Explore topic-wise InterviewSolutions in Current Affairs.

Find the equation of a line passing through $(1,2,3)$ having direction ratios $1,2,4$

Let $P=(-1,0),Q=(0,0)\text{and}R=(3,3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$ is

If $si{n}^{2}4x+co{s}^{2}x=2sin4x.co{s}^{4}x$ then number of values of x satisfying, if $x\in [-2\pi ,2\pi ]$ is

The solution of $y_2-7y_1+12y=0$ is

In how many distinct permutations of the letters of the word MISSISSIPPI do four I's not come together?

The differentiation of ${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)w.r.t.{\tan }^{-1}x$ is

Column – 1 : represent different words
Column – 2 : represent number ways of selecting five letters from the word in column – 1
Column – 3 : represent total number of possible words with or without meaning, using all the alphabets of word in
column - 1 such that all the vowels are together.
$$\begin{array}{ccc}Column1& Column2& Column3\\ \left(I\right)INDEPENDENT& \left(i\right)41& \left(p\right){24.}^8{C}_6{.}^6{C}_3{.}^3{C}_2{.}^3{C}_2\\ \left(II\right)INSTITUTE& \left(ii\right)60& \left(Q\right){24.}^8{C}_5{.}^5{C}_3\\ \left(III\right)CURRICULUM& \left(iii\right)72& \left(R\right){12.}^7{C}_3{.}^4{C}_3{.}^3{C}_2\\ \left(IV\right)MATHEMATICS& \left(iv\right)179& \left(S\right){24.}^6{C}_3{.}^3{C}_2\end{array}$$
Which of the following options is the only CORRECT combination?

If $l_1,m_1,n_1$ and $l_2,m_2,n_2$ are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be

The number of integral values of $a$ such that the quadratic equation $4a{x}^2+5x+a=0$ has two distinct real roots $x_1$ and $x_2$, satisfying the inequality $|x_1-x_2|<1$, is

For positive interger $n,$ if $f\left(n\right)={\sin }^n\theta +{\cos }^n\theta ,$ then $\frac{f\left(3\right)-f\left(5\right)}{f\left(5\right)-f\left(7\right)}$ is

In a class of $100$ students, $55$ students have passed in Maths, $67$ passed in Physics. If all the students pass in at least one subject, then the number of students who passed in physics only is

If $a=cis2\alpha ,b=cis2\beta$ then $\cos (\alpha -\beta )$ is, where $cis\theta =\cos \theta +i\sin \theta$

$\begin{array}{cccccc}& \text{Column - I}& & \text{Column - II}& & \text{Column - III}\\ \left(I\right)& y.(y^{\prime }{)}^2-x{y}^{\prime }(1+y)+x^2=& \left(i\right)& \left[y\right]=1,\text{where [.] is greatest}& \left(p\right)& \text{Curve is bounded with area},\pi \\ & 0,y\left(\sqrt{3}\right)=2& & \text{integer function}& & \\ \left(II\right)& y^{\prime }=\frac{y^2-x^2}{2xy},y\left(1\right)=1& \left(ii\right)& \text{Maximum value of y is 3}& \left(Q\right)& \text{Area bounded by curve in first quadrant with}\\ & & & & & \text{co-ordinate axes is}\frac{3\pi }{4}\\ \left(III\right)& y^{\prime }=\frac{-9x}{y},y\left(1\right)=0& \left(iii\right)& \text{Maximum value of y is not defined}& \left(R\right)& \text{Curve is conic with eccentricty},\frac{1}{2}\\ \left(IV\right)& y^{\prime }=\frac{x}{y},y\left(2\right)=0& \left(iv\right)& \text{Maximum value of y is 1}& \left(S\right)& \text{Curve is conic with eccentricity},\sqrt{2}\end{array}$

The correct combination is

A bag contains 5 white, 7 black and 4 red balls, find the chance that 3 balls drawn at random are all white?

