Explore topic-wise InterviewSolutions in Current Affairs.

α, β are the roots of the equation $x^2$ + 4x + 5. Find ${\alpha }^3$ + ${\beta }^3$

Three faces of a fair dye are yellow, two faces red and one blue. The die is tossed three times. The probability that the colours, yellow red and blue appear in first, second and the third tosses respectively is ............

If the radius of sphere is measured as 7 m with an error of 0.02 m, then the approximate error in calculating its volume is

A straight line, makes an angle of ${60}^{\circ }$ with each of y and z-axis,then the inclination of the line with x-axis is

Three coins are tossed once. Let A denote the event "three heads show ", B denote the event "two heads and one tail show", c denote the event "three tails show" and D denote the event "a head show on the first coin", Which events are (i) mutually exclusive ? (ii) simple ? (iii) compound?

The negation of "Ram and Rahim are not brave" is .

The circle $x^2+y^2+2gx+2fy+c=0$ does not intersect x-axis, if

If $\exp \left[\right({\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+....\infty ){\log }_{e}2$, satisfies the equation $x^2-9x+8=0$, then the value of $\frac{\cos x}{\cos x+\sin x},0<x<\frac{\pi }{2}$ is

If the mode of the data is $18$ and the mean is $24$, then median is

The circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to

Consider a family of straight lines $(x+y)+\lambda (2x-y+1)=0$. Then the equation of the straight line belonging to this family that is farthest from $(1,-3)$ is:

The perpendicular distance of a line from the origin is 5 units and its slope is - 1. Find the equation of the line.

$\int e^x(\frac{2\tan x}{1+\tan x}+{\cot }^2(x+\frac{\pi }{4}))dx$ is equal to

If the major axis is “n” (n>1) times the minor axis of the ellipse, then its eccentricity is

Let $I=\underset{a}{\overset{b}{\int }}(x^4-2x^2)dx$. If $I$ is minimum then the ordered pair $(a,b)$ is :

Prove that the term independent of x in the expansion of ${(x+\frac{1}{x})}^{2n}$ is

$\frac{\mathrm{1.3.5....}(2n-1)}{n!}{.2}^n.$

Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 9& 3& 1\end{array}\right]$ and $Q=\left[q_{ij}\right]$ be two $3\times 3$ matrices such that $Q-P^5=I_3.$ Then $\frac{q_{21}+q_{31}}{q_{32}}$ is equal to

If the system of equations ax + y = 3, x + 2y =3, 3x + 4y =7 is consistent, then value of a is equal to

Which of the following is a unit vector in the direction of $\hat{i}+\hat{j}+\hat{k}$.

If two squares are chosen at random on a chess board, the probability that they have a side in common is:

In $\Delta XYZ$, $YZ=2$ units, $XZ=3$ units and medians $XP,YQ$ are such that $XP$ is perpendicular to $YQ$. Then the area of $\Delta XYZ$ is

$\begin{array}{cccc}& List-I& List-II& \\ P.& Z_k=cos\left(\frac{2k\pi }{2016}\right)+Isin\left(\frac{2k\pi }{2016}\right)k=1,2,3,...,2015then1-{\sum }_{k=1}^{2015}cos\left(\frac{2k\pi }{2016}\right)=& 1.& 0\\ Q.& If(a^2-a+k)(11b^2-4b+2)=\frac{9}{2}haveexactlyoneorderedpair(a,b)thenk=& 2.& 2\\ & InatriangleABC,equationsofmediansADandBEare2x+3y=6,3x& & \\ R.& -2y=10respectivelyandAD=6,BE=11& 3.& 3\\ & andareaoftriangleABCis11kthenK=& & \\ S.& y\left(x\right)=acosInx+bsinInx,(x>0)and\frac{1}{y\left(x\right)}(x^2\frac{d^{2}y\left(x\right)}{d{x}^2}+x\frac{dy\left(x\right)}{dx})+1=& 4.& 4\end{array}$

Area under the curve y = sin 2x + cos 2x between x=0 and $x=\frac{\pi }{4}$is

The area (in sq. units) of the region $\left\{\right(x,y):x\ge 0,x+y\le 3,x^2\le 4y\text{and}y\le 1+\sqrt{x}\}$
is:

If I is the greatest of the definite integrals
$I_1={\int }_0^1{e}^{-x}co{s}^{2}xdx,I_2={\int }_0^1{e}^{-x^2}co{s}^{2}xdx$
$I_3={\int }_0^1{e}^{-x^2}dx,I_4={\int }_0^1{e}^{\frac{-x^2}{2}}dx,then$

The equation of the common tangent touching the circle $(x-3{)}^2+y^2=9$ and the parabola $y^2=4x$ above the X-axis is

If the vertices of a triangle be (0,0), (6,0) and (6,8), then its incentre will be

If $(21.4{)}^a=(0.00214{)}^b=100$, then the value of $\frac{1}{a}-\frac{1}{b}$ is

The set of values of 'c' so that the equations $y=\left|x\right|+cand{x}^2+y^2-8\left|x\right|-9=0$ have no solution is

If $A$ and $B$ are two events such that $P(A\cup B{)}^{\prime }=\frac{1}{6}$, $P(A\cap B)=\frac{1}{4}$ and $P\left(A^{\prime }\right)=\frac{1}{4}$, then events $A$ and $B$ are

A man takes a step forward with the probability of $0.4$ and one step backward with the probability of $0.6$, then the probability that at the end of eleven step he is one step away from the starting point is

Write the value of $sin{12}^{\circ }sin{48}^{\circ }sin{54}^{\circ }$

$\text{Find the ecentrictity, coordinates of foci, equations of directrices and length of the latus-rectum of the hyperbola}\left(i\right)9x^2-16y^2=144\left(ii\right)16x^2-9y^2=-144\left(iiii\right)4x^2-3y^2=36\left(iv\right)3x^2-y^2=4\left(v\right)2x^2-3y^2=5$

The number of solution(s) of the equation $x-\frac{7}{x-3}=3-\frac{7}{x-3}$ is

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $\frac{1}{2}$ , then length of the minor axis is

The probability that a person will travel by plane is 3 / 5 and that he will

travel by train is 1 / 4. What is the probability that he (she) will travel by

plane or train ?

Let $S_n$ denotes the sum of the first $n$ terms of an A.P.. If $S_4=16$ and $S_6=-48,$ then $S_{10}$ is equal to

If one root of the equation $a{x}^2$ + bx + c = 0 be n times the other root, then

When ${32}^{33}$ is divided by 34, it leaves the remainder

Let f be the subset of Z × Z defined by f= {(ab, a+b) : a, b belongs to Z } . Is f a function from Z to Z ?