Explore topic-wise InterviewSolutions in Current Affairs.

If $z$ is a complex number and $\alpha =\frac{z+i}{iz+2}$, where $i=\sqrt{-1}$. Suppose $\alpha$ is a real number then

For natural number n, $(n!{)}^2$ > $n^n$, if

Find the degree of freedom of $C{O}_2$ at room temperature?
(Given: $C{O}_2$ has linear structure at room temperature)

If $z=x+iy,|z|=1$ and $\omega =\frac{(1-z{)}^2}{1-z^2}$, then the locus of $\omega$ is equivalent to

If in a right-angled triangle ABC angles A and B are acute, then evaluate

1 + $\frac{tanA}{tanB}$ =

The value of $\cos \left(\frac{23\pi }{12}\right)$ is

The number of seven digit integers with sum of the digits equal to $10$ and formed by using the digits $1,2$ and $3$ only is :

If $\int {\sin }^{-1}x{\cos }^{-1}xdx=f^{-1}\left(x\right)[Ax-x{f}^{-1}(x)-2\sqrt{1-x^2}]+\frac{\pi }{2}\sqrt{1-x^2}+2x+c,$ then

If the coefficients of $r^{\text{th}},(r+1{)}^{\text{th}}\text{and}(r+2{)}^{\text{th}}$ terms in the expansion of $(1+x{)}^{14}$ are in A.P., then value $r$ can be

Value of the determinant $\left|\begin{array}{ccc}1& 3& 5\\ 3& 4& 5\\ 0& 2& 3\end{array}\right|is..............$

Integrate the rational functions.
$\int \frac{3x-1}{(x-1)(x-2)(x-3)}dx.$

If $C_r$ represents ${}^{100}{C}_r,$ then $5C_0+8C_1+11C_2+\dots$ upto $101$ terms is equal to

Find inverse, by elementary row operations (if possible), of the following matrix:

$\left[\begin{array}{cc}1& -3\\ -2& 6\end{array}\right]$

Prove that:

$\text{sin 3x+ sin 2x - sin x = 4 sin x cos}\frac{x}{2}\text{cos}\frac{3x}{2}$

Summarize the chapter of straight lines with the different formulas?

Which of the following functions is differentiable at $x=0$?

Find the locus of point of intersection of perpendicular tangents to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$

If $A=\{x\in N:{\log }_{2}x+\frac{3}{{\log }_{2}x}<4,x>1\}$ and $B=\{x\in Z:(4-x^2\left)\right(x^2-8x+15)\ge 0\},$ then the number of subsets of the set $(A\cup B)-(A\cap B)$ is

Prove the following identity where the angle involved is acute for which the expression is defined :

((1 + cotA)/ secA ) + (sin²A/ (1 - cosA))

If f(x) has a derivative at x=0, then ${lim}_{x\to a}\frac{xf\left(a\right)-af\left(x\right)}{x-a}=$

The equation of two equal sides of an isosceles triangle are $7x-y+3=0$ and $x+y-3=0.$ If the third side passes through $(1,-10)$ and its slope is negative, then the equation of the third side is

A group of $10$ persons including ''Manager'', ''Assistant manager'' and ''Secretory'' are to be seated around a circular table.
The total number of possible arrangements, if ''Manager'' and ''Secretory'' had to sit together and ''Assistant manager'' had to sit opposite to ''Manager'' is

Prove that the values of x obtained from the equations ax²+by²=1 and ax+by=1 will be equal if a+b=1.

The solution of differential equation x²dy + y(x + y)dx = 0 when x = 1, y = 1 is:

A tangent is drawn at a point on the parabola $y^2=10x$. If this tangent intersect the parabola $y^2=10x+p$ at 2 points; then,

The equation of a line passing through (1,2,3) having direction ratios 1,2,4 is .

Find the value of x if $(2x{)}^{ln2}$ = $(3y{)}^{ln3}$ and $3^{lnx}$ = $2^{lny}$.

${\log }_{e}x$ can also be written as ln(x)

Suppose the tangent to the parabola $y=x^2+px+q$ at $(0,3)$ has slope $–1$. Then $p+q$ equals

If ${17}^{\text{th}}$ and ${18}^{\text{th}}$ terms in the expansion of $(2+a{)}^{50}$ are equal, then the value of $a$ is:

If the system of equation $x–2y+z=a,2x+y–2z=b$ and $x+3y–3z=c$ have atleast one solution, then the relationship between a, b and c is

The value of p $>$ 0, for which both the equations $x^2+px+64$ = 0 and $x^2-8x+p$ = 0 have real roots is:

How many numbers can be formed between 40,000 and 60,000 using the digits 2, 3,4,5,6 without repetition?

$\int \frac{2sinx}{(3+sin2x)}dx$ is equal to

A ship is fitted with three engines $E_1,E_{2}and{E}_3$. The engines function independently of each other with respective probabilities $\frac{1}{2},\frac{1}{4}and\frac{1}{4}$. For the ship to be operational, at least two of its engines must function. Let X denote the event that the ship is operational and let $X_1,X_{2}and{X}_3$ denote, respectively the events that the engines $E_1,E_{2}and{E}_3$ are functioning.
Which of the following is/are true?

Solve for $x:$

$|x-1|+|x-2|+|x-3|\ge 6$

If sin^–1 x + sin^–1 2x = x/3 then value of x is

Prove that the perpendicular drawn from the point (4, 1) on the join of (2, -1) and (6, 5) divides it in the ratio 5 : 8.

If 2${}^x$ - 2 ${}^{x-2}$ = 12, then x${}^2$= ?

Equation of the locus of the pole with respect to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ of any tangent line to the auxiliary circle is the curve
$\frac{x^2}{a^4}+\frac{y^2}{b^4}={\lambda }^2$ where