Explore topic-wise InterviewSolutions in Current Affairs.

Distinguish between centralisation and decentralisation.

There are three events A,B,C one of which must and only one can happen. The odds are 8 to 3 against A. 5 to 2 against B, finds the odds against C.

The value of $si{n}^3{10}^{\circ }+si{n}^3{50}^{\circ }-si{n}^3{70}^{\circ }$ is equal to

Evaluate ${lim}_{x\to 0}\frac{7xcosx-3sinx}{4x+tanx}$

If the image of the point $P(1,–2,3)$ in the plane, $2x+3y–4z+22=0$ measured parallel to the line,$\frac{x}{1}=\frac{y}{4}=\frac{z}{5}\text{is}Q,\text{then}PQ$ is equal to:

Least positive integral value of x satisfying
$(e^x-2)(sinx-cosx)(x-lo{g}_{e}2)(cosx-\frac{1}{\sqrt{2}})<0$ is

If $a=i-j+k,a\cdot b=0,a\times b=c,$, where $c=-2i-j+k$, then $b$ is equal to

The solution of $\frac{dy}{dx}=xlogx$ is
[MP PET 2003]

The correct evaluation of ${\int }_0^{\pi }|si{n}^{4}x|dx$ is [MP PET 1993]

Find the interval in which the following functions are strictly incerasing or decreasing

$x^2+2x-5$

$10-6x-2x^2$

$-2x^3-9x^2-12x+1$

$6-9x-x^2$

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

If $f\left(x\right)=\frac{2-x\cos x}{2+x\cos x}$ and $g\left(x\right)={\log }_{e}x,(x>0)$ then the value of the integral $\underset{-\pi /4}{\overset{\pi /4}{\int }}g\left(f\right(x\left)\right)dx$ is:

If the image of the point (1, 1, 1) with respect to a plane ax + by + cz + d = 0 is (3, –1, 5), then

If the coefficient of $x^2$ and $x^3$ are both zero, in the expansion of the expression $(1+ax+b{x}^2)(1-3x{)}^{15}$ in powers of $x$, then the ordered pair $(a,b)$ is equal to :

${lim}_{x\to 2}\frac{x^4-16}{x-2}$

Which term of the progression 18, - 12, 8, .... is $\frac{512}{729}$ ?

Write the coordinates of the circumcentre of a triangle whose centroid and orthoentre are at (3,3) and (-3,5) respectively.

Find the smallest set A such that $A\cup$

{1,2} = {1,2,3,5,9}

In an infinite G.P., if the first term is $x$ and sum of all terms is $5$, then

If z = x + iy, $z^{\frac{1}{3}}$ = a - ib and $\frac{x}{a}$ - $\frac{y}{b}$ = $\lambda$$(a^2-b^2)$, then $\lambda$ is equal to

Which of the following does not give borax bead test?

If $S$ is the set of all real values of $x$ such that $\frac{2x-1}{2x^3+3x^2+x}$ is positive, then $S$ contains

If $2x^2+7xy+3y^2+8x+14y+k=0$ represents a pair of straight lines, then the value of $k$ is

The equations of the tangents to the circle $x^2+y^2=50$ at the points where the line $x+7=0$ meets it, are

If ${}^{2n}{C}_3{:}^n{C}_2=44:3,$ find n.

If a,b,c and d in any binomial expansion be the 6th, 7th, 8th and 9th terms respectively, then prove that $\frac{b^2-ac}{c^2-bd}=\frac{4a}{3c}.$

Find the equation of a circle whose centre is (3, -1) and which cuts off a chord of length 6 units on the line $2x-5y+18=0$.

A and B participate in a race with acceleration $a_1$ and $a_2$ respectively. A reaches t times earlier than B at finish line and there velocities at finish line are $v_1$ and $v_2$ respectively. If difference between their velocities is v then find the value of v

The set of the solutions for $\frac{(x+1)(x-3)}{(x+5)}<0$ is

Suppose $z_1,z_2,z_3$ are the vertices of an equilateral triangle inscribed in the circle $|z|=2$. If $z_1=1+i\sqrt{3}$, then the other two vertices are

How many different rectangles can be drawn on an 8*8 chess board?

The value of $\frac{\sin 8\theta \cos \theta -\sin 6\theta \cos 3\theta }{\cos 2\theta \cos \theta -\sin 3\theta \sin 4\theta }$ is

Let
$p:2$ is a prime number
$q:\cos {30}^{\circ }=\frac{1}{2}$
$r:{\sec }^{2}x+{\tan }^{2}x=1$
$s:\sqrt{7}$ is an irrational number
$u:{\pi }^2$ is greater than $10$

Then which among the following statements are valid

If a function f(x )is continuous in [2,5] , differentiable in (2,5) and f(2) = f(5) then how many value x can have where f'(x) nullifies for sure?

If the centroid of a triangle formed by the points (0,0), $(cos\theta ,sin\theta )$ and $(sin\theta ,-cos\theta )$ lies on the line y=2x,then wirte the value of $tan\theta$.

If $\overrightarrow{V_1}=3\hat{i}-a\hat{j}-b\hat{k}$ and $\overrightarrow{V_2}=2\hat{i}+\hat{j}+\hat{k}$ represent two perpendicular sides of a triangle where $a,b$ are whole numbers. Then minimum possible area of the triangle is

By using properties of definite integrals, evaluate the integrals
${\int }_0^{2}x\sqrt{2-x}dx.$

Which of the following is the least?

The angles $A,B$ and $C$ of a triangle $ABC$ are in $A.P.$ and $a:b=1:\sqrt{3}.$ If $c=4\text{cm}$, then the area (in sq.cm) of this triangle is:

If $(2,0)$ is vertex and $y-$axis is the directrix of a parabola. Then the length of its latus rectum is

Find the vector equation of the plane passing through the intersection of the planes $r.(2\hat{i}+2\hat{j}-3\hat{k})=7,r.(2\hat{i}+5\hat{j}+3\hat{k})=9$ and through the point (2,1,3).