Explore topic-wise InterviewSolutions in Current Affairs.

Graph of $y=|x-2|-5$ is

If $p_1$ and $p_2$ are the lengths of the perpendiculars from the origin upon the lines $xsec\theta +ycosec\theta =a$ and $xcos\theta -ysin\theta =acos2\theta$ respectively, then

Following is the Receipt and Payment Account of Indian Sports Club for the year ended 31-3-2014 :

$\begin{array}{cccc}\text{Receipts}& \text{Rs}& \text{Payments}& \text{Rs}\\ \text{Balance b/d}& 10,000& \text{Salary}& \text{15,000}\\ \text{Subscriptions}& 52,000& \text{Billiard Table}& 20,000\\ \text{Entrance Fee}& 5,000& \text{Office Expenses}& 6,000\\ \text{Tournament Fund}& 26,000& \text{Tournament Expenses}& 31,000\\ \text{Sale of old newspapers}& 1,000& \text{Sports Equipment}& 40,000\\ \text{Legacy}& 37,000& \text{Balance c/d}& 19,000\\ & \underset{–}{\overline{1,31,000}}& & \underset{–}{\overline{1,31,000}}\end{array}$

Other Information :

On 31-3-2014 Subscription outstanding was Rs 2,000 and on 31-3-2013 subscription outstanding was Rs 3,000 Salary outstanding on 31-3-2014 was Rs 1,500.

On 1-4-2013 the club had building Rs 75,000, furniture Rs 18,000, 12% investment Rs 30,000 and sports equipment Rs 30,000. Depreciation charged on these items including Billiard Table was 10%.

Prepare Income and Expenditure Account of the Club for the year ended 31-3-2014 and a Balance Sheet as at that date.

The equation of the conic with focus at (1, –1), directrix along x – y + 1 = 0 and with eccentricity $\sqrt{2}$ is

Write the equation of the direction of the parabola $x^2-4x-8y+12=0$.

Three persons enter a railway compartment. If there are 5 seats a vacant, in how many ways can they take these seats ?

Suppose $f$ and $g$ are differentiable functions on $(0,\infty )$ such that $f\text{'}\left(x\right)=-\frac{g\left(x\right)}{x}$ and $g\text{'}\left(x\right)=-\frac{f\left(x\right)}{x}$, for all $x>0$. Further, $f\left(1\right)=3$ and $g\left(1\right)=-1$.

If $f\left(x\right)-g\left(x\right)=B{x}^m,$ for all $x>0$ and some constant $B$, then the value of $m$ equals

If tangents are drawn to the parabola $(x-2{)}^2+(y-3{)}^2=\frac{(3x+4y-5{)}^2}{25}$ at the extremities of the chord $3x-y-3=0$, then angle between the tangents is

If a letter is chosen at random from the English alphabet, find the probability that the letter is

(i) a vowel

(ii) a consonant

If a, b, c are perpendicular distance of (3, 4, 5) from X, Y and Z coordinates respectively, then find the value of $a^2+b^2+c^2$ ___

The equations of the sides of a triangle are x + y - 5 = 0; x - y + 1 = 0 and y - 1 = 0, then the coordinates of the

circumcentre are

If $sin\alpha +sin\beta =\alpha$ and $cos\alpha -cos\beta =b$, then $tan\frac{\alpha -\beta }{2}=$

Three - fourths of the active nuclei present in a radioactive sample decay in $\frac{3}{4}$ s.The half life of the sample is -

If $p,q,r$ have truth values $T,F,T$ respectively, then which among the following will have truth value as TRUE.

A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find its coordinates.

Difference between scalar product ( dot product) and vector product.

From the adjoining figure, $A\cap B$ is

If the transformed equation of $xy=c^2$ when the axis are rotated through an angle of $\frac{\pi }{4}$ (in the anti clockwise direction), is $p{X}^2+q{Y}^2=r{c}^2$, then

If $f\left(x\right)=x+\sin x;g\left(x\right)=e^{-x};u=\sqrt{c+1}-\sqrt{c};v=\sqrt{c}-\sqrt{c-1};(c>1),$ then

If $A$ is a square matrix of order $3\times 3,$ then $|KA|$ is equal to

Refer to question 11. How many of circuits of type A and of type B, should be produced by the manufacturer, so as to maximise his profit? Derermine the maximum profit.

If tangents are drawn at the points $A(1,2),B(4,-4)$ and a variable point ${}^{\prime }{C}^{\prime }$ lies on the parabola $y^2=4x$, then the locus of the orthocentre of triangle formed by these tangents is

$Ifsin\alpha +sin\beta +sin\gamma =0=cos\alpha +cos\beta +cos\gamma$ then value of $cos(\alpha -\beta )+cos(\beta -\gamma )+cos(\gamma -\alpha )is$

Show that the function defined by g(x)=x-[x] is discontinuous at all integral points. Here, [x] denotes the greatest integer less than or equal to x.

Find the equation of the x line parallel to the y-axis and drawn through the point of intersection of the lines $x-7y+5=0$ and $3x+y-7=0$

Given an example of a relation. Which is
(iv) Reflexive and transitive but not symmetric.

Find $\frac{dy}{dx}$in the following questions:

$y=se{c}^{-1}\left(\frac{1}{2x^2-1}\right),0<x<\frac{1}{\sqrt{2}}$

Find the coordinates of the point on the curve $\sqrt{x}+\sqrt{y}=4$ at which tangent is equally inclined to the axes.

Angle between the tangents drawn from the origin to the parabola $y^2=4a(x-a)$ is

Find the equation of the plane which contains line of intersection of the planes $r.(\hat{i}+2\hat{j}+3\hat{k})-4=0,r.(2\hat{i}+\hat{j}-\hat{k})+5=0$ and which is perpendicular to the plane $r.(5\hat{i}+3\hat{j}-6\hat{k})+8=0$ .

If the tangents to the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}$ at any point on it cuts the axes OX and OY at P and Q respectively, then OP + OQ is

The number of solutions of the matrix equation $A^2$ = $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ is

An equilateral triangle $ABC$ has one vertex at $(2,0)$ and ortho center at $(1,\frac{1}{\sqrt{3}})$. Let $P=(\frac{1}{2},\frac{1}{4})$ and distances of $P$ from the sides $BC,AC,$ and $AB$ are $x,y$ and $z$ respectively, then $x+y+z$ is equal to

If f(x) = |x|, then f’(x), where $x\ne 0$ is equal to

${lim}_{x\to \sqrt{2}}\frac{\sqrt{3+2x}-(\sqrt{2}+1)}{x^2-2}$

Find $\int \frac{2cosx}{(1-sinx)(1+si{n}^{2}x)}dx$

sinA+sinB=√3(cosB-cosA) thensin3A+sin3B=?

Options 1)0

2)2

3)1

4) -1

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P(A and not B)

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$-axis, the equation of the reflected ray is

For the following question verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

$y=e^x(acosx+bsinx):\frac{d^{2}y}{d{x}^2}-2\frac{dy}{dx}+2y=0$

The number of ways in which 8 red roses and 5 white roses of different sizes can be made out to form a garland so that no two white roses come together is

If $co{s}^{-1}x-si{n}^{-1}x=0$ then x is equal to

Find the equation of all lines having slope 2 which are tangents to the curve $y=\frac{1}{x-3},x\ne 3$.

Area bounded by y = x sin x and x - axis between x=0 and x = 2$\pi$ is [Roorkee 1981; RPET 1995]