Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following linear in equations in R.

Solve :12x < 50,then

(i) $xϵR$ (ii) $xϵZ$ (iii) $xϵN$

Determine whether the following compound statements are true or false :

(i) Delhi is in India and 2 + 2 = 4

(ii) Delhi is in England and 2 + 2 = 4.

(iii) Delhi is in India and 2 + 2 = 5.

(iv) Delhi is in England and 2 + 2 = 5.

If P(n-1,3) : P (n,4) = 1:9, find n.

If f, g, h are three functions defined from R to R as follows:
(i) $f\left(x\right)=x^2$
(ii) $g\left(x\right)=sinx$
(iii) $h\left(x\right)=x^2+1$

Normals are drawn from a point P(h, k) with slopes $m_1,m_2,m_3$ to the parabola $C_1:y^2=4x$

${\sum }_{\alpha =0}^{\infty }(m_1{)}^{\alpha }+{\sum }_{\alpha =0}^{\infty }(m_2{)}^{\alpha }+{\sum }_{\alpha =0}^{\infty }(m_3{)}^{\alpha }=\frac{89}{22},where|m_i|<1\forall i=1,2,3then67h-89k=$

If $(x,y)$ represents the Cartesian coordinates for the polar coordinates $(4,\theta )$, then the correct relationship between $x$ and $y$ is

In In $\Delta ABC,$ if $8R^2=a^2+b^2+c^2,$ then the triangle is

Match the following by appropiately matching the lists based on the information given in Column I and Column II.
​​​​​​$\begin{array}{cc}Column1& Column2\\ \text{(a) The probability of a bomb hitting a bridge is}& \\ \frac{1}{2}.\text{Two direct hits are needed to destroy it.}& \\ \text{The number of bombs recquired so that the}& \\ \text{probability of the bridge being destroyed is}& \\ \text{greater than}0.9\text{can be}& \text{(p)}4\\ \text{(b) A bag contains}2\text{red,}3\text{white,}5\text{black balls, a}& \\ \text{ball is drawn its color is noted and replaced}& \\ \text{The number of times, a ball can be drawn}& \\ \text{so that the probability of getting a red ball}& \\ \text{for the first time is atleast}1/2& \text{(q)}6\\ \text{(c) A drawer contains a mixture of red socks}& \\ \text{and blue socks, at most}17\text{in all. It so}& \\ \text{happens that when two socks are selected}& \\ \text{randomly without replacement, there is a}& \\ \text{probability of exactly}1/2\text{that both are red}& \\ \text{or both are blue. Then number of red}& \\ \text{socks in drawer can be}& \text{(r)}7\\ \text{(d) There are two red, two blue, two white and}& \\ \text{certain number (greater than}0\text{) of green}& \\ \text{socks in a drawer. If two socks are taken at}& \\ \text{random from the drawer without}& \\ \text{replacement, the probability that they}& \\ \text{are of same color is}\frac{1}{5}\text{, then the number of}& \\ \text{green socks are}& \text{(s)}10\end{array}$

If $x,y,z$ are positive numbers, then the minimum value of $(x+y)(y+z)(z+x)(\frac{1}{x}+\frac{1}{y})(\frac{1}{y}+\frac{1}{z})(\frac{1}{z}+\frac{1}{x})$ is

If $ta{n}^{-1}\left(x\right)+ta{n}^{-1}\left(y\right)+ta{n}^{-1}\left(z\right)=\pi$, then $\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}=$

If a tangent drawn from the point (4, 0) to the circle $x^2+y^2=8$ touches it at a point A in the first quadrant, then the coordinates of another point B on the circle such that AB = 4 are

How will you deal with the Entrance Fees while preparing the final accounts of New Delhi Sports Club for the year ended 31st March, 2017 in each of the following cases:

Case 1. During the year 2016-17, Entrance Fees received Rs
1,20,000.

Case 2. During the year 2016-17, Entrance Fees received Rs 1,20,000. It is the policy of the club to treat the Entrance Fees as ' Revenue Receipt'.

Case 3. During the year 2016-17, Entrance Fees received Rs 1,20,000. It is the policy of the club to treat the Entrance Fees as 'Capital Receipt'.

Case 4. During the year 2016-17, Entrance Fees received Rs 1,20,000. According to the policy of the club, 30% of the Entrance Fees is to be capitalised.

