Explore topic-wise InterviewSolutions in Current Affairs.

(–6, 0), (0, 6) and (–7, 7) are the vertices of a $\Delta$ ABC. The incircle of the triangle has the equation

If $a_k=\frac{1}{k(k+1)},fork=1,2,\mathrm{3.....}n,then{\left(\sum _{k=1}^n{a}_k\right)}^2=$

If $a$ is a complex number such that $|a|=1$ and $a{z}^2+z+1=0$ has one purely imaginary root, then $\cos \left(\arg \right(a\left)\right)$ is

2(bc cos A+ ca cos B + ab cos C)=

The family of curves passing through (0,0) and satisfying the differential equation $\frac{y_2}{y_1}=1$ (where $y_n=\frac{d^{n}y}{d{x}^n}$ is

In bridge game of playing cards, 4 players are distributed one card each by turn so that each player gets 13 cards. Find out the probability of a specified player getting a black ace and a king.

If a.a = 0 and a.b = 0, then what can be conclude about the vector b?

The slope of the tangent of the curve $y={\int }_0^x\frac{dx}{1+x^3}$ at the point where x = 1 is

Value of the numerically greatest term in the expansion of $\sqrt{3}(1+\frac{x}{\sqrt{3}}{)}^{20}$ at x=1 is

The integral $\int \frac{2x^3-1}{x^4+x}dx$ is equal to : (Here $C$ is a constant of integration)

If one of the foci of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ coincide with the focus of the parabola $y^2=8x$ and they intersect at a point where the ordinate is double the abscissa, then the value of $\left[b^2\right]$ is
(where [.] represents greatest integer function)

Evaluate the following limits:

${lim}_{x\to -5}\frac{2x^2+9x-5}{x+5}$

The locus of the vertices of the family of parabolas $y=\frac{a^3{x}^2}{3}+\frac{a^{2}x}{2}-2a$ is

If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to :

The area (in sq. units) of the region $\left\{\right(x,y)\in R^2|4x^2\le y\le 8x+12\}$ is :

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3. Then, $R^{-1}$ is

If $3A+4B^{\prime }$ =$\left[\begin{array}{ccc}7& -10& 17\\ 0& 6& 31\end{array}\right]$ and $2B-3A^{\prime }$=$\left[\begin{array}{cc}-1& 18\\ 4& 0\\ -5& -7\end{array}\right]$ then $B$=

Suppose C = 100 + 0.75YD, I = 500, G = 750, taxes are 20% of income, X = 150, M = 100 + 0.2Y.

Calculate equilibrium income, the budget deficit or surplus and the trade deficit or surplus.

Which of the following points lie on the parabola $x^2=4ay?$

If $\underset{x\to 0}{lim}\varphi \left(x\right)=a^3,a\ne 0$, then $\underset{x\to 0}{lim}\varphi \left(\frac{x}{a}\right)$ is

Let$f\left(x\right)={\log }_e\left(\sin x\right),(0<x<\pi )$ and $g\left(x\right)={\sin }^{-1}\left(e^x\right),(x\ge 0).$If $\alpha$ is a positive real number such that $a=\left(fog{)}^{\prime }\right(\alpha )$ and $b=\left(fog\right)\left(\alpha \right),$ then :

If $A=\{1,2,3,4,5,6,7,8\},B=\{1,3,5,6,7,8,9\}$ then $n\left(\right(A\Delta B)\times (B\Delta A\left)\right)$ is equal to

If the line $3x+4y-24=0$ intersects the x-axis at the point $A$ and y-axis at the point $B$, then the incentre of the triangle $OAB$, where $O$ is the origin is :

If ${}^n{C}_4={}^n{C}_5$, then the value of ${}^n{C}_2$ is

If $a=cos\theta +isin\theta$, find the value of $\frac{1+a}{1-a}.$.

$2(bccosA+cacosB+abcosC)=a^2+b^2+c^2$

The equation of chord of the circle $x^2+y^2-6x-4y-12=0$ which passes through the origin such that origin divides it in the ratio 3 : 2 is

The area bounded by the graphs of functions $f\left(x\right)=x^4-2x^2$ and $g\left(x\right)=2x^2$ is

${lim}_{x\to 0}\frac{xtanx}{1-cos2x}$

If $\alpha ,\beta ,\gamma$ are the roots of $x^3+lx+m=0$, then the value of ${\alpha }^3+{\beta }^3+{\gamma }^3$ is

The equation of straight line passing through the point $(3,6)$ and cutting $y=\sqrt{x}$ orthogonally is

Show that the product of perpendiculars on the line $\frac{x}{a}cos\theta +\frac{y}{b}sin\theta =1$ from the points $(\pm \sqrt{a^2-b^2},0)$ is $b^2$.

If $\frac{7}{2}$ and $1$ are the roots of the equation

$\left|\begin{array}{ccc}2x& 3& 7\\ 2& 2x& 2\\ 7& 6& 2x\end{array}\right|=0$, then the third root is

Integrate the following functions.
$\int \frac{1}{\sqrt{(x-1)(x-2)}}dx.$

Find the differential equation of all non-vertical lines in a plane.

Find the maximum and minimum values, if any, of the following function given by,

$g\left(x\right)=-|x+1|+3$

Events A and B ar such that $P\left(A\right)=\frac{1}{2}P\left(B\right)=\frac{7}{12}$ and P (not A or not B) $=\frac{1}{4}.$ State whether A and B are independent?

Integrate the function.
$\int xlogxdx.$

Consider the quadratic polynomial f(x)=x²-4x+5a²-6a.

Find the largest distance between the roots of the equation f(x)=0

The general solution of $4{\sin }^{2}x+{\tan }^{2}x+{\text{cosec}}^{2}x+{\cot }^{2}x-6=0$ is
(where $n\in Z$)