Explore topic-wise InterviewSolutions in Current Affairs.

If $co{s}^6\alpha +si{n}^6\alpha +Ksi{n}^{2}2\alpha =1$, then K=

If $\cot \alpha +\tan \alpha =m$ and $\frac{1}{\cos \alpha }-\cos \alpha =n$, then

If A = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ and B = $\left[\begin{array}{ccc}4& 5& 6\\ 7& 8& 9\\ 1& 2& 3\end{array}\right]$ then the order of A+B will be nxn where n= -----

f(x) is a differentiable function satisfying the relation $f\left(x\right)=x^2+{\int }_0^x{e}^{-t}f(x-t)dt$, then

Compute P$\left(\frac{A}{B}\right)ifP\left(B\right)=0.5P(A\cap B)=0.32$

The distance between the origin and the normal to the curve
​$y=e^{2x}$ to $x^2$ at x = 0 is

Let $f\left(\theta \right)=sin\theta (sin\theta +sin3\theta ),thenf\left(\theta \right)$

Find the equations of the two lines through the origin which intersect the line $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at angles of $\frac{\pi }{3}$ each.

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

In the matrix $\left[\begin{array}{cccc}2& 5& 19& -7\\ 35& -2& \frac{5}{2}& 12,\\ \sqrt{3}& 1& -5& 17\end{array}\right]$,write
(ii)The elements $a_{13},a_{21},a_{33},a_{24},a_{23}.$

In the expansion of ${(\frac{3x^2}{5}+\frac{5}{3x^2})}^{10}$ mid term is

The point of intersection of the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z+2}{3}$ and the plane 2x + 3y + z = 0 is
[MP PET 1989]

The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

Find the equation of the straight line through the point $(\alpha ,\beta )$ and perpendicular to the line $lx+my+n=0.$

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

Pick the correct plot for the function $y=x^2-2x+6$

${\int }_0^{\pi /2}log\left(tanx\right)dx=$

If $\frac{dy}{dx}+\frac{3}{{\cos }^{2}x}y=\frac{1}{{\cos }^{2}x},x\in (\frac{-\pi }{3},\frac{\pi }{3}),$ and $y\left(\frac{\pi }{4}\right)=\frac{4}{3}$, then $y(-\frac{\pi }{4})$ equals :

The locus of mid point of chords of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ which passes through the foot of the directrix from focus is

A parabolic curve is described parametrically by $x-3=t^2,$ $y=4t.$ Then equation of the parabola is

If $cos\theta =\frac{cos\alpha +cos\beta }{1+cos\alpha cos\beta }$, prove that $tan\frac{\theta }{2}=\pm tan\frac{\alpha }{2}tan\frac{\beta }{2}$

The angle between the lines joining the origin to the points of intersection of the line $y=3x+2$ with the curve $x^2+2xy+3y^2+4x+8y=11,$ is

If $a{x}^2+bx+6=0$ does not have distinct real roots, then the least value of $3a+b$ is

The equation of the tangents to the circle $x^2+y^2=a^2$, which makes a triangle of area $a^2$ sq. units with coordinate axes, is/are

Consider a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ at any point. The locus of the midpoint of the portion intercepted between the axes is

If $y=log\left(\frac{1-x^2}{1+x^2}\right),then\frac{dy}{dx}$ then dy/dx is equal to……

A man crosses the river perpendicular to river flow in time t seconds and travels an equal distance down the stream in T second. The ratio of man’s speed in still water to the speed of river water will be:

A projectile is fired at an angle $\theta$ with the horizontal. Find the condition under which it lands perpendicular on an inclined plane of inclination $\alpha$ as shown in figure.

If the vertices of a variable triangle are $(4,3),(-5\cos \theta ,-5\sin \theta ),\text{and}(5\sin \theta ,-5\cos \theta )$, where $\theta \in R,$ then the locus of its orthocenter is

The origin of the coordinate axes is shifted to (-1,3) and the axes is rotated through an angle of 90 degrees in anticlockwise direction. If (a, b) is the new coordinates of (2,3) in the new coordinate system, then find the value of 2a sq. + 3b sq.

The value of $\cos (n+1)\alpha \cos (n-1)\alpha +\sin (n+1)\alpha \sin (n-1)\alpha$ is

Evaluate the integrals using substitution.
${\int }_1^2(\frac{1}{x}-\frac{1}{2x^2})e^{x}dx.$

Let $\ast$ be a binary operation on the set Q of rational number as follows:
$\left(iii\right)a\ast b=a+ab$
Show that none of the operations has an identity.

Integrate the following functions.
$\int \frac{sinx}{(1+cosx{)}^2}dx.$

What is the number of ways of choosing 4cards from a bag of 52 playing cards ? In how many of these :

1) 4 cards are of the same suite

2) 4 cards belong to 4 different suites

3) 4 cards are face cards

4) two are red cards and two are black cards

Find the area between the curves y = x and $y=x^2$.

$\frac{(2x-1)}{3}\ge \frac{(3x-2)}{3}\ge \frac{(3x-2)}{4}-\frac{(2-x)}{5}$

Examine the applicable of MVT for all three functions.

$f\left(x\right)=\left[x\right]forxϵ[-2,2]$

If $z=\sqrt{-7-24i}$, then $z$ is equal to

A random variable X has the following probability distribution.

$\begin{array}{ccccccccc}X& 0& 1& 2& 3& 4& 5& 6& 7\\ P\left(X\right)& 0& k& 2k& 2k& 3k& k^2& 2k^2& 7k^2+k\end{array}$
k

$\begin{array}{ccccccccc}X& 0& 1& 2& 3& 4& 5& 6& 7\\ P\left(X\right)& 0& k& 2k& 2k& 3k& k^2& 2k^2& 7k^2+k\end{array}$
P(X<3)

$\begin{array}{ccccccccc}X& 0& 1& 2& 3& 4& 5& 6& 7\\ P\left(X\right)& 0& k& 2k& 2k& 3k& k^2& 2k^2& 7k^2+k\end{array}$

P(X > 6)

$\begin{array}{ccccccccc}X& 0& 1& 2& 3& 4& 5& 6& 7\\ P\left(X\right)& 0& k& 2k& 2k& 3k& k^2& 2k^2& 7k^2+k\end{array}$
P(0 < X < 3)

Equation of circles passing through (3, -6) and touching both the axes is