If square root of 8 - 15i is $\pm$ (a - ib). The a + b is _____

Let $\overrightarrow{\alpha }=(\lambda -2)\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}$ be two given vectors where vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-collinear. The value of $\lambda$ for which vectors $\overrightarrow{\alpha }$ and $\overrightarrow{\beta }$ are collinear, is:

The number of positive integral solutions of ${\tan }^{-1}x+{\cos }^{-1}\frac{y}{\sqrt{1+y^2}}={\sin }^{-1}\frac{3}{\sqrt{10}}$ is

If 5th, 8th and 11th terms of a G.P. are p, q and s respectively, prove that $q^2=ps$.

If $f\left(x\right)=max(x^3,x^2,\frac{1}{64})\forall x\in [0,\infty )$, then

The mean deviation from the data 3,10,4,7,10,5:

If $\underset{-\pi /4}{\overset{3\pi /4}{\int }}\frac{e^{\pi /4}dx}{(e^x+e^{\pi /4})(\sin x+\cos x)}=\lambda \underset{-\pi /2}{\overset{\pi /2}{\int }}\sec xdx,$ then $\lambda$ is equal to

Can l' hospital rule be applied to function giving (infinity/infinity) form?

Consider the parabola whose focus at $(0,0)$ and tangent at vertex is $x-y+1=0$.
The equation of the parabola is

If the line $L:3x-4y=0$ is rotated about the centre of the circle $(x-4{)}^2+(y-3{)}^2=25$ through an acute angle of $\theta$ in anticlockwise sense such that after rotation it becomes one of the members of the family of lines $x+\lambda y-3-\lambda =0,\lambda \in R$, then $\theta$ equals

Prove that :

$(2^{\frac{1}{4}}{.4}^{\frac{2}{8}}{.8}^{\frac{3}{16}}{.16}^{\frac{4}{32}}....\infty )=2.$

Four persons $A,B,C$ and $D$ throw an unbiased die, turn by turn, in succession till one gets an even numbers and win the game. What is the probability that $A$ wins if $A$ begins?

If domain of the function $f\left(x\right)=x^2-6x+7$ is $(-\infty ,\infty )$ then its range is

Area in the first quadrant between the ellipses $x^2+2y^2=a^2$ and $2x^2+y^2=a^2$ is

If $z$ is a complex number such that $-\frac{\pi }{2}\le argz\le \frac{\pi }{2}$, then which of the following inequality is true

Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = $\pi$

Out of $7$ consonants and $4$ vowels, words are formed each having $3$ consonants and $2$ vowels. The number of such words that can be formed is

If $P$ is a point on the rectangular hyperbola $x^2-y^2=a^2$, $C$ is its centre and $S$ and $S^{\prime }$ are foci, then $SP\cdot S^{\prime }P$ is equal to

Suppose $a$ is a positive real number such that $a^5-a^3+a=2$. Then

Jackie has two summer jobs. She works as a tutor, which pays $\$12$ per hour, and she works as a lifeguard, which pays $\$9.50$ per hour. She can work no more than 20 hours per week, but she wants to earn at least $\$220$ per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

Consider two displacements , one of magnitude 6 meters and another of magnitude 7 meters . Show how the displacement vectors may be combined to get a resultant displacement of magnitude

(a) 13 meters

(b) 1 meter

(c) 8 meters

Explain

[These questions are not clubbed together for convenience . So pls answer them ]

The value of $0.7+0.77+0.777+\dots \dots \text{upto}20\text{terms}$ is

Let $P\left(x\right)=a{x}^2+bx+8$ is a quadratic polynomial. If the minimum value of $P\left(x\right)$ is $6$ at $x=2,$ then

Given are the observations of runs scored by batsmen between India - Sri Lanka combined. Find the mean deviation about mean for the scores of batsmen

$\begin{array}{ccccccc}Score& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ numberofBatsmen& 12& 18& 27& 20& 17& 6\end{array}$

Select the correct structure of the sentence.

N = noun phrase; V = verb phrase; Adj = adjective phrase; p = prepositional phrase

The crowd dispersed.

The values of a for which( $a^2-1$)$x^2$ + 2(a-1)x + 2 is positive for any x are

The general solution of $(\sqrt{3}-1)\sin \theta +(\sqrt{3}+1)\cos \theta =2$ is
(where $n\in Z$)

Let $f\left(x\right)=\frac{x}{1-x}$ and ${}^{\prime }{a}^{\prime }$ be a real number, if $x_0=a,x_1=f\left(x_0\right),x_2=f\left(x_1\right),x_3=f\left(x_2\right)...$
If $x_{2009}=1$, then the value of ${}^{\prime }{a}^{\prime }$ is

Numbers ≥ 1000 but ≤ 4000 are formed using digits '0,1,2,3,4' . How many numbers can be formed (repetition allowed)?