Explore topic-wise InterviewSolutions in Current Affairs.

The range of f(x) = |x – 2| + |x – 12| is

The coefficient of $x^{18}$ in the product $(1+x)(1-x{)}^{10}(1+x+x^2{)}^9$

The equation of the ellipse which passes through origin and has its foci at the points $(1,0)$ and $(3,0),$ is

For positive integer n, ${10}^{n-2}$ > 81n, if

The value of ${}^{10}{C}_1+{}^{10}{C}_3+{}^{10}{C}_5+{}^{10}{C}_7+{}^{10}{C}_9$ is

The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is

(a) If $sinA=\frac{12}{13}$ and $sinB=\frac{4}{5},$ where $\frac{\pi }{2}<A<\pi$ and $0<B<\frac{\pi }{2},$ find the following:
(i) sin(A+B)
(ii) cos(A+B)
(b) If sinA= $\frac{3}{5}$, $cosB=\frac{12}{13}$, where A and B both lie in second quadrant, find the value of sin(A+B).

If $a_1,a_2,a_3,\cdots ,a_n$ are in A.P. and $a_1+a_4+a_7+\cdots +a_{16}=114$ , then $a_1+a_6+a_{11}+a_{16}$ is equal to :

Let $I=\int \frac{{\sin }^{2}x+\sin x}{1+\sin x+\cos x}dx$, $J=\int \frac{{\cos }^{2}x+\cos x}{1+\sin x+\cos x}dx$ and $c$ is the constant of integration.

$$\begin{array}{cc}\text{Function}& \text{Integral}\\ \begin{array}{c}\text{(a) I}\end{array}& \text{(p)}\frac{1}{2}(x-\sin x-\cos x)+c\\ \begin{array}{c}\text{(b) J}\end{array}& \text{(q)}\frac{1}{2}(x+\sin x+\cos x)+c\\ \begin{array}{c}\text{(c) I + J}\end{array}& \text{(r)}x+c\\ \begin{array}{c}\text{(d) I - J}\end{array}& \text{(s)}c-\cos x-\sin x\\ \begin{array}{}\end{array}& \text{(t)}c+\cos x+\sin x\\ \begin{array}{}\end{array}& \text{(u)}-\frac{1}{2}(x+\sin x+\cos x+c)\end{array}$$

Then the value of $\frac{d(I+J)}{dx}$ at $x=\sqrt{2}$ is

$\frac{(1+cot\theta +tan\theta )(sin\theta -cos\theta )}{se{c}^3\theta -cose{c}^3\theta }=si{n}^2\theta co{s}^2\theta$

Find (A - B) $\cup$ (B - A), if A = {1, 3, 4} and B = {2, 5, 9, 11} .

Value of the determinant $\left|\begin{array}{ccc}secx& sinx& tanx\\ 0& 1& 0\\ tanx& cotx& secx\end{array}\right|$ is given by___

Also try to think on the lines that expanding along which row or column will make the calculation easier.

If A and B are invertible matrices, then which of the following is not correct?

(a) $adjA=|A|.A^{-1}$
(b) $det(A{)}^{-1}=[det\left(A\right){]}^{-1}$
(c) $(AB{)}^{-1}=B^{-1}{A}^{-1}$
(d) $(A+B{)}^{-1}=B^{-1}+A^{-1}$

Find the area of the smaller region bounded by the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and the line $\frac{x}{3}+\frac{y}{2}=1.$

Let $\ast$ be a binary operation on the set Q of rational number as follows:
$\left(i\right)a\ast b=\frac{ab}{4}$
Show that none of the operations has an identity.

If the determinant of a matrix of order $3\times 3$ is formed by using the numbers 1 or -1 and minimum value of the determinant is $-\lambda$, then the value of $\lambda$ is ___ .

Consider the parabola $x^2+4y=0.$ Let $P(a,b)$ be any fixed point inside the parabola and let $S$ be the focus of parabola. Then the minimum value of $SQ+PQ$ as point $Q$ moves on parabola is:

From the following Receipts and Payments Account of a Cricket club and the additional information, prepare an Income and Expenditure Account for the year ended on 31st March, 2014 and a Balance Sheet as at that date :

$\begin{array}{ccccc}\text{Receipts}& \text{Rs}& \text{Payments}& & \text{Rs}\\ \text{Balance b/d :}& & \text{Crockery purchased}& & 2,650\\ \text{Cash}& 3,520& \text{Maintenance}& & 6,820\\ \text{Bank}& 27,380& \text{Match Expenses}& & 13,240\\ \text{Fixed Deposit at}6\%\text{p.a.}& 30,000& \text{Salaries}& & 11,000\\ \text{Membership Subscription}& & \text{Conveyance}& & 820\\ \text{(including Rs 6,000 for the year}& & \text{Upkeep of lawn}& & 4,240\\ \text{year ending 31st March, 2013)}& 40,000& \text{Postage Stamps}& & 1,050\\ \text{Entrance Fees}& 2,750& \text{Purchase of Cricket Materials}& & 9,720\\ \text{Donation}& 5,010& \text{Sundry Expenses}& & 2,000\\ \text{Interest on Fixed Deposit}& 900& \text{Investments}& & 5,700\\ \text{Tournament Fund}& 20,000& \text{Tournament Expenses}& & 18,800\\ \text{Sales of Crockery}& & \text{Balance c/d :}& & \\ \text{(Book value Rs 1,200)}& 2,000& \text{Cash}& 2,200& \\ & & \text{Bank}& 23,320& \\ & & \text{Fixed Deposit at}6\%\text{p.a.}& \underset{–}{30,000}& 55,520\\ & \underset{–}{\overline{1,31,560}}& & & \underset{–}{\overline{1,31,560}}\end{array}$

