Explore topic-wise InterviewSolutions in Current Affairs.

Integrate the following functions.
$\int \frac{x+2}{\sqrt{x^2+2x+3}}dx.$

Suppose that $5\%$ of men and $0.25\%$ of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

If the matrix A =$\left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ b& 1& 0\end{array}\right]$ is skew symmetric, find the value of 'a' and 'b'.

If $f\left(x\right)=2x$ and $g\left(x\right)=\frac{x^2}{2}+1$ , then which of the following can be a discontinuous function

Find the value of x for which the following expressions attain minimum value:

a) x^2 +1

The differential equation for a family of curves is $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{y}{2x}.$ What is the differential equation for the orthogonal trajectory of the curves?

If $A,B,C\ne \frac{(2n+1)\pi }{2}$, then the numerical value of $\frac{\sin (B-C)}{\cos B\cos C}+\frac{\sin (C-A)}{\cos C\cos A}+\frac{\sin (A-B)}{\cos A\cos B}$ is

If ${}^n{C}_4{=}^n{C}_6,$ find ${}^{12}{C}_n$.

If the lines $ax+y+1=0,x+by+1=0,\text{and}x+y+c=0(a,b,c\text{being different from 1})$ are concurrent, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is

What is tan (135) ?

The multiplicative inverse of a non-zero complex number $z$ is

If $A\times B=\left\{\right(1,1),(1,2),(1,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3\left)\right\}$ then

Find the 4th term from the end in the expansion of ${(\frac{4x}{5}-\frac{5}{2x})}^9$

The set of points on the axis of the parabola $y^2-2y-4x+5=0$ from which all the three normals to the parabola are real is :

A student is standing at a distance of $50$ meters from the bus. As soon as the bus starts its motion with an acceleration of $1\frac{m}{s},$ the student starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is

$Iff\left(x\right)=\{\begin{array}{cc}\frac{3x-x^2}{2}& x<2\\ [x-1],& 2\le x<3\\ x^2-8x+17,& x\ge 3\end{array}$

then which of the following hold(s) good?

[Note ; [x] denotes largest integer less than or equal to x,]

Prove the following,

$ta{n}^{-1}\frac{2}{11}+ta{n}^{-1}\frac{7}{24}=ta{n}^{-1}\frac{1}{2}$

Find the equation of the hyperbola satisfying the given conditions.
Vertices $(\pm 7,0),e=\frac{4}{3}$

A variable straight line through $A(-1,-1)$ is drawn to cut the circle $x^2+y^2=1$ at the points $B,C.$ If $P$ is chosen on the line $ABC$ such that $AB,AP,AC$ are in $H.P$ then the locus of $P$ is

Using integration, find the area of the region bounded by he triangle whose vertices are (-1, 2), (1,5) and (3,4)

If a+in form of the liar representation 5(cos3pie/2+isin3pie/2) is:

1. 7-5I

2. 7+5I

3. 0+5I

4. 0-5i

For the differential equation given in the question find a particular solution satisfying the given condition.

$\frac{dy}{dx}-3ycotx=sin2x,wherey=2andx=\frac{\pi }{2}$

The range of f(x) = $\frac{x-\left[x\right]}{1+x-\left[x\right]}$ where [] represents greatest integer function.

sin(2n+1)AsinA=sin²(n+1)A-sin²nA . Prove this .

The solution of the linear inequality $\frac{3(x-2)}{5}\le \frac{5(2-x)}{3}$ is

The product of the slopes of the tangents to the ellipse $2x^2+3y^2=6$ drawn from the point (1, 2) is

Let S = Z x (Z - {0}) and the binary operation * is defined as (a , b) * (c ,d) = (ad + bc , bd) for all a,b,c,d ϵZ. The identity element of of S for the binary operation * on S is __

A square matrix A is said to be a symmetric matrix if

The vector joining the points A (2, – 3, 1) and B (1, – 2, – 5) directed from B to A is:

Which of the following point lie inside the circle $x^2+y^2-2x+3y-11=0$

The expression $E=\frac{1}{cosec\theta -cot\theta }-\frac{1}{sin\theta }$ is equal to which of the following expression?

In how many ways can six persons be seated in a row ?

${}^n{P}_r÷{}^n{C}_r$ =

Equation of latus rectum of hyberbola $(10x-5{)}^2+(10y-2{)}^2=9(3x+4y-7{)}^2$ is

If $x_1,x_2,x_3,....,x_n$ are in A.P. whose common difference is $\alpha$, then the value of $sin\alpha (sec{x}_{1}sec{x}_2+sec{x}_{2}sec{x}_3+......+sec{x}_{n-1}sec{x}_n)=$

If $y=\frac{1+\frac{1}{x^2}}{1-\frac{1}{x^2}},$ then $\frac{dy}{dx}=$

If $co{s}^6\alpha +si{n}^6\alpha +Ksi{n}^{2}2\alpha =1,$ then K=

In a test student either guesses or copies or knows the answer to a multiple choice questions with four choices in which exactly one choice is correct. The probability that he makes a guess is $\frac{1}{3}$. The probability that he copies the answer is $\frac{1}{6}$. The Probability that his answer is correct given that he copied it is $\frac{1}{8}$. Find the probability that he knew the answer to the question given that he correctly answered it is

The points of intersection of the curves whose parametric equations are $x=t^2+1,y=2tandx=2s,y=\frac{2}{s}$ Is given by

Find x in each of the following :
(i) $\frac{1}{4!}+\frac{1}{5!}=\frac{x}{6!}$
(ii) $\frac{x}{10!}=\frac{1}{8!}+\frac{1}{9!}$
(iii) $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}$

What is the Relation between the direction cosines of a line?

If OA and OB are two equal chords of the circle $x^2+y^2-2x+4y=0$ perpendicular to each passing through the origin O,the slopes of OA and OB are the roots of the equation

If three points A,B&C have position vectors (1,x,3),(3,4,7) and (y,-2,-5) respectively.If they are collinear find the values of x&y.

$\text{Write the values of x in}[0,\pi ]forwhichsin2x,\frac{1}{2}andcos2xareinA.P.$