Explore topic-wise InterviewSolutions in Current Affairs.

The coordinates (x0,y0) of the point on the line y = x + 2 which is close to the parabola y²= 4x is :

${\sum }_{i=1}^{n}6i^2=a{n}^3+b{n}^2+cn+dn$.Then d =

The centre of the hyperbola 2xy+3x+4y+1=0 is

Solution set of

${\log }_3(x^2-2)<{\log }_3(\frac{3}{2}|x|-1)\text{is}$

If 5 different things are placed at random in 3 different boxes, then the probability of placing them such that no box remains empty is

If the intercepts of the variable circle on the $x$ and $y$-axis are $2$ units and $4$ units respectively, then the locus of the centre of the variable circle is

The set of points on the axis of the parabola $y^2-2y-4x+5=0$ from which all the three normals to the parabola are real is :

If n(A) = 3, m(B) = 4, then write $n(A\times A\times B).$

Five cards arc drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.

The distance of the point $(-2,4,-5)$ from the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is

Consider a plane $x+y-z=1$ and point $A(1,2,-3).$ A line $L$ has the equation $x=1+3r,y=2-r$ and $z=3+4r.$

The coordinate of a point $B$ of Line $L$ such that $AB$ is parallel to the plane is

Mr. A lives at origin on the Cartesian plane and has his office at (4, 5). His friend lives at (2, 3) on the same plane. Mr. A can go to his office travelling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considered)

The number of hydroxyl group(s) in Q is ___

The equation of the ellipse whose extremities of minor axis are $(3,1)$ and $(3,5)$ and eccentricity is $\frac{1}{2},$ is

$\int \frac{dx}{x^2\sqrt{16-x^2}}$ has the value equal to

Let X = {1, 2, 3, 4, 5, 6}. The number of ways of different ordered pairs (A, B) that can be formed such that A and B are subsets of X and $A\cap B=\phi$, is

A ball is dropped from a height of 5 m onto a sandy floor and penetrates the sound up to 10 cm before coming to rest. Find the retardation of the ball in sand assuming it to be uniform.

If the tangents form the point $(\lambda ,3)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ are at right angles, then $\lambda$ =

The equation of the chord joining two points$(x_1,y_1)and(x_1,y_1)ontherectangularhyperbolaxy=c^{2}is$

If $f\left(x\right)$ = $(a-x^n{)}^{\frac{1}{n}}$ , where $a>0$ and $n$ is a positive interger , then $f\left[f\right(x\left)\right]$=

Find the volume of a sphere whose radius is 7 cm
$[Assume\pi =\frac{22}{7}]$

Let $f\left(x\right)=\left[x\right]+\sqrt{x-\left[x\right]}$, where [x] denotes the greatest integer function. Then

A company makes 3 model of calculators; A, B and C at factory I and factory II. The company has orders for atleast 6400 calculators of model A, 4000 calculators of model B and 4800 calculators of model C. At factory I, 50 calculators of model A, 50 of model 8 and 30 of model C are made everyday; at factory II, 40 calculators of model A, 20 of model B and 40 of model C are made everyday. It costs ! 12000 and Z 15000 each day to operate factory I and II, respectively. Find the number of days each factory should operate to minimise the operating costs and still meet the demand.

Find $\underset{x\to 0}{\text{lim}}$ f(x) and $\underset{x\to 1}{\text{lim}}$ f(x) where f(x)= $\{\begin{array}{cc}2x+3& x\le 0\\ 3(x+1)& x>0\end{array}$

Standard Deviation of $n$ observation $a_1,a_2,a_3,........,a_n$ is $\sigma .$ Then the standard deviation of the observation $\lambda a_1,\lambda a_2,........,\lambda a_n$ is

ABCD is a square with side a(=9). Find the equation to the circle circumscribing the square if A is the origin

Integrate the following functions.
$\int \frac{e^{ta{n}^{-1}x}}{1+x^2}dx.$

Evaluate $\left|\begin{array}{ccc}x& y& x+y\\ y& x+y& x\\ x+y& x& y\end{array}\right|$

${lim}_{x\to 0}\frac{(1+x{)}^6-1}{(1+x{)}^2-1}$

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through IS. Find the probability that a marble drawn is

(i) white

(ii) white and odd numbered

(ill) even numbered

(iv) red or even numbered.

If the different of the roots of $x^2-px+q=0$ is unity, then

$\text{If}z=\frac{1+7i}{(2-i{)}^2},\text{then}$

For two sets $A\cup B$ A iff

A pack of playing cards was found to contain only 51 cards. If the first 13 cards, which are examined are all red, the probability that the missing card is black, is

${lim}_{n\to \infty }\{cos\frac{x}{2}cos\frac{x}{4}cos\frac{x}{8}.....cos\frac{x}{2^n}\}$=

The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.

Which of the following graphs represents the motion of the planet moving around the Sun.T is the

period of revolution and r is the average distance (from centre to centre) between the Sun and the

planet

In order to fuse two nuclei, they must be brought at a separation of about 2 fm or less. Let two deuterium nuclei may be brought to fuse together by colliding them with equal and opposite velocities. Minimum speed required for above process must be around.

A reversible adiabatic path on a $P-V$ diagram for an ideal gas passes through state $A$ where $P=0.7\times {10}^5{\text{N/m}}^{–2}$ and $V=0.0049{\text{m}}^3$. The ratio of specific heat of the gas is $1.4$. The slope of path at $A$ is

Identify the appropriate question tag for the sentence.

He has decided to not tell his friend, _____________?

The number of integeral values of $m,$ for which the $x$ -coordinate of the point of intersection of the lines $3x+4y=9$ and $y=mx+1$ is an integer is

A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball What are outcomes of the experiment?