Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\tan {20}^{\circ }\tan {80}^{\circ }\cot {50}^{\circ }$ is

$\frac{{}^n{c}_0}{n}$ + $\frac{{}^n{c}_1}{n+1}$ + $\frac{{}^n{c}_2}{n+2}$+_ _ _ _ _ _ + $\frac{{}^n{c}_n}{2n}$ =

Evaluate the following one sided limits:

$\left(i\right){lim}_{x\to 2^{+}}\frac{x-3}{x^2-4}$

$\left(ii\right){lim}_{x\to 2^{-}}\frac{x-3}{x^2-4}$

$\left(iii\right){lim}_{x\to 0^{+}}\frac{1}{3x}$

$\left(iv\right){lim}_{x\to 8^{+}}\frac{2x}{x+8}$

$\left(v\right){lim}_{x\to 0^{+}}\frac{2}{x^{\frac{1}{5}}}$

$\left(vi\right){lim}_{x\to \frac{{\pi }^{-}}{2}}tanx$

$\left(vii\right){lim}_{x\to \frac{\pi }{2^{+}}}secx$

$\left(viii\right){lim}_{x\to 0^{-}}\frac{x^2-3x+2}{x^3-2x^2}$

$\left(ix\right){lim}_{x\to -2^{+}}\frac{x^2-1}{2x+4}$

$\left(x\right){lim}_{x\to 0^{+}}(2-cotx)$

$\left(xi\right){lim}_{x\to 0^{-}}1+cosecx$

$cos{7}^{\circ }cos{14}^{\circ }cos{28}^{\circ }cos{56}^{\circ }=\frac{sin{68}^{\circ }}{16cos{83}^{\circ }}$

If the seventh term from the beginning and end in the binomial expansion of ${(\sqrt[3]{32}+\frac{1}{\sqrt[3]{33}})}^n$ are equal, find n.

Sketch the graph of the following functions :
$y=co{s}^{2}x$

Find the sum of the following arithmetic progressions:
(i) 50, 46, 42, ...... to 10 terms
(ii) 1, 3, 5, 7, ..... to 12 terms
(iii) $3,\frac{9}{2},6,\frac{15}{2},\dots \dots 25terms$
(iv) 41, 36, 31, ..... to 12 terms
(v) a + b, a - b, a - 3b, ... to 22 terms
(vi) $(x-y{)}^2,(x^2+y^2),(x+y{)}^2,\dots \dots \text{to n terms}$
(vii) $\frac{x-y}{x+y},\frac{3x-2y}{x+y},\frac{5x-3y}{x+y},\dots \dots \text{to n terms}$

Deepak had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product?

For what value of n will $\frac{4}{16-5n}$achieve maximum value if $nϵN.$

Let $A_n=[a_{ij}{]}_{n\times n}$ be a $(n\times n)$ determinant with the following conditions
$a_{ij}=\left\{\begin{array}{cc}9,& i=j\\ 3,& |i-j|=1\\ 0,& \text{other wise}\end{array}\right\}$ then

Find out the appropriate word which fits the 1st blank.

Let C be the curve $y=x^3$ (where x takes all real values). The tangent at a point A meets the curve again at B. If the gradient at B is K times the gradient at A then K is equal to

Find the second derivative of e^xcosx

Find the point at which the given ray crosses the principal axis after refraction as shown in figure.
(where $\theta$ is very-very small)

The polynomial $x^{4a}+x^{4b+1}+x^{4c+2}+x^{4d-1}$ where $a,b,c\&d\in N$ is divisible by

The solution of $(y+x+5)dy=(y-x+1)dx$ is

If $\alpha ,\beta$ are roots of the equation $a{x}^2+bx+c=0$ then the quadratic equation whose roots are $\frac{1}{(a\alpha +b{)}^2},\frac{1}{(a\beta +b{)}^2}$, is

The normal at $P\left(\theta \right)$ and D$(\theta +\frac{\pi }{2})$ meet the major axis of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at Q and R. Then $P{Q}^2+D{R}^2=$

Find the sign of the quadratic polynomial.
$f\left(x\right)=x^2+5|x|+6$

Find the sum of the first n natural numbers.

Find the equation of a sphere whose centre is (1,2,3) and touches the plane x+2y+3z = 0

The approximate value of square root of 25.2 is

The equation $a_8{x}^8+a_7{x}^7+a_6{x}^6+...+a_0=0$ has all its roots positive and real $(where{a}_8=1,a_7=-4,a_0={\frac{1}{2}}^8)$, then

Prove that the line y - x + 2 = 0 divides the join of points (3, -1) and (8, 9) in the ratio 2 : 3.

For any two sets $A$ and $B,$ if $(A\cup B{)}^{\prime }=A^{\prime }\cup B^{\prime },$ then

If $\underset{0}{\overset{\infty }{\int }}\frac{dx}{x^{3/2}+1}=\frac{a\pi }{b^{3/2}},$ where $\text{gcd}(a,b)=1,$ then

ABCD is a square of side 1 unit. A circle passes through vertices A,B of the square and the remaining two vertices of the square lie out side the circle. The length of the tangent drawn to the circle from vertex D is 2 units. The radius of the circle is

If then x is equal to

Equation of plane passing through points given by position vectors $\overline{a}and\overline{b}$ and origin will be

A plane meets the coordinate axes in $A,B,C$ such that the centroid of $△ABC$ is the point $(p,q,r).$ The equation of the plane is

Three lines

$L_1$ = x-y+6 = 0

$L_2$ = 2x+y-3 = 0

$L_3$ = x-2y+m = 0 are given. Which of the following can be the value of m if $L_1$_, $L_2$ and $L_3$ form a triangle.

If the sum of $n$ terms of the series $5+7+13+31+85+\dots$ is $\frac{1}{2}(a^n+bn+c)$, then

Find the point on y-axis which is equidistant from the points $(3,1,2)$ and $(5,5,2)$.

The sum to $n$ terms of the series $(1\times 2\times 3)+(2\times 3\times 4)+(3\times 4\times 5)+\dots$ is

If x and a are real numbers such that a>0 and |x|>a,then

The value of $ta{n}^{-1}\frac{1}{2}+ta{n}^{-1}\frac{1}{3}$ is

If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio $r$ is ___.