Explore topic-wise InterviewSolutions in Current Affairs.

The range of $\theta$ for which $2{\cos }^2\theta +\sin \theta \le 2$ if $\theta \in \left(\frac{\pi }{2},\frac{3\pi }{2}\right]$ is

ABCD is a square, the length of whose side is a. Taking AB and AD as the coordinate axes, the equation of the

circle passing through the vertices of the square, is

If $f\left(x\right)={\int }_1^x\frac{dt}{2+t^4}$, then

If X = $\{8^n-7n-1:n\in N\}andY=\left\{49\right(n-1):n\in N\}$ , then

If $li{m}_{x\to 2}$ $\frac{\left(x^n\right)-\left(2^n\right)}{x-2}$ =80 , where n is a positive integer,
then n=

The value of $\underset{x\to \infty }{lim}\frac{5^{\sin x}+2x+1}{\cos x-\sqrt{1+x^2}}$ is

If [.] denotes greatest integer function, then at which of the following points $f\left(x\right)=\left[x\right]\sin \left(\frac{\pi }{2}\left(\right[x]+x)\right)$ is discontinuous?

In a committee 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. The number of persons speaking at least one of these two languages is

Find the shortest distance between the lines
$\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}and\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$

The differential equation of family of curves $y^2=4a(x+a)$ is
a) $y^2=4\frac{dy}{dx}(x+\frac{dy}{dx})$
b) $2y\frac{dy}{dx}=4a$
c) $y\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$
d) $2x\frac{dy}{dx}+y{\left(\frac{dy}{dx}\right)}^2-y=0$

Differentiate the following questions w.r.t. x.

$sin\left(ta{n}^{-1}{e}^{-x}\right).$

A man throws a die until he gets a number bigger than 3. The probability that he gets 5 in the last throw

A manufacturer produces nuts and bolts. It takes 1 h of work on machine A and 3 h on machine B to produce a package of nuts. It takes 3 h on machine A and 1 h on maching B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many package of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 12 h a day ?

Area bounded by curve $y=x^3,x-axis$ axis and ordinates x=1 and x=4, is

The shortest distance between the line $y=x-5$ and the parabola $y=x^2+3x+6$ is

The equation of a circle with radius 5 and touching both die coordinate axes is

If $\sin \theta =\left(\frac{z-1}{i}\right),$ where $z$ is non real, $\theta$ represents angle of a triangle, then

In the adjoining figure P,M,Q,R are collinear and

PM = MQ = MS, SR² = PR . QR. Then

Show that the points A(1, 2, 3), B(-1, -2, -1), C(2, 3, 2) and D (4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.

Write the number of numbers that can be formed using all for digits 1,2,3,4.

If $C_0+C_1+C_2+...+C_n=256$ = then ${}^{2n}{C}_2$ is equal to

If k = sin$\frac{\pi }{18}$.sin$\frac{5\pi }{18}$.sin$\frac{7\pi }{18}$, then the numerical value of k is

If $sin\theta +cos\theta =0$ and $\theta$ lies in the fourth quadrant, find $sin\theta$ and $cos\theta$.

$\int sec\left(2x\right)tan\left(2x\right)dx=k$ sec(mx) + C

Find the value of 2k+m

If A and B are the sums of odd and even terms respectively in the expansion of $(x+a{)}^n$, then $(x+a{)}^{2n}-(x-a{)}^{2n}$ is equal to

If $A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right]$, prove that $A^n=\left[\begin{array}{ccc}{3}^{n-1}& 3^{n-1}& 3^{n-1}\\ 3^{n-1}& 3^{n-1}& 3^{n-1}\\ 3^{n-1}& 3^{n-1}& 3^{n-1}\end{array}\right],n\in N$.

Let $f$ be a positive function
Let $I_1={\int }_{1-k}^{k}xf\left\{x\right(1-x\left)\right\}dxand{I}_2={\int }_{1-k}^{k}f\left\{x\right(1-x\left)\right\}dx$
where $2k-1>0,$ then $\frac{I_1}{I_2}$ is

Let $A$ and $B$ be two independent events such that $P\left(A\right)=\frac{1}{3}$ and $P\left(B\right)=\frac{1}{6}$. Then, which of the following is TRUE ?

If $p>0,q>0$ then roots of $x^2$ - px - q = 0 are :

If $1,{\log }_9(3^{1-x}+2),{\log }_3(4\cdot 3^x-1)$ are in A.P., then $x$ is equal to

The number of arrangements of the word "DELHI" in which E precedes 1 is

Let $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. A vector $\overrightarrow{v}$ in the plane of
$\overrightarrow{a}$ and $\overrightarrow{b}$, whose projection on $\overrightarrow{c}$ is $\frac{1}{\sqrt{3}}$, is given by

A bird is flying up at angle sin^-1(3/5) with the horizontal. A fish in a pond looks at that bird when it is vertically above the fish. The angle at which the bird appears to fly (to be fish)is (μ_ω=4/3)

Differentiate the following functions with respect to x :

$log\left(\frac{1}{\sqrt{x}}\right)+5x^a-3a^x+3\sqrt{x^2}+6^4\sqrt{x^{-3}}$

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i,y_i)$ for $i=1,2,3,and4$ then $y_1+y_2+y_3+y_4=$

Find the equation of a straight line on which the perpendicular from the origin makes an angle of ${30}^{\circ }$ with x-axis and which forms a triangle of area $50/\sqrt{3}$ with the axes.

The points $z_1,z_2,z_{3}and{z}_4$ in the complex plane are the vertices of a parallelogram taken in order if and only if