${lim}_{x\to \frac{\pi }{2}}\frac{2^{-\cos x}-1}{x(x-\frac{\pi }{2})}$

Find the equation of straight line which passes through the point (2,-3) and the point of intersection of the lines x+y +4 = 0 and 3x-y-8=0

Which of the following are the properties of transpose :-

If $f\left(x\right)=\frac{x+1}{x-1},$ show that $f\left[f\right(x\left)\right]=x.$

Number of rational terms in the expansion of $(3^{\frac{1}{8}}+5^{\frac{1}{3}}{)}^{400}$ is

If the reduction formula for $I_n=\int {\tan }^n\mathrm{xdx}$ is given by
$I_n=\frac{1}{n-1}{\tan }^{n-1}x-I_{n-2}$, then $\int {\tan }^{3}x\mathrm{dx}\mathrm{is}$

Let $a_1,a_2,\dots ,a_{10}$ be a G.P. If $\frac{a_3}{a_1}=25$, then $\frac{a_9}{a_5}$ equals:

How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD' ?

Find :

(i) the ninth term of the G.P. 1, 4, 16, 64, ....

(ii) the 10th term of the G.P. $-\frac{3}{4},\frac{1}{2},-\frac{1}{3},\frac{2}{9},......$

(iii) the 8th term of the G.P. 0.3, 0.06, 0.012, ....

(iv) the 12th term of the G.P. $\frac{1}{a^3{x}^3},ax,a^5{x}^5,$.......

(v) nth term of the G.P. $\sqrt{3},\frac{1}{\sqrt{3}},\frac{1}{3\sqrt{3}},.....$

(vi) the 10th term of the G.P. $\sqrt{2},\frac{1}{\sqrt{2}},\frac{1}{2\sqrt{2}}$, ......

If the system of equations $x+\alpha y+{\alpha }^{2}z=1,\alpha x+y+\alpha z=-1,{\alpha }^{2}x+\alpha y+z=1$ has infinitely many solutions then $1+\alpha +{\alpha }^2=$

The coordinates of the mid-points of sides AB, BC and CA of $△$ are D (1, 2, -3) E(3, 0, 1) and F(-1, 1, -4) respectively. Write the coordinates of its centroid.

Show that the three points A(2, 3, 4), B(-1, 2, -3) and C(-4. 1, -10) are collinear and find the ratio in which C divides AB.

The eccentricity of the ellipse is $4x^2+9y^2$ = 36 is

Acute angle between the lines represented by $(x^2+y^2)\sqrt{3}=4xy$ is

If a particle moving along a line follows the law $s=\sqrt{1+t}$ then the acceleration is proportional to

The solution set of inequality $\left({\tan }^{-1}x\right)\left({\cot }^{-1}x\right)-\left({\tan }^{-1}x\right)(1+\frac{\pi }{2})-2{\cot }^{-1}x+2(1+\frac{\pi }{2})>\underset{y\to -\infty }{lim}[{\sec }^{-1}y-\frac{\pi }{2}]$ is
(where [.] denotes the greatest integer function)

$co{s}^{-1}(-\frac{1}{2})-2si{n}^{-1}\left(\frac{1}{2}\right)+3co{s}^{-1}(-\frac{1}{\sqrt{2}})-4ta{n}^{-1}(-1)$ equals to

In a triangle ABC,
$\angle A=60°andb:c=\sqrt{3}+1:2,thenthevalueof\angle B-\angle C=$ .

If f(x) = (1 + x) $(1+x^2)(1+x^3)$, then f'(1) =

$co{t}^{-1}\frac{xy+1}{x-y}+co{t}^{-1}\frac{yz+1}{y-z}+co{t}^{-1}\frac{xz+1}{z-x}$ is equal to

${lim}_{x\to \frac{1}{2}}\frac{8x^3+1}{2x+1}$

${lim}_{n\to \infty }\frac{1^3+2^3+3^3+....+n^3}{n^4}$

Sum of the series 0.5 + 0.55 + 0.555 + . . . . . . . . . upto n terms is

How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?

$\text{The vertices of a triangle ABC are}A(0,0),B(2,-1)andC(9,2).FindcosB.$

The number of integral values of $m$ for which the equation $sinx-\sqrt{3}cosx=\frac{4m-6}{4-m}$ has solution is:

If $f\left(x\right)=\sqrt{x+3}$ and $g\left(x\right)=x^2+1$, then $f\left(g\right(x)$ =

Show that ${lim}_{x\to 2^{-}}\frac{x}{\left[x\right]}\ne {lim}_{x\to 2^{+}}\frac{x}{\left[x\right]}$.

(i) If $(\frac{a}{3}+1,b-\frac{2}{3})=(\frac{5}{3},\frac{1}{3}),$ find the values of a and b.

(ii) If (x + 1, 1) = (3, y - 2), find the values of x and y.

What is the derivative at the point $x=-2$ on the curve $y=x^2$?
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