Explore topic-wise InterviewSolutions in Current Affairs.

If the sum of first p terms, first q terms and first r terms of an A.P. be a, b and c respectively,

Then $\frac{a}{p}$(a - r) + $\frac{b}{q}$(r - p) + $\frac{c}{r}$(p - q) is equal to

If $y=\sqrt{\frac{1-\cos 2x}{1+\cos 2x}},x\in \left(0,\frac{\pi }{2}\right)\cup \left(\frac{\pi }{2},\pi \right)$, then $\frac{dy}{dx}$ is equal to

If $\theta$ is the acute angle between the tangents drawn from $(1,4)$ to the parabola $y^2=12x,$ then the value of $\sin \theta +2\cos \theta$ is equal to

A triangle has a vertex at $(1,2)$ and the mid points of the two sides through it are $(–1,1)$ and $(2,3)$. Then the centroid of this triangle is :

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

The number of real roots of the equation $x^2-12|x|+20=0$ is $P.$ Then the values of $a$ for which the equation $||x-2|+a|=P$ can have four distinct solutions, is

The domain of the function $f\left(x\right)=\frac{7}{\left[|x|\right]-5}$ is
(where $[.]$ denotes the greatest integer function)

Evaluate

Let f:
R → R be defined as f(x) = x⁴.
Choose the correct answer.

(A) f
is one-one onto (B) f is many-one onto

(C) f
is one-one but not onto (D) f is neither one-one nor onto

If $n^2-10n+21=p$ where $p$ is a prime number and $n\in N,$ then $n$ can be equal to

Let $y={\tan }^{-1}\left(\frac{x+y}{1-xy}\right),x\ge 0,y\ge 0$ and $xy<1$, then $\frac{dy}{dx}$ is equal to

Let $f$ be any function continuous on $[a,b]$ and twice differentaible on $(a,b)$. If for all $x\in (a,b),f^{\prime }\left(x\right)>0$ and $f^{\prime \prime }\left(x\right)<0$, then for any $c\in (a,b),\frac{f\left(c\right)-f\left(a\right)}{f\left(b\right)-f\left(c\right)}$ is greater than :

If $\alpha ,\beta$ are the roots of $x^2+7x+5=0$, then the equation whose roots are $\alpha -1,\beta -1$ is

The angle of elevation of a cloud $C$ from a point $P,200$ m above a still lake is ${30}^{\circ }$. If the angle of depression of the image of $C$ in the lake from the point $P$ is ${60}^{\circ }$, then $PC$ (in m) is equal to

Let $f$ be a function satisfying $f\left(0\right)=2,f^{\prime }\left(0\right)=3$ and $f^{\prime \prime }\left(x\right)=f\left(x\right)$. Then

If the roots of the equation 6x^2-7x+k are rational, then the value of k is.

Let $a=min\{x^2+2x+3,x\in R\},$ $b=\underset{\theta \to 0}{lim}\frac{1-\cos \theta }{{\theta }^2}$ and $\sum _{r=0}^n{a}^r\cdot b^{n-r}=f\left(n\right),$ then which of the following is/are correct?

Write the number of poits of intersection of the curves $2y=1andy=cosx,0\le x\le 2\pi .$

The point (4, 1)undergoes the following two successive transformation
(i) Reflection about the line y=x
(ii) Translation through a distance 2 units along the positive x-axis
Then the final coordinates of the point are

Let $E^c$ denotes the complement of an event E. If E, F, G are pairwise independent evens with P(G) > 0 and $P(E\cap F\cap G)=0.$ Then, $P(E^c\cap F^c|G)$ equals

A body takes 4 minutes to cool from ${100}^{\circ }C$

to ${70}^{\circ }C$ . To cool from ${70}^{\circ }C$ to ${40}^{\circ }C$ it will take

( room temperature is ${15}^{\circ }C$ )

${\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}\frac{dx}{1+cos2x}$ is equal to

Consider the family of lines $(x-y-6)+\lambda (2x+y+3)=0$ and $(x+2y-4)+\mu (3x-2y-4)=0.$ If the lines of these two families are at right angle to each other, then the locus of their point of intersection is

The values of $a$ and $b$ for which the function $y=a{\log }_{e}x+b{x}^2+x$, has extremum at the points $x_1=1$ and $x_2=2$ are :

Show
that the function defined by
is a continuous function.

Find the mean and variance of frequency distribution given below :

$\begin{array}{ccccc}{x}_i:& 1\le x<3& 3\le x<5& 5\le x<7& 7\le x<10\\ f_i:& 6& 4& 5& 1\end{array}$

Let $f\left(\frac{x+y}{2}\right)=\frac{f\left(x\right)+f\left(y\right)}{2}$ for all real $x$ and $y$. If $f^{\prime }\left(0\right)$ exists and equals to $-1$ and $f\left(0\right)=1$, then $f^{\prime }\left(2\right)$ is equal to

When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6}-x$ and its opposite face occurs with probability $\frac{1}{6}+x$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0<x<\frac{1}{6}$, and the probability of obtaining total sum $=7$, when such a die is rolled twice, is $\frac{13}{96}$, then the value of $x$ is

A tangent $PT$ is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3},1).$ A straight line $L,$ perpendicular to $PT$ is a tangent to the circle $(x-3{)}^2+y^2=1.$

A common tangent of the two circle is