Explore topic-wise InterviewSolutions in Current Affairs.

Let A =R -{3} and B=R -{1}. Consider the function $f:A\to B$ defined by $f\left(x\right)=\left(\frac{x-2}{x-3}\right)$ is f one-one and onto? Justify your answer.

If $0\le x\le 3\pi ,0\le y\le 3\pi$ and $\cos x\sin y=1$, then the possible number of values of the ordered pair $(x,y)$ is

Express the complex numbers in the form of a + ib:

${(\frac{1}{3}+3i)}^3$

If $A(-2,1),B(2,3)$ and $C(-2,-4)$ are three points, then the acute angle between the lines $BA$ and $BC$ is

If $f\left(x\right)=\{\begin{array}{cc}{x}^2-3x+2,& x<2\\ x-3,& x\ge 2\end{array}$
$g\left(x\right)=\{\begin{array}{cc}x-2,& x<3\\ x^2+x+1,& x\ge 3\end{array}$
Then which of the following is/are true

if $2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$, then the value of $x$ and $y$ are

Which of the following relations are transitive?

$Iff\left(x\right)=x-x^2+x^3-x^4+.......\infty ,|x|<1,then{f}^{\prime }\left(x\right)=$

Find the slope of the normal to the curve x=1-a sin $\theta ,y=bco{s}^2\theta at\theta =\frac{\pi }{2}$

Value of $C_0+2C_1+3C_2+4C_3+\dots +(n+1)C_n$ is
( where $C_r={}^n{C}_r$)

Find the sum to n terms

$1^2+(1^2+2^2)+(1^2+2^2+3^2)+\dots$

If $\frac{|x+2|}{|x-4|}=3$, then the value(s) of $x$ is/are

A man goes 80m due East and 150m due north.Howfar is he from the starting point

Value of sin[1/4arc sin((√63)/8)

Which of the following statements are true about [x], greater integer Function?

1.$x-1)<[x]\le x$

2.$[-x]=1-\left[x\right]$, when x is NOT an integer

Differential equation representing the family of curves given by y = ax + x² is:

The value of x which satisfy $\sqrt{17se{c}^{2}x+16(\frac{1}{2}tanxsecx-1)}=2tan(1+4sinx)$ is

A party of $9$ persons are to travel in two vehicles, one of which will not hold more than $7$ and other not more than $4.$ The number of ways the party can travel is

If the cartesian product A $\times$ A has 16 elements among which a few elements are found to be (-1, 0), (0, 1), (1, 2), then find set A.

If $\overrightarrow{a}$ is a vector of magnitude 3 units, then ${|\overrightarrow{a}\times \hat{i}|}^2+{|\overrightarrow{a}\times \hat{j}|}^2+{|\overrightarrow{a}\times \hat{k}|}^2$ is equal to

If $n$ is the degree of the polynomial, ${\left[\frac{2}{\sqrt{5x^3+1}-\sqrt{5x^3-1}}\right]}^8+{\left[\frac{2}{\sqrt{5x^3+1}+\sqrt{5x^3-1}}\right]}^8$ and $m$ is the coefficient of $x^n$ in it, then the ordered pair $(n,m)$ is equal to :

A triangle has its two sides along the lines $y=m_{1}x$ and $y=m_{2}x$, where $m_1,m_2$ are the roots of $2x^2-5x+2=0.$ If $(2,2)$ is the orthocentre of the triangle, then the equation of the third side is

A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer

If n = 4 and p = 6, then the probability that there will be at least one passenger in each carriage is

In which one of the following subsets , $co{s}^{2}A$ + $si{n}^{2}A$ = 1 is valid

Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is ${30}^{\circ }$.

If $A,B$ and $C$ are invertible matrices and $BAC=I,$ the value of $A$ is

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl ?

(i) at least one boy and one girl ?

(iii) at least 3 girls ?

Among Preet, Kuna, Deep and Rana, who is the son of Mann? I. Preet and Kuna are sisters of Rana. II. Deep is the mother of Kuna and wife of Mann.

The quadratic curve y = f (x) if it touches the line y = x at the point x = 1 and passes through the point (- 1, 0) is... .

Laxman had 100 cows at the beginning of the year 1992 and the number of cows each year increases by 10%. At the end of each year he doubles the present no. of cows by buying extra cows. What is the number of cows he has at the beginning of 1994?

If the mean of the set of numbers $x_1,x_2,....x_n$ is $\overline{x}$, then the mean of the numbers $x_i+2i,1\le i\le n$ is

The smallest value of k, for which both the roots of the equation $x^2-8kx+16(k^2-k+1)$ = 0 are real, distinct and have values at least 4,is

A water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ with in a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly $3kW$ of heat (thermal load). The temperature of water fed into the device cannot exceed ${30}^{o}C$ and the entire stored $120$ litres of water is initially cooled to ${10}^{o}C$. The entire system is thermally insulated. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is

(Specific heat of water is $4.2kJ$ ${kg}^{-1}$ $K^{-1}$ and density of water is $1000kg$ $m^{-3}$)

Let R= {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A={1, 2, 3, 4}. The relation R is

$f\left(x\right)=\{\begin{array}{cc}3x-8& \text{if}x\le 5\\ 2k& \text{if}x>5\end{array}$ is continuous, find k

Find the equation whose roots are reciprocals of the roots of $2x^2+5x+4=0$ .

The locus of mid point of the chords of $x^2-y^2=4,$ that also touches the parabola $y^2=8x$ is

Differentiate the following functions with respect to x :

$\frac{xtanx}{secx+tanx}$

$Ina\Delta ABC,ifa=\sqrt{2},b=\sqrt{3}andc=\sqrt{5},\text{show that its area is}\frac{1}{2}\sqrt{6}sq.units.$

Find the values of y for which the distance between the points A(2, -3) and B(10, y) is 10 units.

The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 square units. The equation of the circle is