\frac{1}{2}x{)}^3}{(1-x{)}^{\frac{1}{2}}}$ may be approximated

If a, b, c and d are the position vectors of the points A, B, C and D such that a + c = b + d, then ABCD is a

The value of k for which the polynomial $x^3+10x^2+kx+1$ is continuous for all values of x is

The area (in sq. units) of the quadrilateral whose vertices are $A(1,1),$ $B(3,4),$ $C(5,-2)$ and $D(4,-7)$ is

$f\left(x\right)=\frac{1}{x+|x-1|},g\left(x\right)=\frac{1}{x+|x+1|}$

If S be the sum, P the product and R the sum of the reciprocals of n terms of a G.P., then ${\left(\frac{S}{R}\right)}^n$ =

If A and B are two square matrices such that $B=-A^{-1}$ BA, then $(A+B{)}^2=$

Z is rotated through an angle of anticlockwise to get $z_1$ and clockwise to get $z_2$, then

Find the cube roots of -27.

The optimal value of the objective function is attained at the points

If f : D $\to$R $f\left(x\right)=\frac{x^2+bx+c}{x^2+b_{1}x+c_1},where\alpha ,\beta$ are th roots of the equation $x^2+bx+c=0$ and ${\alpha }_1,{\beta }_1$ are the roots of $x^2+b_{1}x+c_1=0$. Now, answer the following question for f(x). A combination of graphical and analytical approach may be helpful in solving these problems. If ${\alpha }_{1}and{\beta }_1$ are real, then f(x) has vertical asymptote at $x=({\alpha }_1,{\beta }_1$).
If the equations $x^2$ + bx + c = 0 and $x^2+b_{1}x+c_1=0$ do not have real roots, then

f(x) and g(x) are continuous functions such that ${lim}_{x\to a}\left[3f\right(x)+g(x\left)\right]=6and{lim}_{x\to a}\left[2f\right(x)-g(x\left)\right]=4$. Given that the function h(x).g(x) is continuous at x = a and h(a)=4, which of the following must be true?

The ends of latus rectum of parabola $x^2+8y=0$ are

If two jobs A and B can be done independentely by m and n ways respectiveley, then the number of ways by which job A and job B can be done?

Let $P$ be the point $(1,0)$ and $Q$ be a point on the curve $y^2=8x$. Then the locus of the mid-point of $PQ$ is

If $P=\sum _{r=1}^{\infty }{\tan }^{-1}\left(\frac{1}{r+3}\right)Q=\sum _{r=1}^{\infty }{\tan }^{-1}\left(\frac{1}{r+1}\right)R=\sum _{r=1}^{\infty }{\tan }^{-1}\left(\frac{1}{r}\right)$
, then $P-2Q+R$ is

If, getting a number greater than $4$ on a fair die is considered a success, then the variance of the distribution of success on tossing a die five times is

Prove that $\overrightarrow{A}(\overrightarrow{A}\times \overrightarrow{B})$ = 0.

A student appears for test 1,2 and 3. The student is successul if he passes either in tests 1 and 2 or tests 1 and 3. The probability of student passing in tests 1,2 and 3 is a,b,$\frac{1}{2}$ respectively.If the probability that the student is successful is $\frac{1}{2}$. Then,

If $a=sin\frac{\pi }{18}sin\frac{5\pi }{18}sin\frac{7\pi }{18}$, and $x$ is the solution of the equation. $y=2\left[x\right]+2$ and $y=3[x-2]$, where [x] denotes the integral part of x, then ‘a’ is equal to