Informations :- (a) Monthly Salary is Rs 1,000;

(b) The value of unused Postage Stamps is as follows :

31st March, 2013, Rs 750;

31st March, 2014, Rs 900.

(c) Stock of Cricket Materials is as follows :

31st March, 2013, Rs 3,210;

31st March, 2014, Rs 2,800.

(d) Arrear of membership subscriptions :

On 31st March, 2013, Rs 6,600;

On 31st March, 2014, (for 2013-14) Rs 8,000.

(e) Donation and Entrance Fees are not to be capitalised

A focal chord is drawn on the parabola $y^2=8x$. if one end of it is (8,8) what is the other end?

Latus rectum of the parabola whose focus is (3,4) and whose tangent at vertex has the equation x + y = 7 + 5√2 is ?

The point at which the line joining the points (2, -3, 1) and (3, -4, -5)
intersects the plane 2x + y + z = 7 is
[DSSE 1987; MP PET 1991]

The sum of the intercepts on the coordinate axes of the plane passing through the point $(–2,–2,2)$ and containing the line joining the points $(1,–1,2)$ and $(1,1,1)$, is :

Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is

The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman, is :

The set of solutions for $\frac{4x}{3}-\frac{9}{4}<x+\frac{3}{4}$ and $\frac{7x-1}{3}-\frac{7x+2}{6}>x$ is

Find the equation of a parabola with vertex at the origin,the axis along x-axis and passing through (2,3).

Sketch the graph of the following functions:
y= tan 2x

Of the students in a school,it is known that 30% have 100% attendance and 70% students are irregular.Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination.At the end of the year,one student is chosen at random from the school and he was found to have an A grade.What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer.

If $x{\log }_e\left({\log }_{e}x\right)-x^2+y^2=4(y>0)$, then $\frac{dy}{dx}$ at $x=e$ is equal to :

Let $PS$ be the median of the triangle with vertices $P(2,2),Q(6,-1)\text{and}R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is

If $y=(ta{n}^{-1}x{)}^2,then(x^2+1{)}^2{y}_2+2x(x^2+1)y_1$ is equal to

Find the length of subnormal at x= 2 on the curve y = $x^3$.

Refer to question 7, maximum value of Z + minimum value of Z is equal to
(a)13
(b)1
(c)-13
(d)-17

Differentiate the following functions with respect to x :

$\left(\frac{2x-1}{x^2+1}\right)$

Integrate the following functions w.r.t. x.

$\int \frac{sinx}{sin(x-a)}dx.$

If $f\left(x\right)=\{\begin{array}{cc}{e}^{x-1}& 0\le x\le 1\\ x+1-\left\{x\right\},& 1<x<3\end{array}$ and $g\left(x\right)=x^2-ax+b$, such that f(x). g(x) is continuous in $[0,3)$ then the values of a and b is

If a=cos$\alpha$+isin$\alpha$, b=cos$\beta$+isin$\beta$,

c=cos$\gamma$+isin$\gamma$ and $\frac{b}{c}$+$\frac{c}{a}$+$\frac{a}{b}$=1,Then

cos($\beta$-$\gamma$)+cos($\gamma$-$\alpha$)+cos($\alpha$-$\beta$) is equal to

If [2 1 3] $\left[\begin{array}{c}-10-1\\ -110\\ 011\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]$=A, then find the value of A.

The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A,B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is :

$\text{Write the coordinates of the foci of the hyperbola}9x^2-16y^2=144$

The number of ordered pairs $(r,k)$ for which $6{\cdot }^{35}{C}_r=(k^2-3){\cdot }^{36}{C}_{r+1}$, where $k$ is an integer, is :

In order to supplement daily diet, a person wishes to take some X and some wishes Y tablets. The contents of iron, calcium and vitamins in X and Y (in mg/tablet) are given as below

$\begin{array}{cccc}Tablets& Iron& Calcium& Vitamin\\ X& 6& 3& 2\\ Y& 2& 3& 4\end{array}$

The person needs atleast 18 mg of iron, 21 mg of calcium and 16 mg of vitamins. The price of each tablet of X and Y is Rs 2 and R1, respectively. How many tablets of each should the person take in order to stisfy the above requirement at the minimum cost?