Explore topic-wise InterviewSolutions in Current Affairs.

If the axes are rotated in anticlockwise through an angle of ${90}^{\circ }$ then the equation $x^2=4ay$ will chane into

If R = \{x, y : x, y \epsilon Z, x^2 + y^2 \leq 4\} is a relation defined on the set Z of integers, then write domain of R.

If x > -x^2 and y > 1, then prove that xy < 0 for all possible values of x and y.

The angle between the $x-$axis and the line joining the points $(3,-1)$ and $(4,-2)$ is

Consider the point $A\equiv (0,1)$ and $B\equiv (2,0).{}^{\prime }{P}^{\prime }$ be a point on the line $4x+3y+9=0.$ Coordinate of the point $P$ such that $|PA-PB|$ is minimum, is

The number of ways in which ten candidates A1, A2........A10 can be arranged in vertical row(column) when

1)if A1, A2 are next to each other. [9!.2!]

2)if A1 is just above A2. [9!]

3)if A1 is always above A2. [10!/2!]

4)if A1 is always above A2 and A2 is above A3 is.[10!/3!]

5)if A1, A2, A3 sit together in a specified order is. [8!]

Please explain solution in detail for the 3,4,5 specially. And kindly don't close the question for whatsoever reason as i typed it with a lot of hard work.[ Answers in bracket.]

The triangle formed by the points (0, 7, 10), (–1, 6, 6),(– 4, 9, 6) is [RPET 2001]

If $\alpha .\beta ,\gamma ,\delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to positive quantity k, then the value of $4sin\left(\frac{\alpha }{2}\right)+3sin\left(\frac{\beta }{2}\right)+2sin\left(\frac{\gamma }{2}\right)+sin\left(\frac{\delta }{2}\right)$ is not equal to

The points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear because.

What does 'd' stands for in dy/dx?

A function $y=f\left(x\right)$ satisfies the condition $f^{\prime }\left(x\right)sinx+f\left(x\right)cosx=1,f\left(x\right)$ being bounded when $x\to 0$. if $I={\int }_0^{\frac{\pi }{2}}f\left(x\right)dx,$ then

If $y={\sin }^{-1}\left(\frac{4\cos x+3\sin x}{5}\right)$, then $\frac{dy}{dx}=$

The area of the region bounded by $x^2=4y,y=2,y=4$ and the y-axis in the first quadrant is

If $3^x=4^{x-1}$, then $x=$

A bag initially contains one red and two blue balls. A trial consists of selecting a ball at random, noting its colour and replacing it together with an additional ball of the same colour. Three such trials are made. Let probability of event listed in column I is $\frac{\alpha }{\beta }$, where $\alpha$ and $\beta$ are coprime numbers. Match them with Column II
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(I) Atleast one blue is drawn}& \text{(P)}\beta -\alpha =1\\ \text{(I) Exactly one blue is drawn}& \text{(Q)}\beta -\alpha =4\\ \text{(III) Probability that drawn balls}& \text{(R)}\alpha +\beta =6\\ \text{are all red given that all drawn}& \\ \text{balls are same colour}& \\ \text{(IV) Atleast one red balls is drawn}& \text{(S)}\beta \text{is even}\\ & \text{(T)}\beta \text{is odd}\end{array}$

Which of the following is only INCORRECT
combination?

If line y = 2x + c neither cuts the circle $(x–2{)}^2+(y–3{)}^2=4$ nor the ellipse $x^2+6y^2=6$, then the range of c is

Two point charges +2q and -q are placed at (-a, 0) and (+a, 0) along X-axis respectively. Which of the following graph correctly shows potential as a function of position along x-axis?

