Explore topic-wise InterviewSolutions in Current Affairs.

Identify the subordinating conjunction in the sentence below.

Riya went for a walk on the beach whenever she felt lonely.

In the third quadrant the value of the sine function

The law a + b = b + a is called

A set of parallel chords of the parabola $y^2=4ax$ have their mid points on

The value of m for which the area of the triangle included between the axes and any tangent to the curve $x^{m}y=b^m$ is constant, is

The centre of a circle of radius $4\sqrt{5}$ lies on the line y=x and satisfies the inequality 3x+6y>10. If the line x+2y=3 is a tangent to the circle, then the equation of the circle is

If $f\left(x\right)=\left|\begin{array}{ccc}5+{\sin }^{2}x& {\cos }^{2}x& 4\sin 2x\\ {\sin }^{2}x& 5+{\cos }^{2}x& 4\sin 2x\\ {\sin }^{2}x& {\cos }^{2}x& 5+4\sin 2x\end{array}\right|$ then

If $x$ is real and $k=\frac{x^2-x+1}{x^2+x+1}$, then

${lim}_{x\to +2}\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}$is equal to

Differentiate the following functions with respect to x :

$\frac{ax+b}{p{x}^2+qx+r}$

If $\Phi \left(x\right)={lim}_{n\to \infty }\frac{x^n-x^{-n}}{x^n+x^{-n}},0<x<1,ϵN$, then $\int \left(si{n}^{-1}x\right)\left(\Phi \right(x\left)\right)dx$ is equal to

The solution of the differential equation is

[DCE 2002]

${\int }_0^{\frac{\pi }{4}}se{c}^7\theta si{n}^3\theta d\theta =$

The function $f\left(x\right)=sin\left(log\right(x+\sqrt{x^2+1}\left)\right)$ is

Find the value of $\lambda$,if four points with position vectors $3\hat{i}+6\hat{j}+9\hat{k},\hat{i}+2\hat{j}+3\hat{k},2\hat{i}+3\hat{j}+\hat{k}$ and $4\hat{i}+6\hat{j}+\lambda \hat{k}$ are coplanar.

The principal value of $co{s}^{-1}cos\frac{7\pi }{6}$ is

$\text{If}3x^2+4y^2=7xy,\text{then}\frac{d^{2}y}{d{x}^2}\text{at}(1,1)\text{is}$

Find the equation of the line of intersection of planes 4x + 4y – 5z = 12 and 8x + 12y – 13z = 32 in the symmetric form.

If complex numbers $(-3+iy{x}^2)$ and $(x^2+y+4i)$ are conjugates of each other, where $x,y\in R,$ then $(x,y)$ can be

The value of $\underset{x\to 0}{lim}\frac{\sin x-x}{x^3}$ is

A hyperbola has $y$-axis and $x$-axis as its conjugate axis and transverse axis respectively. If one of the points of intersection of $x$-axis with the hyperbola is $(4,0)$ and equation of one of the tangents is $x-y=\sqrt{7},$ then the equation of the hyperbola is

Prove that:
(i)$\frac{cos{11}^{\circ }+sin{11}^{\circ }}{cos{11}^{\circ }-sin{11}^{\circ }}=tan{56}^{\circ }$
(ii)$\frac{cos{9}^{\circ }+sin{9}^{\circ }}{cos{9}^{\circ }-sin{9}^{\circ }}=tan{54}^{\circ }$
(iii)$\frac{cos{8}^{\circ }-sin{8}^{\circ }}{cos{8}^{\circ }+sin{8}^{\circ }}=tan{37}^{\circ }$

Let $\overrightarrow{A}=A\cos \theta \hat{i}+A\sin \theta \hat{j}$ be any vector. Another vector $\overrightarrow{B}$ which is perpendicular to $\overrightarrow{A}$ can be expressed as

If f(x) and f’(x) are differentiable at x = c, then the necessary condition for f(c) to be an extremum of f(x) is -

Differentiate $ta{n}^{-1}\left(\frac{1+cosx}{sinx}\right)$ with respect to x.

The value of $\underset{x\to \infty }{lim}\left[\frac{(8^{\left(x^n/e^x\right)}-{27}^{\left(x^n/e^x\right)})e^x}{(4^{\left(x^n/e^x\right)}+6^{\left(x^n/e^x\right)}+9^{\left(x^n/e^x\right)})x^n}\right],$ where $n\in N$ is

If $sin(si{n}^{-1}\frac{1}{5}+co{s}^{-1}x)=1$, then find the value of x.

The equations of the transverse and conjugate axes of a hyperbola are respectively $x+2y-3=0,2x-y+4=0$ and their respective lengths are $\sqrt{2}$ & $\frac{2}{\sqrt{3}}$. The equation of the hyperbola is

Find the equation of the circle concentric with the circle $x^2+y^2-4x-6y-3=0$ and which touches the y-axis.

Find the equation of the tangent and normal to the given curve at the given points $y=x^{2}at(0,0)$

Find the total number of permutations of the letters of the word 'INSTITUTE'.

Refer to question 12. What will be the minimum cost?

A bag consists of balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag. What is the probability that none is marked with the digit 0?

The equation of the chord joining two points $(x_1,y_1)$ and $(x_2,y_2)$ on the rectangular hyperbola $xy=c^2$ is

Let P(n) be the statement : $2^n\le 3n$. If P(r) is true, show that P(r + 1) is true. Do you conclude that P(n) is true for all $nϵN$.

The differential equation ydx +$y^2$dy = xdy and y(1) = 1 represents a parabola whose

For two events A and B, if
P(A)=P(A | B) =1/4 and P(B | A) =1/2, then