Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\int \frac{2x^5-3x^4+8x^3-8x^2+2x+19}{x^2+4}dx$ is

(where $C$ is constant of integration)

Solve the inequalities and represent the solution graphically on number line: 5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47

Find a
if the coefficients of x²
and x³
in the expansion of (3 + ax)⁹
are equal.

Four identical particles each of mass $m$ are arranged at the corners of a square of side length $L$. If one of the masses is doubled, the shift in the centre of mass of the system w.r.t the diagonally opposite mass is

9^x+2 – 6 x 3^x+1 + 1 = 0, find x.

Two events $A$ and $B$ have the probabilities $0.25$ and $0.5$ respectively. The probability that both $A$ and $B$ occur simultaneously is 0.14. Then the probability of neither A nor B occurs is equal to:

Two lines $4x+2y=10$ and $2x-y=20$ are touching a circle whose radius is $\sqrt{5}$ units. Then the equation of the circle which is nearest to the $x$-axis, is

In how many ways a commitee of six members be formed from 7 men and 5 women if the commitee contains 4 men and 2 women?

The integral of $\frac{x^2-x}{x^3-x^2+x-1}$ with respect to $x$ is

(where $C$ is constant of integration)

If the letters of the word PROBABILITY are written down at random in a row, the probability that two B-s are together is

Question 4(ii)

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions:



How many more marks were obtained by the students in Mathematics than in Hindi?

The number of different items available at two different shops are given as below:





What is the marginal frequency for the number of markers ?

If $\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|$



$=(a+b+c)(x+a+b+c{)}^2,x\ne 0$ and $a+b+c\ne 0$, then $x$ is equal to :

If $p$ and $q$ are the lengths of the perpendiculars from the origin on the lines, $x\text{cosec}\alpha -y\sec \alpha =k\cot 2\alpha$ and $x\sin \alpha +y\cos \alpha =k\sin 2\alpha$ respectively, then $k^2$ is equal to :

A two span beam with an intemal hinge is shown below





Conjugate beam corresponding to this is

If $f\left(x\right)=co{s}^{-1}\left(\frac{\sqrt{2x^2+1}}{x^2+1}\right)$, then range of f(x) is

In a $△ABC,$ the value of $a^3\cos (B-C)+b^3\cos (C-A)+c^3\cos (A-B)=$

Find the derivative of the function given by $f\left(x\right)=(1+x)(1+x^2)(1+x^4)(1+x^8)$ and hence find f ' (I).

The equation x- y = 4 and $x^2+4xy+y^2=0$ represent the sides of

The value of $(3\cdot 2\cdot {}^1{P}_0-4\cdot 3\cdot {}^2{P}_1+5\cdot 4\cdot {}^3{P}_2-\cdots \text{upto}101\text{terms})$ $+(2!-3!+4!-\cdots \text{upto}101\text{terms})$ is equal to

If $\alpha$ is positive root of the equation, $p\left(x\right)=x^2-x-2=0,$, then $\underset{x\to {\alpha }^{+}}{lim}\frac{\sqrt{1-\cos \left(p\left(x\right)\right)}}{x+\alpha -4}$ is equal to :

If S₁, S₂,
S₃ are the sum of first n natural numbers, their
squares and their cubes, respectively, show that

The image of point $P(1,-2,3)$ in the plane $2x+3y-4z+22=0$ measured parallel to the line $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is

If $x$ is a whole number, than $x^2(x^2-1)$ is always divisible by

Find
of
function.

If $|z-\frac{4}{2}|=2,$ then the maximum value of is

Consider a parabola $y=\frac{x^2}{4}$ and the point $F(0,1)$. Let $A_1(x_1,y_1),A_2(x_2,y_2),A_3(x_3,y_3),...,A_k(x_k,y_k)$ are $\text{'}n\text{'}$ points on parabola such as $x_k>0$ and $\angle OF{A}_k=\frac{k\pi }{2n},(k=1,2,3,...,n)$. Then the value of $\underset{n\to \infty }{lim}\frac{1}{n}\sum _{k=1}^{n}F{A}_k$ is