Explore topic-wise InterviewSolutions in Current Affairs.

The number of ways in which mn students , can be distributed equally among ‘m’ sections is?

The inverse of the proposition $(p\lambda \sim q)\to r$ is ________

If ${}^{2n}{C}_3:{}^n{C}_3=11:1,$ find n.

If the nth term of the A.P. 9, 7, 5, ..... is sameas the nth term of the A.P. 15, 12, 9, ..... find n.

If $R=\left\{\right(x,y):x,y,ϵW,2x+y=8\},$ then write the domain and range of R.

If $cosA=-\frac{24}{25}$ and $cosB=\frac{3}{5}$, where $\pi <A<\frac{3\pi }{2}$ and $\frac{3\pi }{2}<B<2\pi$, find the following:
(i)sin(A+B) (ii)cos(A+B)

$Therangeoff\left(x\right)=\frac{3}{5+4sin3x}is$

Let $f(x,y)=\sqrt{x^2+y^2}+\sqrt{x^2+y^2-2x+1}+\sqrt{x^2+y^2-2y+1}+\sqrt{x^2+y^2-6x-8y+25}\forall x,yϵR,then$

Let $S=\{1,2,3,...,100\}$. The number of non empty subsets $A$ of $S$ such that the product of elements in $A$ is even is:

Prove that following identities:

$cotA+cot({60}^{\circ }+A)-cot({60}^{\circ }-A)=3cot3A$

$\text{If}y={(sin\frac{x}{2}+cos\frac{x}{2})}^2,\text{find}\frac{dy}{dx}\text{at}x=\frac{\pi }{6}.$

(1+cosx) (1+sinx) = 5/4 Find (1-cosx) and (1-sinx)

Let $a-2b+c=1$, If $f\left(x\right)=\left|\begin{array}{ccc}x+a& x+2& x+1\\ x+b& x+3& x+2\\ x+c& x+4& x+3\end{array}\right|,$ then:

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

The sum of real solutions of the equation $(x^2+2{)}^2+8x^2=6x(x^2+2)$, given that $x\ne 0,$ is

If $x=cos\theta +isin\theta andy=cos\varphi +isin\varphi ,then{x}^m{y}^n+x^{-m}{y}^{-n}$ ,is equal to

If $p_{1}p=2(q_1+q)$ then which of following statement about the quadratic equations $x^2+px+q=0;x^2+p_{1}x+q_1=0$ is always true (Here $p,p_1,q,q_1,\in R$)

Find the equations to the straight lines passing through the point (2, 3) and inclined at an angle of ${45}^{\circ }$ to the line $3x+y-5=0$

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are three vectors such that $|\overrightarrow{a}|=3$, $|\overrightarrow{b}|=1$ and $|\overrightarrow{c}|=2$ and $|\overrightarrow{b}\times \overrightarrow{c}|=\sqrt{3}$ and $\overrightarrow{b}-3\overrightarrow{c}=\lambda \overrightarrow{a}$, then the possible value of $\left[\lambda \right]$ is (where $[.]$ denotes greatest integer function)

Distinguish between formal and informal organisation.

(i) Meaning (ii) Origin (iii) Authority (iv) Behaviour (v) Flow of communication (vi) Nature

Let $A$ and $B$ be acute angles. If $\sin (A+B)=\frac{12}{13}$ and $\cos (A-B)=\frac{3}{5}$, then $\sin \left(2A\right)$ is equal to

Find the equation of the ellipse whose focus is (1,-2), the directrix 3x-2y+5=0 and eccentricity equal to 1/2.

If $x\in [-4,-1]$,
then $\frac{1}{x^2}$ belongs to

(i) If A = {1,2,3,4,5},

B= {4,5,6,7,8},

C= {7,8,9,10,11} and

D= {10,11,12,13,14}. Find :

(i) $A\cup B$ (ii) $A\cup C$

(iii) $B\cup C$ (iv) $B\cup D$

(v) $A\cup B\cup C$ (vi) $A\cup B\cup D$

(vii) $B\cup C\cup D$ (viii) $A\cap (B\cup C)$

(ix) $(A\cap B)\cap (B\cap C)$

(x) $(A\cup D)\cap (B\cup C)$

Check the injectivity and surjectivity of the following functions:
$\left(i\right)f:N\to N$ given by $f\left(x\right)=x^3$

Differentiate the given functions w.r.t. x.

$(sinx{)}^x+si{n}^{-1}\sqrt{x}.$

${\int }_0^{1}xlog(1+2x)dx$

Show that the normal at any point $\theta$ to the curve $x=acos\theta +a\theta ,y=asin\theta -a\theta cos\theta$ is. at a constant distance from the origin.

A man , 2 m tall, walks at the rate of $1\frac{2}{3}$ m/s towards a street light which is $5\frac{1}{3}$ m above the ground. At what rate is the tip of his shadow moving and at what rate is the length of the shadow changing when he is $3\frac{1}{3}$ m from the base of the light?

The domain of $f\left(x\right)={\log }_3\{-{\log }_4\left(\frac{6x-4}{6x+5}\right)\}$ is

If 8x=π,show that cos7x + cosx =0

In a $\Delta ABC$, side b is equal to

State which part of speech is the underlined word.

The crowd stoned the thief to death.

For the quadratic equation $x^2$ - (t - 3) x + t = 0 (t ∈ R), the values of 't' for which both the roots are greater than 2, are

If $4^x+2^{2x-1}=3^{x+\frac{1}{2}}+3^{x-\frac{1}{2}}$, then $x=$

If $\overline{a},\overline{b}$ are two non collinear and non zero vectors such that $(x-y)(\overline{a}\times \overline{b})+(y-z)\overline{a}+(z-x)\overline{b}=\overline{0}$ where x, y, z are the lengths of the sides of a triangle, then the triangle is

If in a triangle ABC, a=6cm, b=8cm, c=10cm, then the value of sin 2A is

In a triangle $ABC,$ the sides are of length $17,25$ and $28$ units. Then the length of the largest altitude is

Let $S$ be the set of all complex numbers $z$ satisfying $|z-2+i|$ $\ge \sqrt{5}$. If the complex number $z_0$ is such that $\frac{1}{|z_0-1|}$ is the maximum of the set $\{\frac{1}{|z-1|}:z\in S\}$,then the principal argument of $\frac{4-z_0-\overline{z_0}}{z-\overline{z_0}+2i}$ is

If $a_1,a_2,a_3,...,a_n$ are in A.P. with $s_n$ as the sum of first 'n' terms $(S_0=0),then{\sum }_{k=0}^n{}^n{C}_k{S}_k$ is equal to

The number of common tangents to the circles $x^2+y^2+6x+6y+14=0$ and $x^2+y^2-2x-4y-4=0$ is

If $\sin x=\frac{12}{13}$ and $x\in [0,\pi ]$, then the possible value(s) of $\sec x+\tan x$ is/are

${lim}_{x\to 0}\frac{\sqrt{1+x+x^2}-\sqrt{x+1}}{2x^2}$

Find the angle between the lines where direction ratios are (a, b, c) and (b - c, c - a, a - b).