Explore topic-wise InterviewSolutions in Current Affairs.

The origin and the roots of the equation $x^2+ax+b$ = 0 form an equilateral triangle, if :

The maximum possible integral value of $\frac{\beta -\alpha }{{\tan }^{-1}\beta -{\tan }^{-1}\alpha },0<\alpha <\beta <\sqrt{3},$ is

Which of the following is a homogeneous differential equation?
(a) (4x +6y+5)dy-(3y+2x+4)dx=0
(b) $xydx-(x^3+y^3)dy=0$
(c) $(x^3+2y^2)dx+2xydy=0$
(d) $y^{2}dx+(x^2-xy-y^2)dy=0$

If $z=\cos \theta +i\sin \theta$ be a root of the equation $a_0{z}^n+a_1{z}^{n-1}+a_2{z}^{n-2}+\dots \dots +a_{n-1}z+a_n=0$, then

Find the simplified form of $co{s}^{-1}(\frac{3}{5}cosx+\frac{4}{5}sinx)wherex\in [\frac{-3\pi }{4},\frac{\pi }{4}].$

In a game, a man wins a rupee for a six and losses a rupee for any other number when a fair die is thrown. The man decide to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.

An urn contains 25 balls of which 10 balls bear a mark X and the remaining 15 bear a mark Y. A ball is drawn at random from the urn, its mark note down and it is replaced. If 6 balls are drawn in this way, find the probability that

not more than 2 will bear Y mark

In $\Delta$ ABC, if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c},$ then C is equal to

If $f"\left(x\right)=kin[0,a],then{\int }_0^{a}f\left(x\right)dx-{\left\{\begin{array}{c}xf\left(x\right)-\frac{x^2}{2!}{f}^{\prime }\left(x\right)+\frac{x^3}{3!}f"\left(x\right)\end{array}\right\}}_0^a$ is

Let $n$ be four digit positive integer in which all the digits are different. If $x$ is number of odd integers and $y$ is number of even integers, then

Find the direction cosines of the line segment joining the points A(2, 5, 7) and B (3,2,5) .

If $z_1,z_2$ and $z_3,z_4$ are two pairs of conjugate complex numbers, then the value of $\arg \left(\frac{z_1}{z_4}\right)+\arg \left(\frac{z_2}{z_3}\right)$ is

The vertex and focus of a parabola are (1,2) and (1,-1). Then the equation of the tangent at the vertex is

$x^2+y^2\mp 2kx\mp 2ky+k^2$ is a set of circles. Which of the following statements are true about them?

If det $\left[\begin{array}{ccc}1& 1& 2\\ 2& 4& 9\\ t& t^2& 1+t^3\end{array}\right]=0$, then the values of $t$ are

The number of solution(s) of the equation $\text{sgn}\left(\ln x\right)=3$ is
(Here, sgn denotes the signum function)

If $F\left(x\right)={\left(f\left(\frac{x}{2}\right)\right)}^2+{\left(g\left(\frac{x}{2}\right)\right)}^2$ where $f^{\prime }\left(x\right)=-f\left(x\right)$ and $g\left(x\right)=f^{\prime }\left(x\right)$ and given that $F\left(5\right)=5$, then $F\left(10\right)$ is equal to

If the sum of length of the hypotenuse and a side of a right angled triangle is given, then show that if the area of triangle is maximum, then the angle between them is $\frac{\pi }{3}$.

The general solution of the differential equation $e^{x}dy+(y{e}^x+2x)dx=0$ is

a) $x{e}^y+x^2=C$

b) $x{e}^y+y^2=C$

c) $y{e}^x+x^2=C$

d) $y{e}^y+x^2=C$

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{ccc}2& -3& 3\\ 2& 2& 3\\ 3& -2& 2\end{array}\right]$

Find $\frac{d}{dx}\left(se{c}^{-1}\left(\frac{1}{4x^3-3x}\right)\right),0<x<\frac{1}{\sqrt{2}}$

Let $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right],C=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$. Find each of the following:
(i)A+B

(ii)A-B

(iii)3A-C

(iv)AB

(v)BA

Differentiate given problems w.r.t.x.
$y=(logx{)}^{logx}$

20 cards are numbered from 1 to 20. One card is then drawn at random. What is the probability that the number of the card drawn is

(i) A prime number ?

(ii) An odd number ?

(iii) A multiple of 5 ?

(iv) Not divisible by 3 ?

R=$(5\sqrt{5}+11{)}^{2n+1}$ and $f=R-\left[R\right]$, where [] denotes the greatest integer function. Then the value of $Rf$ is

$Find\underset{x\to 0}{lim}+sgn\left(x\right)+\underset{x\to 0}{lim}-sgn\left(x\right),wheresgn\left(x\right)$ represents the signum function

[cos(π+x) cos(-x)] divided by / sin(π-x) cos(π/2 + x) = cot^2x

If $A=(6,-7),B=(-6,5)$ and $P,Q$ are two points on $AB$ such that $AP=PQ=QB$, then which of the following is/are correct?

$2ta{n}^{-1}\left(cosx\right)=ta{n}^{-1}\left(cose{c}^{2}x\right)$,then x=

Following is a set of four sentences. Choose the sentence which is most appropriate – grammatically, semantically and logically.

To every square matrix A = [] of order , we can associate a number called ___________ of the square matrix A, where = (, )th element of A.

If differentiation of a constant with respect to a variable is 0 , then differentiation of a variable with respect to a constant is infinity?

Yes or no I'm confused

$\underset{x\to 2}{lim}\frac{sin(e^{x-2}-1)}{log(x-1)}$

Prove that sinA/(cotA+cosecA)=2+sinA/(cotA-cosecA)

If the area of the parallelogram whose sides are x + 2y + 3 = 0, 3x + 4y - 5 = 0, 2x+4y+5=0 and 3x + 4y - 10 = 0 is 'a' sq. unit. Find the value of 4a

In a group of $400$ people, $160$ are smokers and non-vegetarian; $100$ are smokers and vegetarian and the remaining $140$ are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35\%,20\%$ and $10\%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:

The curve y = f(x) is such that the area of the trapezium formed by the coordinate axes, ordinate of an arbitrary point and the tangent at this point equals half the square of its abscissa. The equation of the curve can be

If the lines $a_{1}x+b_{1}y+c_1=0\text{and}{a}_{2}x+b_{2}y+c_2=0$ cut the coordinates axes in concyclic points, then

If $\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}$ are three non-coplanar unit vectors then $\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]$ is equal to

If $\sqrt{x^{\frac{1}{x}}.(2x{)}^{\frac{1}{2x}}.(4x{)}^{\frac{1}{4x}}.(8x{)}^{\frac{1}{8x}}\dots \infty }=\frac{32}{3125},$ then $x$ equals