Explore topic-wise InterviewSolutions in Current Affairs.

In these questions, certain symbols have been used to indicate relationships between elements as follows
A # B means A is either equal to or greater than B.
A $ B means A is equal to B.
A pounds B means A is either equal to or smaller than B.
A & B means A is smaller than B.
A B means that A is greater than B.

In each question, three statements showing relationships have been given, which are followed by two conclusions I and II. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true.
Statements:
T & K, K # B, S # K
Conclusions:
I. B * T
II. S pounds T

${\int }_0^{1}x{e}^{x}dx=$

The straight line through $(P{x}_1,y_1)$ inclined at an angle $\theta$ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.

The following particulars relate to Madura Club for the year 31st March, 2016 :

Receipts and Payments Account
$\begin{array}{ccccc}\text{Receipts}& & \text{Rs}& \text{Payments}& \text{Rs}\\ \text{Balance b/d}& & 60,000& \text{Salaries}& 1,24,500\\ \text{Subscriptions :}& & & \text{Stationery}& 24,000\\ \text{Arrear}& 2,400& & \text{Rates}\&\text{Taxes}& 36,000\\ \text{Current}& 1,26,600& & \text{Telephone Expenses}& 6,000\\ \text{Advance}& \underset{–}{4,800}& 1,33,800& \text{Investments}& 75,000\\ \text{Profit from Canteen}& & 90,000& \text{Advertisement}& 10,500\\ \text{Miscellaneous}& & 4,500& \text{Postages}& 10,000\\ \text{Sale of Old Newspapers}& & 11,200& \text{Sundry Expenses}& 50,000\\ \text{Dividends}& & 48,500& \text{Balance c/d}& 1,72,000\\ \text{Donation}& & 1,00,000& & \\ \text{Entrance Fee}& & 60,000& & \\ & & \underset{–}{\overline{5,08,000}}& & \underset{–}{\overline{5,08,000}}\end{array}$

You are required to prepare an Income and Expenditure Account and a Balance Sheet after making the following adjustments :

(i) There are 450 members each paying an annual subscription of Rs 300; Rs 2,700 being in arrears for 2014-15 at the beginning of this year.

(ii) A donation of Rs 20,000 was wrongly included in subscriptions of the current year.

(iii) Entire donation and $\frac{3}{4}$ of entrance fees are to be capitalised.

(iv) Stock of Stationery on 31st March, 2015 was Rs 3,000; and on 31st March, 2016 was Rs 5,400.

(v) Cost of Building is Rs 6,00,000. Depreciate it at $5\%$ p.a.

The value of p and q$p\ne 0,q\ne 0$ for which p,q are the roots of the equation: $x^2+px+q=0$ are

The value of the determinant $\left(\begin{array}{ccc}x& a& x+a\\ y& b& y+b\\ z& c& z+c\end{array}\right|$ is

If h(x) = min {x,x²} for x ϵ R. Find LHD and RHD at x = 1.

1. undefined
2. undefined
3. undefined
4. undefined

If $A={45}^{\circ },$ then the value of ${\cos }^{2}B+{\sin }^2(A+B)+2\sin A\sin ({180}^{\circ }+B)\cos ({360}^{\circ }+A+B)$ is

A coin is tossed once. Find the probability of getting a head.

Consider a triangular plot $ABC$ with sides $AB=7m,BC=5m$ and $CA=6m$. A vertical lamp-post at the mid point $D$ of $AC$ subtends an angle ${30}^{\circ }$ at $B$. The height (in $m$) of the lamp-post is :

Find the equation of a circle with centre (h, k) and touching both the positive axes.

The image of the point $A(1,2,3)$ relative to the plane $\pi$ is $B(3,6,-1)$. The equation of the plane $\pi$ is

Sum of all two digit numbers which when divided by 4 yield unity as remainder is

What is the adjoint of the matrix $\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 3& 4\end{array}\right]$?

If the line ax + by = 1 passes through point of intersection of $y=xtan\alpha +psec\alpha ,ysin({30}^{\circ }-\alpha )-xcos({30}^{\circ }-\alpha )=p$ and is inclined at ${30}^{\circ }$ with $y=xtan\alpha$, then the value of $a^2+b^2$ can be

Find the value of c in Rolle's Theorem for the function f(x)=$x^3-3xin[-\sqrt{3},0].$

Find the general solution of $(x+2y^3)\frac{dy}{dx}=y.$

Integrate the rational functions.
$\int \frac{x}{(x^2+1)(x-1)}dx.$

A factory manufactures two types of screws A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 min on the automatic and 6 min on hand operated machines to manufacture a package of screws A, while it takes 6 min on automatic and 3 min on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 h on any day. The manufacturer can sell a package of screws A at a profit on Rs. 7 and screws B at a profit of Rs.10. Assuming that he can sell all the screws he manufactured, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.

