Explore topic-wise InterviewSolutions in Current Affairs.

Let $n_1$ and $n_2$ be the number of red and black balls, respectively in box I. Let $n_3$ and $n_4$ be the number of red and black balls, respectively in box II.
One of the two boxes, box I and box II was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II, is $\frac{1}{3},$ then the correct option(s) with the possible values of $n_1,n_2,n_3$ and $n_4$ is/are

${lim}_{x\to 0}\frac{cos3x-cos7x}{x^2}$

Tangents drawn from the point P(1, 8) to the circle $x^2+y^2-6x-4y–11=0$ touch the circle at the points A and B. The equation of the circum circle of the trianglePAB is

There are m-stations on a railway line. A train has to stop at 3 intermediate stations. Then probability that no two stopping stations are adjacent is

$\int \frac{{\cos }^{3}x+{\cos }^{5}x}{{\sin }^{2}x+{\sin }^{4}x}dx=$

The value of 5! is _____

Find the Derivation of $f\left(x\right)=x^2.atx=0$

The perpendicular distance of the point $P(6,7,8)$ from $XY$- plane is

Differentiate the following functions with respect to x :

$\frac{1}{a{x}^2+bx+c}$

If A = { n: n is a digit in the number 33591 } and B = { n: n is natural number less than 10 } , then B – A =

Write down all possible subsets of each of the following sets :

(i) {a} (ii) {0, 1}

(iii) {a, b, c} (iv) {1, {1}}

(v) {$\varphi$}

Express $sin\frac{\pi }{5}+i(1-cos\frac{\pi }{5})$ in polar form.

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

If in the expansion of $(a+b{)}^n$ and $(a+b{)}^{n+3}$, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is

The possible value(s) of $a$ for which the equation $x^2+2x-(a^3-3a-3)=0$ has real roots is/are

If $a\le ta{n}^{-1}x+co{t}^{-1}x+si{n}^{-1}x\le b$, then

If $f:R\to R$ is defined by $f\left(x\right)=x^2-3x+2$, write $f\left\{f\right(x\left)\right\}$.

The value(s) of the parameter $\alpha (\alpha \ge 2)$ for which the area of region bounded by pair of straight lines $y^2-3y+2=0$ and the curves $y=\left[\alpha \right]x^2$, $y=\frac{1}{2}\left[\alpha \right]x^2$ is greatest, where $[.]$ denotes the greatest integer function, is

Find the equation of the line joining (3,1) and (9,3) using determinants.

Write the value of $sin\frac{\pi }{12}sin\frac{5\pi }{12}$

By appropriately matching the information given in the three columns of the following table.

$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ & & & \text{Number of divisors of type}& & \\ \left(I\right)& N=490& \left(i\right)& (4p+2),\text{where p is non-}& \left(P\right)& 44\\ & & & \text{negative integer}& & \\ \left(II\right)& N=2^5{3}^4{5}^{10}& \left(ii\right)& \text{Number of divisors which are}& \left(Q\right)& 55\\ & & & \text{divisible by 3 or 2 or both}& & \\ \left(III\right)& N=378& \left(iii\right)& \text{Number of divisors which are}& \left(R\right)& 32\\ & & & \text{perfect squares}.& & \\ & & & \text{Number of ways to resolve the}& & \\ \left(IV\right)& N=300300& \left(iv\right)& \text{Number as product of two}& \left(S\right)& 02\\ & & & \text{relatively prime factors}.& & \end{array}$

If $A=\{0,1,2,3,5\},B=\{0,1,2,3\},C=\{0,1,4,5\}$, then $n\left(A\Delta B\right)+n\left(B\Delta C\right)+n\left(C\Delta A\right)$ is equal to

If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.

Let $A=\{z_1:z_1^{16}=1,z_1ϵC\},B=\{z_2:z_2^{72}=1,z_2ϵC\}andP=\{z_1{z}_2:z_1ϵA,z_2ϵB\}$ are three sets of complex roots of unity (where C denotes set of complex numbers), then

If the line y=mx+1 is tangent to the parabola $y^2=4x,$ then find the value of m.

Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line $5x+12y-1=0$

A coin is tossed twice. if the second draw results in a head, a die is rolled. Write the sample space for this experiment.

Solve the following system of equations in R.

$4x-1\le 0,3-4x<0$

Find the equation of the circle which circumscribes the triangle formed by the lines $x=0,y=0$ and $lx+my=1$.

Find the 21st term of -6 , -2 , +2 ,+........

Let f(x) =[n+p sin x],x belongs to (0,π),n belongs to Z ,p is a prime number and [x] is greatest integer less than or equal to x .The number of points at which f(x) is not differentiable is

A. p

B. p-1

C. 2p+1

D. 2p-1

For what value of k, are the roots of the quadratic equation kx (x - 2) + 6 = 0 equal?

Equation of the parabola obtained by taking reflection of $y=4x^2-4x+3$ about the line $y=x,$ will be

The locus of the center of a variable circle which cuts-off the intercept of 2 units and 4 units respectively on the X-axis and the Y-axis is .

Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years.

Integrate the following functions.
$\int \frac{x^2}{1-x^6}dx.$

The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to the circle $x^2+y^2=1$ pass through a fixed point

Find the equation of the normal at the point $(a{m}^2,a{m}^3)$ for the curve $a{y}^2=x^3$

The shaded area enclosed between the parabolas with equations y = 1 + 10x - 2x² and y = 1 + 5x - x² is equal to: