Explore topic-wise InterviewSolutions in Current Affairs.

Prove the following question.

${\int }_1^3\frac{1}{x^2(x+1)}dx=\frac{2}{3}+log\frac{2}{3}$

Centroid of the tetrahedron OABC, where coordinates of A, B, C are (a, 2, 3), (1, b, 3) and (2, 1, c) respectively, is (1, 2, 3). Find the distance of the point (a, b, c) from the origin O

The equation of a circle whose $x$-coordinate of the centre is $5$ and radius is $4$ units and also touches the $x$-axis, is

Suppose, X has a binomial distribution B$(6,\frac{1}{2})$. Show that X=3 is the most likely outcome.

If a=2^p*3^q*5^r and b=p^2*q^3*r^5 , where p,q,r are primes,find the value of p+q+r, given that a=b.

Points P, Q and the centre of the circle O lies on a straight line. P, Q are both outside the circle. When chords of contact of P and Q are drawn to the circle they are found to coincide. Whats the distance between P and Q?

In a quiz, positive marks were given for correct answers and negative marks for incorrect answers. If Guru's scores in five successive rounds were $35,-10,-15,20,$ and $5,$ what is his total score at the end?

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\alpha \overrightarrow{d},$ $\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=\beta \overrightarrow{a}$ and $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar, then the sum of $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=$

The value of $\cot (2{\cos }^{-1}x+{\sin }^{-1}x)$ at $x=\frac{1}{5}$ is

The value of $\underset{x\to 0}{lim}{\left(\frac{e^{\ln (2^x-1{)}^x}-(2^x-1{)}^x\sin x}{e^{x\ln x}}\right)}^{1/x}$ is equal to

Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.

Which one of the following functions is analytic over the entire complex plane?

Find the value of tan $\left[\frac{1}{2}\{si{n}^{-1}\left(\frac{2x}{1+x^2}\right)+co{s}^{-1}\left(\frac{1-y^2}{1+y^2}\right)\}\right],|x|<1,y>0,xy<1$ .

The solution set of ${\log }_{(1-x)}(x-2)\ge -1$ is

If $\int f\left(x\right)dx=F\left(x\right)$, then $\int 5\times f\left(x\right)dx$ =

${lim}_{x\to \frac{\pi }{4}}\frac{1-sin2x}{1+cos4x}$

Find the area of the region bounded by
y² = 9x, x = 2, x = 4 and the
x-axis in the first quadrant.

Find the equation of director circle of a circle whose equation is $x^2+y^2-4x+6y+12=0$

If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_1}{r_2}-\frac{r_2}{r_3}$

If tangents drawn to the ellipse at the parametric point $\theta$, where $\tan \theta =2$ meets the auxillary circle at $P$ and $Q$ and $PQ$ subtends rightangle at the centre of the ellipse, then eccentricity of the ellipse is

Find the correct statement about the roots of the equation $x^2-4\sqrt{2}+8=0$.

Find the remainder when $7^{98}$ is divided by 5.

Ragini going with a boy is asked by another woman about the relationship between them. Ragini replied, “My maternal uncle and the uncle of his maternal uncle is the same.” How is Ragini related to the boy?

Life of bulbs producedby two factories A and B are given below :
$\begin{array}{cccccc}\text{Length of life}& 550-650& 650-750& 750-850& 850-950& 950-1050\\ \text{(in hours)}:& & & & & \\ \text{Factory A}:& & & & & \\ \text{(Number of bulbs)}& 10& 22& 52& 20& 16\\ \text{Factory B}:& & & & & \\ \text{(Number of bulbs)}& 8& 60& 24& 16& 12\end{array}$

The bulbs of which factory are more consistent from the point of view of length of

If $m,n$ are the roots of the equation $x^2+7x-8=0,$ then the equation equation whose roots are $5m-11,5n-11$ is

$a{x}^2+2hxy+b{y}^2=0$ always represents a pair of straight lines passing through the origin. If

$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{a.}{h}^2>ab& \text{1. Lines are coincident}\\ \text{b.}{h}^2=ab& \text{2. Lines are real and distinct}\\ \text{c.}{h}^2<ab\text{3. Lines are imaginary with real point of intersection i.e. (0,0)}& \end{array}$