Explore topic-wise InterviewSolutions in Current Affairs.

The solution of primitive equation $-y\frac{dy}{dx}=x\sqrt{1-y^2}$ is $y=y\left(x\right)$, where $y\left(x\right)$ is non-constant. If $y\left(0\right)=1$, then which of the following is/are correct

If $a,b,c$ are in A.P. and $a,c-b,b-a$ are in G.P., where$a\ne b\ne c$, then $a:b:c$ is ___.

If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}\times \overrightarrow{c},$ then $(\overrightarrow{a}\times \overrightarrow{b}).(\overrightarrow{a}\times \overrightarrow{c})+(\overrightarrow{a}\times \overrightarrow{b}).\left(\overrightarrow{a}\right(\overrightarrow{b}\times \overrightarrow{c}\left)\right)$ is ?

Let $P(x_1,y_1)$ and $Q(x_2,y_2)$, $y_1<0,y_2<0$ be the ends of the latus rectum of the ellipse $y^2+4x^2=4$. the equations of parabolas with latus rectum PQ are

If $\alpha$, $\beta$ are the roots of $x^2+px+q=0$, then the value of ${\alpha }^3+{\beta }^3$ is

If $A=\{-1,0,2,5,6,11\},B=\{-2,-1,0,18,28,108\}$ and $f\left(x\right)=x^2-x-2,$ find $f\left(A\right).$ Is $f\left(A\right)=B?$

There are $12$ persons in a party, and if each two of them shake hands with each other, then how many hand shakes happen in the party?

Find the value of $si{n}^4{735}^{\circ }$ + $co{s}^4{735}^{\circ }$ - $si{n}^2{735}^{\circ }$ $co{s}^2{735}^{\circ }$.

The value of $\left|\begin{array}{ccc}a-b& b+c& a\\ b-a& c+a& b\\ c-a& a+b& c\end{array}\right|$

(a) $a^3+b^3+c^3$
(b) $3bc$
(c) $a^3+b^3+c^3-3abc$
(d) None of these

The solution of $(x+2y^3)\left(\frac{dy}{dx}\right)=y$ is (where c is arbitrary constant)

If the domain of the function $y=f\left(x\right)$ is $[-3,2],$ then the domain of $f\left(|\right[x\left]|\right)$ is

(where [.] denotes the greatest integer function)

Find the equation of a line passing through $(1,2,3)$ having direction ratios $1,2,4$

The values of x between 0 and $2\pi$ which satisfy the equation $sinx\sqrt{8co{s}^{2}x}=1$ are in A.P. The common difference of the A.P. is

Evaluate $\int \frac{x^{7}dx}{{(1-x^2)}^5}$

(where $C$ is constant of integration)

$\text{Express the det}A=\left|\begin{array}{ccc}a& bc& abc\\ b& ca& abc\\ c& ab& abc\end{array}\right|\text{as product of factors}$

The value of $\sum _{n=1}^{10}\underset{-2n-1}{\overset{-2n}{\int }}{\sin }^{27}xdx+\sum _{n=1}^{10}\underset{2n}{\overset{2n+1}{\int }}{\sin }^{27}xdx=$

Matrix A is such that $A^2=2A-I,$ where I is the Identity matrix. Then for $n\ge 2,A^n$ is equal to

If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3, is

Reduce the expression $y=\frac{x^2-x+1}{x^2+x+1}$ to the form $a{x}^2+bx+c$ and give condition for x to be real.

The value of remainder when $3^{2n+1}+2^{n+2}$, where $n\ge 10$ is divided by $7$ is

One of the eigen vectors of the matrix $A=\left[\begin{array}{cc}2& 2\\ 1& 3\end{array}\right]$ is

If the last term in the binomial expansion of ${(2^{1/3}-\frac{1}{\sqrt{2}})}^n$ is ${\left(\frac{1}{3^{5/3}}\right)}^{{\log }_{3}8}$, then the $5^{\text{th}}$ term from the beginning is

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to a line, whose direction ratios are $2,3,-6$ is

For the parabola $y^2=4ax$, the ratio of the sub-tangent to the abcissa is

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ is

If two matrices $A$ and $B$ are commutative, then which of the following is(are) not equal to $A^2{B}^5$

When x is so small that its square and higher powers may be neglected, find the value of

$\frac{{(1+\frac{2}{3}x)}^{-5}+\sqrt{4+2x}}{\sqrt{(4+x{)}^3}}$.

The locus of mid points of chords of the parabola $y^2=8x$ drawn through the vertex is a parabola whose

Find the tangent to the parabola $y^2=8x$ which makes an angle of ${45}^{\circ }$ to the line
$2x+y+3=0$

Let A, B , and C be three independent events with $P\left(A\right)=\frac{1}{3},P\left(B\right)=\frac{1}{2},andP\left(C\right)=\frac{1}{4}.$ . The probability of exactly 2 of these events occurring, is equal to

If $x=\sec \theta -\cos \theta$ and $y={\sec }^n\theta -{\cos }^n\theta$, then ${\left(\frac{dy}{dx}\right)}^2$ is equal to

Consider the parabola whose focus at $(0,0)$ and tangent at vertex is $x-y+1=0$.

The length of the latus rectum is

The value of ${\tan }^{-1}\left(\cot \frac{43\pi }{4}\right)$ is