Explore topic-wise InterviewSolutions in Current Affairs.

Prove that:

$\left(i\right)tan{720}^{\circ }-cos{270}^{\circ }-sin{150}^{\circ }cos{120}^{\circ }=\frac{1}{4}$

$\left(ii\right)sin{780}^{\circ }sin{480}^{\circ }+cos{120}^{\circ }sin{150}^{\circ }=\frac{1}{2}$

$\left(iii\right)sin{780}^{\circ }sin{120}^{\circ }+cos{240}^{\circ }sin{390}^{\circ }=\frac{1}{2}$

$\left(iv\right)sin{600}^{\circ }cos{390}^{\circ }+cos{480}^{\circ }sin{150}^{\circ }=-1$

$\left(v\right)tan{250}^{\circ }cot{405}^{\circ }+tan{765}^{\circ }cot{675}^{\circ }=0$

$si{n}^2\frac{\pi }{18}+si{n}^2\frac{\pi }{9}+si{n}^2\frac{7\pi }{18}+si{n}^{2}4\frac{\pi }{9}=$

If the plane 2ax - 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres and $\begin{array}{c}{x}^2+y^2+z^2+6x-8y-2z=13\\ x^2+y^2+z^2-10x+4y-2z=8\end{array}$, then a equals
[AIEEE 2005]

$In\Delta ABC,(a+b+c)(tan\frac{A}{2}+tan\frac{B}{2})\text{is equal to}$

For the differential equation in given question find a particular solution satisfying the given condition.​​

$cos\left(\frac{dy}{dx}\right)=a\left(aϵR\right),y=2whenx=0.$

Solve

$x^2+3x+5=0$

Choose the correct answer in the following question:
If $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]$
is such that $A^2=I$. then
$\left(a\right)1+{\alpha }^2+\beta \gamma =0\left(b\right)1-{\alpha }^2+\beta \gamma =0\left(c\right)1-{\alpha }^2-\beta \gamma =0\left(d\right)1+{\alpha }^2-\beta \gamma =0$

Find the interval in which the following function is strictly incerasing or decreasing,

$(x+1{)}^3(x-3{)}^3$

Let X={1,2,3} and Y ={4,5}. Find whether the following subsets of $X\times Y$ are functions from X to Y or not.
(iv) k={(1,4),(2,5)}

Prove, $si{n}^{-1}\frac{8}{17}+si{n}^{-1}\frac{3}{5}=ta{n}^{-1}\frac{77}{36}$

If $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the A.M. between 'a' and 'b' the find the value of n.

If the number of terms in the expansion of $(x+y+z{)}^n$ is $231$, then the value of $n$ is

If $3p+2q=25$ where $p,q$ are prime numbers, then $\frac{q}{p-1}$ is equal to

The graph of $f\left(x\right)=x^2-3|x|+2$ is

The set of values of $a$ for which the point$(a-1,a+1)$ lies outside the circle $x^2+y^2=8$ and inside the circle $x^2+y^2-12x+12y-62=0$ is

If $z$ is a complex number satisfying $\overline{z^2}=1$, where $\overline{z}$ is the conjugate of $z$, then

Let $z$ be a complex such that $-\frac{\pi }{4}\le \arg \left(z\right)\le \frac{\pi }{4}$ and $|z|\le 4$. Then the area enclosed between them is

A box contains I red and 3 black balls. Two balls are dawn at random in succession without replacement.
Write the sample space for this experiment.

Which of the following are functions ?

Equation of the plane passing through the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{4}$ and perpendicular to the plane $x+2y+z=12$ is given by $ax+by+cz+4=0$ then -

Let $n$ and $k$ be positive integers such that $n\ge {}^{k+1}{C}_2$ .The number of integral solutions of $x_1+x_2+\cdots +x_k=n,$ $x_1\ge 1,x_2\ge 2,\cdots x_k\ge k$ is

Write the number of solutions of the equation 4 sin x-3 cos x =7.

The minimum value of $\cos \theta +\sin \theta +\frac{2}{\sin 2\theta }$ for $\theta \in (0,\pi /2)$ is

Let $P_i$ and $P_i^{\prime }$ be the feet of perpendiculars drawn from foci $S,S^{\prime }$ on a tangent $T_i$ to an ellipse whose length of semi major axis is $20,$ if $\sum _{i=1}^{10}\left(S{P}_i\right)\left(S{P}_i^{\prime }\right)=2560,$ then the value of eccentricity is

Find : $\int \frac{(2x-5)e^{2x}}{(2x-3{)}^3}dx.$ OR Find : $\int \frac{(x^2+x+1)}{(x^2+1)(x+2)}dx.$

Find the equation of the plane passing through (a, b, c) and parallel to the plane $r.(\hat{i}+\hat{j}+\hat{k})=2$

If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on

Given $P\left(A\right)=\frac{3}{5},P\left(B\right)=\frac{1}{5}$ Find P(A or B), If A and B are mutually exclusive events.

Solve the triangle in which $a=(\sqrt{3}+1),b=(\sqrt{3}-1)and\angle C={60}^{\circ }$

y= f(x)= ax-b/bx-a, show that x=f(y)

Let Z = ax + by be the objective function at each corner point. Let m and n, respectively denote the largest and smallest values of these points. When the feasible region is ………, m and n are the maximum and minimum values of Z.

Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5.

A+B+C=π and cosA =cosBcosC then cotBcotC=

Options1) 0

2)1

3)1/2

4)1/6

Answer is option 3

Tangents are drawn from the points on the line $2x-y+3=0$ to the parabola $y^2=4x$. Then the variable chords of contact pass through a fixed point whose coordinates is

If the length of latusrectum of an Ellipse is equal tosemi minor axisthen Its eccentricity is