If $A=\{x:|x|\le 5;x\in Z-\{0\left\}\right\}$, $B=\{x:x\le 100;x\in W\}$ and $f:A\to B$ is a function defined by $f\left(x\right)=x^2+1$, then the number of elements in the range of $f$ that lie in $[5,26)$ is

${lim}_{x\to a}\frac{cosx-cosa}{x-a}$

$\frac{co{t}^2{15}^{\circ }-1}{co{t}^2{15}^{\circ }+1}$ =

[MP PET 1998]

The shaded region in the figure is the solution set of the inequations

If in the expansion of $(1+y{)}^n$, the coefficients of $5^{th}$, $6^{th}$ and $7^{th}$ terms are in A.P., then n is equal to

Show that the following system of linear equations has no solution:

$x+2y\le 3,3x+4y\ge 12,x\ge 0,y\ge 1.$

Let $y=y\left(x\right)$ be the solution of the differential equation, $x\frac{dy}{dx}+y=x{\log }_{e}x,(x>1).$ If $2y\left(2\right)={\log }_{e}4-1,$ then $y\left(e\right)$ is equal to:

Let R = {(x, y) : x, y $ϵ$ A, and x + y =5} where A ={1,2,3,4,5}, then R is

If $f\left(x\right)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+\frac{x^{98}}{98}+\cdots +\frac{x^2}{2}+x+1$, then $f^{\prime }\left(1\right)=$

If the circle $x^2+y^2=a^2$ intersect the hyperbola $xy=c^2$ in four points P$(x_1,y_2),Q(x_2,y_2),R(x_3,y_3),S(x_4,y_4),$ then which of the following does not hold

The consumption function of an economy is $C=75+0.75Y.$ What will be the change in income, when consumption changes by Rs 300 crores?

OR

Complete the table:

$\begin{array}{ccccc}\text{Income}& \text{C = 75 + 0.75 Y}& \text{Savings}& \text{APC}& \text{APS}\\ 100& & & & \\ 200& & & & \\ 300& & & & \\ 400& & & & \end{array}$

If n is the smallest natural number such that n + 2n + 3n +....+ 99n is a perfect square, then the number of digits in n${}^2$ is

Prove that the centres of the three circles
$x^2+y^2-4x-6y—-12=0,x^2+y^2+2x+4y-10=0$
and $x^2+y^2-10x-16y-1=0$
are collinear.

The two parabolas $y^2=4ax$ and $y^2=4c(x-b)$ cannot have a common normal, other than the axis unless, if

Evaluate $\left|\begin{array}{ccc}cos\alpha cos\beta & cos\alpha sin\beta & -sin\alpha \\ -sin\beta & cos\beta & 0\\ sin\alpha cos\beta & sin\alpha sin\beta & cos\alpha \end{array}\right|$

Given ellipse $x^2+4y^2=16$ and parabola $y^2–4x–4=0.$ The quadratic equation whose roots are squares of the slopes of the common tangent to parabola and ellipse, is

$\text{Solve the following equations}:\left(i\right)si{n}^2\theta -cos\theta =\frac{1}{4}\left(ii\right)2co{s}^2\theta -5cos\theta +2=0\left(iii\right)2si{n}^{2}x+\sqrt{3}cosx+1=0\left(iv\right)4si{n}^2\theta -8cos\theta +1=0\left(v\right)ta{n}^{2}x+(1-\sqrt{3})tanx-\sqrt{3}=0\left(vi\right)3co{s}^2\theta -2\sqrt{3}sin\theta cos\theta -3si{n}^2\theta =0\left(vii\right)cos4\theta =cos2\theta$

If $\int \frac{cos8x+1}{tan2x-cot2x}dx=acos8x+C$, then

If the tangent at (1, 1) on $y^2=x(2-x{)}^2$ meets the curve again at P, then ‘P’ is

If R = {(2, 1), (4, 7), (1, -2), .....}, then write the linear relation between the components of the ordered pairs of the relation R.

The slope of a line is double of the slope of another line. If tangents of the angle between them is $\frac{1}{3}$, find the slopes of the other line.

If the line $3x+4y=12$ is a tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=2$ then find the point of contact.

The area (in sq. units) of a pentagon whose vertices are $(4,3),(-5,6),(-7,-2),(0,-7)$ and $(3,-6)$ taken in order, is ?

${lim}_{x\to 1}\frac{x^3-3x+1}{x-1}$

If $\frac{2-|x|}{3+|x|}\ge 5$, then $x\in$