Explore topic-wise InterviewSolutions in Current Affairs.

A straight line $L$ with negative slope passes through the point $(8,4)$ and cuts the positive co-ordinate axes at points $A$ and $B$. The minimum value of $OA+OB$, as $L$ varies, is (Here $O$ is the origin)

Find the value of x: 3x-4=0

If $a_1,a_2,.....$ is a sequence for which $a_1=2,a_2=3$ and $a_n=\frac{a_{n-1}}{a_{n-2}}$ for every natural number $n\ge 3$. Then the value of $a_{2011}$ is

If $\omega$ is a complex cube root of unity, then the value of $(a+b{)}^2+{(a\omega +b{\omega }^2)}^2+{(a{\omega }^2+b\omega )}^2$ is

Let $C_1$ be a curve with parametric point $(t^2+1,2t)$ and $C_2$ be a curve with parametric point $(2s,\frac{2}{s}).$ The number of points of intersection of the two curves $C_1$ and $C_2$ is

If $y=y\left(x\right)$ is the the solution of differential equation $x^2(xdx+ydy)+2y(ydx-xdy)=0,y\left(1\right)=1$ then which of the following is/are correct ?

If $\underset{x\to 1}{lim}\frac{n{x}^{n+1}-(n+1)x^n+1}{(e^x-e)\sin \pi x}=f\left(n\right)$, then which of the following is/are CORRECT?

Find the
perpendicular distance from the origin to the line joining the points

Find points on the curve

at which the tangents are

(i) parallel to x-axis (ii) parallel to y-axis

In a model, it is shown that an arc of a bridge is semi elliptical with major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal; then the height of the arch, 2m from the centre of the base is (in meters)

Let $E^c$ denote the complement of an event $E$. Let $E_1,E_2$ and $E_3$ be any pairwise independent events with $P\left(E_1\right)>0$ and $P(E_1\cap E_2\cap E_3)=0$. Then $P\left(\frac{E_2^c\cap E_3^c}{E_1}\right)$ is equal to:

If $g\left(x\right)=\underset{0}{\overset{x}{\int }}\cos \left(4t\right)dt$, then $g(x+\pi )$ equals

A fair coin is tossed repeatedly until the outcomes of both types have been obtained. The probability that the coin will be tossed exactly 5 times, is equal to:

Two equal sides of an isoceles triangle are given by $7x-y+3=0$ and $x+y-3=0$ and the third side passes through the point $(1,10)$ then the slope $m$ of the third side is given by

If the line $2y=4x-6$ cuts the curve $y^2=-16x$ at points $A$ and $B$, then the equation of circle having $AB$ as diameter is

equals

A. x
tan⁻¹ (x + 1) + C

B. tan^−
1 (x + 1) + C

C. (x +
1) tan⁻¹ x + C

D. tan⁻¹
x + C

For each real number x such that $-1<x<1,letA\left(x\right)bethematrix(1-x{)}^{-1}\left[\begin{array}{cc}1& -x\\ -x& 1\end{array}\right]andz=\frac{x+y}{1+xy}Then,$

Suppose $a^2=5a-8$ and $b^2=5b-8$. Then the equation whose roots are $\frac{a}{b}$ and $\frac{b}{a}$ is

Prove the following:-

Cos4x=1-8sin^2xcos^2x

If $U=(1+\cos \theta )(1+\cos 2\theta )-\sin \theta \sin 2\theta ,V=\sin \theta (1+\cos 2\theta )+\sin 2\theta (1+\cos \theta )$, then complete solution of the equation $U^2+V^2=16$ is

The value of the expression

$2(1+\frac{1}{\omega })(1+\frac{1}{{\omega }^2})+3(2+\frac{1}{\omega })(2+\frac{1}{{\omega }^2})+4(3+\frac{1}{\omega })(3+\frac{1}{{\omega }^2})+\cdots +(n+1)(n+\frac{1}{\omega })(n+\frac{1}{{\omega }^2}),$

where $\omega$ is an imaginary cube root of unity, is

If 8, 2 are the roots of $x^2+ax+\beta =0$ and 3, 3 are the roots of $x^2+\alpha x+b=0$ , then the roots of $x^2+ax+b=0$ are

Solve for $x:ta{n}^{-1}(x-1)+ta{n}^{-1}x+ta{n}^{-1}(x+1)=ta{n}^{-1}3x.$

OR

Prove that : $\left(\begin{array}{c}\frac{6x-8x^3}{1-12x^2}\end{array}\right)-ta{n}^{-1}\left(\begin{array}{c}\frac{4x}{1-4x^2}\end{array}\right)=ta{n}^{-1}2x;|2x|<\frac{1}{\sqrt{3}}.$

If the radius of a cone is 3 cm and its height is 7 cm, then its volume is _____ cubic cm.

If in the determinant $\Delta =\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|,A_1,B_1,C_1$etc. be the co-factors of $a_1,b_1,c_1$ etc., then which of the following relations is incorrect

If $Z=3x+4y,$ subject to the constraints: $x+y\le 4,$ $x\ge 0,$ $y\ge 0,$ then $Z_{max}$ is equal to



[1 mark]