Explore topic-wise InterviewSolutions in Current Affairs.

The sum to n terms of the series $\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+...$

If $\sin \theta +\sin 2\theta +sin3\theta +\sin 4\theta =0,$ then $\theta =$

Let $a_n$ be the nth term of an AP. If ${\Sigma }_{r=1}^{50}{a}_{2r}=\alpha$ and ${\Sigma }_{r=1}^{50}{a}_{2r-1}=\beta$, then the common difference of the A.P

Differentiate the following functions with respect to x :

$\frac{e^x}{1+e^x}$

Find the equation of the line joining (1,2) and (3,6) using determinants.

Find the equation of the line joining (3,1) and (9,3) using determinants

The inequality representing the following graph is

Let z be a complex number such that the imaginary part of z is non - zero and $a=z^2+z+1$ is real. Then, $a$ cannot take the value

Sketch the graph of the following pairs of functions on the same axes:
(i) y=sin x, y = sin $(x+\frac{\pi }{4})$
(ii) y=sin x, y = sin 3x

If α + β = 90^o and α : β = 2 : 1, then, sin α : sin β =

The orthocentre of the triangle formed by the vertices $(5,0),(0,0)$ and $(\frac{5}{2},\frac{5\sqrt{3}}{2})$ is

If f(x) and g(x) have equal derivatives, then f(x) - g(x) is a ___________ function

The general solution(s) of $\theta$ which satisfy $3-2\cos \theta –4\sin \theta -\cos 2\theta +\sin 2\theta =0$ is/are (where $n\in Z$)

The distance of origin to the line $3x+4y-5=0$ measured along the line $x-y+2=0$ 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 INCORRECT combination?

Let $f\left(x\right)=\frac{tanx}{x},thenlo{g}_e{lim}_{x\to 0}\left(\right[f\left(x\right)]+x^2{)}^{\frac{1}{\left\{f\right(x\left)\right\}}}$ is equal to, (where [.] denotes greatest integer function and { } fractional part)

$Ify=c{t}^{3}andx=\frac{c}{t},then\frac{d^{2}y}{d{x}^2}=$

The solution of $\frac{dy}{dx}=\frac{y}{x}+tan\frac{y}{x}$ is

If a,b,c,d be in H.P., then

If the product of all solutions of the equation $\frac{\left(2019\right)x}{2020}=(2019{)}^{{\log }_x\left(2020\right)}$ can be expressed in the lowest form as$\frac{m}{n}$, then the value of $m-n$ is

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs.x each, Rs.y each and Rs.z each for the three respective values to its 3, 2 and 1 students with a total award money of Rs.1600. School B wants to spend Rs.2300 to award its 4, 1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs.900, using matrices, find the award money for each value.

Apart from these three values, suggest one more value which should be considered for award.

The set of values of $x$ satisfying the equation $1+\cos 3x=2\cos 2x$ can be
(where $n\in Z$)

If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his

chance of winning prize are

Derive the equation of a plane passing through three non-collinear points both in the vector and cartesian form .

Show that the are of the triangle formed by the lines $y=m_{1}x,y=m_2$ x and y = c is equal to $\frac{c^2}{4}(\sqrt{33}+\sqrt{11})$, where $m_1,m_2$ are the roots of the equation $x^2+(\sqrt{3}+2)x+\sqrt{3}-1=0.$

Which of the following is the integral of the function $e^x$

If the line drawn from the point (-2,-1,-3) meets a plane at right angle at the point (1,-3,3), then find the equation of the plane.

The number of values of $x$ between 0 and $2\pi$ such that the equation $\sin x+\sin 2x+\sin 3x=\cos x+\cos 2x+\cos 3x$ must be ___

The discriminant of the quadratic equation $3x^2-4\sqrt{3}x+4=0$ is

The vector c directed along the internal bisector of the angle between the vectors a = 7i - 4j - 4k and b = -2i - j + 2k with |c| = 5√6 ?

If ${\log }_{0.3}(x-1)<{\log }_{0.09}(x-1)$, then $x$ lies in the interval

A determinant may be considered to bea function which associates each square matrix with a unique number , either real or complex .Which of the following represents the correct definition of this function, if M denotes a matrix and c a real or complex number ?

If $f\left(x\right)=\frac{x^2-1}{x}$ and $g\left(x\right)=\frac{x+2}{x-3},$ then the domain of $\frac{f\left(x\right)}{g\left(x\right)}$ is

The equation of the circle which touches both axis and whose centre is $x_1,y_1$ is

The function $f\left(x\right)=2x^3-3x^2+90x+174$ is increasing in the interval

A single letter is selected at random from the word 'PROBABILITY'. What is the probability that it is a vowel ?

If the angles of a triangle are in the ratio 1:2:3, then the ratio of its corresponding sides is .

In the figure given below four small, equal circles are circumscribed by a larger one. If “R” and ‘r’ denotes the radius of circumscribed circle and small circle, then $\frac{R}{r}$ is greater than

Prove that: $cos{105}^{\circ }+cos{15}^{\circ }=sin{75}^{\circ }-sin{15}^{\circ }$