Explore topic-wise InterviewSolutions in Current Affairs.

If the $2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ terms in the expansion of $(x+a{)}^n$ are $240,720$ and $1080$ respectively, then the value of least term in the expansion is

The area of the triangle formed by $1+i,i-1$ and $2i$ in the Argand plane is

The value of the integral ${\int }_3^6\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dxis$

Prove that:

sin 4A = 4 sin A $co{s}^3$ A - 4 cos A $si{n}^3$ A

Perpendicular distance of P(x, y, z ) from XY, YZ and XZ planes respectively are 1, 2 and 3. Which of the following could be the coordinates of P?

Question 4 (vi)

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(vi) 0.2, 0.22, 0.222, 0.2222 ….

$3x–5y=4$

$9x=2y+7$

Solve the above equations by elimination method and find the value of x.

Let $A=\{x:x\text{is a prime factor of}30\}$ and $B=\{y:y\in N,-3\le y+3<8\}$. If $R$ is a relation from $A$ to $B$, then $R^{-1}$ can be

1. 4

Show that $A\cap B=A\cap C$ need not imply $B=C.$

$1.2+{2.2}^2+{3.2}^3+....+n{.2}^n=(n-1)2^{n+1}+2$

The volume of a right triangular prism $ABC{A}_1{B}_1{C}_1$ is equal to 3. Than the co-ordinates of the vertex A1, if the co-ordinates of the base vertices of the prism are A(1, 0, 1), B(2, 0, 0) and C(0, 1, 0)

Find the area of the region enclosed by
the parabola x² = y, the line y = x
+ 2 and x-axis

Let the circles $C_1:x^2+y^2=9$ and $C_2:(x-3{)}^2+(y-4{)}^2=16,$ intersect at the points $X$ and $Y.$ Suppose that another circle $C_3:(x-h{)}^2+(y-k{)}^2=r^2$ satisfies the following conditions:

$\left(i\right)$ centre of $C_3$ is collinear with the centres of $C_1$ and $C_2.$

$\left(ii\right)$$C_1$ and $C_2$ both lie inside $C_3$, and

$\left(iii\right)$ $C_3$ touches $C_1$ at $M$ and $C_2$ at $N$

Let the line through $X$ and $Y$ intersect $C_3$ at $Z$ and $W$, and let a common tangent of $C_1$ and $C_3$ be the tangent to the parabola $x^2=8\alpha y.$
There are some expressions given in $List-I$ whose values are given in $List-II$ below:

$\begin{array}{cccc}& \text{List}I& & \text{List}II\\ \left(I\right)& 2h+k& \left(P\right)& 6\\ \left(II\right)& \frac{\text{length of}ZW}{\text{length of}XY}& \left(Q\right)& \sqrt{6}\\ \left(III\right)& \frac{\text{Area of triangle}MZN}{\text{Area of triangle}ZMW}& \left(R\right)& \frac{5}{4}\\ \left(IV\right)& \alpha & \left(S\right)& \frac{21}{5}\\ & & \left(T\right)& 2\sqrt{6}\\ & & \left(U\right)& \frac{10}{3}\end{array}$
Which of the following is the only CORRECT combination?

1. 110

The interval(s) in which the value of $2{\tan }^{-1}x+{\sin }^{-1}\left(\frac{2x}{1+x^2}\right)$ is independent of $x$ is

The domain of two definition of the function f(x) is given by the equation $2^x+2^y=2$ is

Find the integrals of the functions.
$\int sin4xsin8x$ dx

Which of the following is a homogeneous differential equation?

A.

B.

C.

D.

The chord joining the points of contact of tangents drawn from any point on $x-1=0$ to $y^2-6y+4x+9=0$ passes through the point

A function $f:R-\left\{\right(2k-1\left)\pi \right\}\to R$ is defined as, $f\left(x\right)=\frac{1}{\sqrt{m^2-n^2}}\ln \left(\frac{\sqrt{m+n}+\sqrt{m-n}\tan \left(x/2\right)}{\sqrt{m+n}-\sqrt{m-n}\tan \left(x/2\right)}\right)$ where $k,m,n\in Z^{+}$ and $n<m$

If $f^{\prime }\left(\frac{\pi }{3}\right)=\frac{1}{9}$, then which of the following ordered pairs of $(m,n)$ is/are correct?

​​​​​​$\begin{array}{cc}ColumnI& ColumnII\\ \text{a. If}I=\underset{-2}{\overset{2}{\int }}(\alpha x^3+\beta x+\gamma )dx,\text{then}I\text{is}& \text{p.}\text{independent of}\alpha \\ \text{b. Let}\alpha ,\beta \text{be the distinct positive roots}& \\ \text{of the equation}\tan x=2x,\text{then}& \\ \gamma \underset{0}{\overset{1}{\int }}(\sin \alpha x\cdot \sin \beta x)dx(\text{where}\gamma \ne 0)\text{is}& \text{q.}\text{independent of}\beta \\ \text{c. If}f(x+\alpha )+f\left(x\right)=0,\text{where}\alpha >0,& \\ \text{then}\underset{\beta }{\overset{\beta +2\gamma \alpha }{\int }}f\left(x\right)dx,\text{where}\gamma \in N,\text{is}& \text{r.}\text{independent of}\gamma \\ & \text{s.}\text{depends on}\alpha \end{array}$

Then which of the following is correct ?

If $\frac{2\pi }{3}<\alpha <\pi$, then the distance between the points $(\sin \alpha ,0)$ and $(0,\cos \alpha )$ is

Argument of $z$ if $z=\sin \left(\frac{\pi }{5}\right)+i(1-\cos \left(\frac{\pi }{5}\right))$ is

If the lines
and
are
perpendicular, find the value of k.

(Vector (A)×vector(B))^2 + (vector (A).vector(B))^2 =

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

$y=x^{sinx}+sin{x}^{cosx}$

If $4$ dice are rolled once, the number of ways of getting the sum as $10$ is

If $\int \frac{1-{\left(\cot x\right)}^{2008}}{\tan x+{\left(\cot x\right)}^{2009}}dx=\frac{1}{k}\ln |{\sin }^{k}x+{\cos }^{k}x|+C$ for arbitrary constant of integration $C,$ then the value of $k$ is

The equation of the tangent to the curve $y=2t^2+t,x=t^2$ at $(1,3)$ is