Find the general solution of $\frac{dy}{dx}+ay=e^{mx}.$

If $A=\left[\begin{array}{ccc}1& 0& 2\\ 0& 2& 1\\ 2& 0& 3\end{array}\right]$, prove that $A^3-6A^2+7A+2I=0.$

$\left|\begin{array}{ccc}1& a& a^2\\ 1& b& b^2\\ 1& c& c^2\end{array}\right|=(a-b)(b-c)(c-a)$

$\left|\begin{array}{ccc}1& 1& 1\\ a& b& c\\ a^3& b^3& c^3\end{array}\right|=(a-b)(b-c)(c-a)(a+b+c)$

Explain why the experiment of tossing a coin three times is said to have Binomial distribution.

If $ta{n}^{-1}\frac{x-3}{x-4}+ta{n}^{-1}\frac{x+3}{x+4}=\frac{\pi }{4}$,then find the value of x.

What is the condition for the circle $x^2+y^2+2gx+2fy+c=0$ to cut the x-axis at more than one point.

Show that $\left(i\right)\left[\begin{array}{cc}5& -1\\ 6& 7\end{array}\right]\left[\begin{array}{cc}2& 1\\ 3& 4\end{array}\right]\ne \left[\begin{array}{cc}2& 1\\ 3& 4\end{array}\right]\left[\begin{array}{cc}5& -1\\ 6& 7\end{array}\right]$

$\left(ii\right)\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 0\\ 1& 1& 0\end{array}\right]\left[\begin{array}{ccc}-1& 1& 0\\ 0& -1& 1\\ 2& 3& 4\end{array}\right]\ne \left[\begin{array}{ccc}-1& 1& 0\\ 0& -1& 1\\ 2& 3& 4\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 0\\ 1& 1& 0\end{array}\right]$

3√108×4√64÷4√81,evaluate

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$y^2=10x$

Solve the equation, $z^2=\overline{z},$ where z is a complex number.

Describe the sample space for the indicated experiment.
A coin is tossed and then a die is rolled only in case a head is shown on the coin.

If A and B are square matrices of order 3 such that $(A+B)(A-B)=A^2-B^2$, then $(AB{A}^{-1}{)}^2$ is -

A man bought 15 out of 100 tickets of a lottery. If the reward for the winning ticket is Rs.1000, the expectation of the man would be:

Let $f\left(x\right)=x+2|x+1|+2|x-1|$. If $f\left(x\right)=k$ has exactly one real solution, then the value of $k$ is

A(3,2,0) , B(5,3,2) and C(-9,6,-3) are three points joining a triangle and AD is bisector of the angle $\angle$ BAC. AD meets BC at the point

From the given options pick the time at which the speed of the particle is maximum?

Let the ellipse $C_1:\frac{x^2}{a_1^2}+\frac{y^2}{b_1^2}=1(a_1>b_1)$ and the hyperbola $C_2:\frac{x^2}{a_2^2}-\frac{y^2}{b_2^2}=1$ have the same focus point $F_1$ and $F_2$. If point $P$ is the intersection point of $C_1$​ and $C_2$​ in the first quadrant and $|F_1{F}_2|=2|P{F}_2|$, then which of the following is (are) CORRECT?
( $e_1$ and $e_2$ are eccentricities of ellipse and hyperbola respectively.)

If x = 3 sec²θ - 1, y = tan²θ - 2 then x - 3y is equal to

An equilatral triangle inscribed in parabola $y^2=4ax$ whose one vertex is at the vertex of parabola. Then the length of the side of the triangle is

Let for all $x>0,f\left(x\right)=\underset{n\to \infty }{lim}n(x^{1/n}-1)$, then

An ellipse having co-ordinate axes as its axes having lengths $2a$ and $2b$ units respectively, Where $a$ and $b$ are middle terms of a series $a_1,a_2,a_3\cdots a_{10},$ $a_i{a}_{11-i}=5\sqrt{3}\forall i\in N,i<11.$ If $B,F,F^{\prime }$ are one end of minor axis and foci of the ellipse respectively,such that triangle $FB{F}^{\prime }$ is an equilateral triangle, then equation of ellipse is

The differential equation whose solution is is

[CEE 1993; Kerala (Engg.) 2002]

Find the maximum value of z = 3x + 4y subject to constraints x + y ≤ 4, x ≥ 0 and y ≥ 0