Explore topic-wise InterviewSolutions in Current Affairs.

If $\omega$ is the cubic root of unity, then value
of the $(1+\omega -{\omega }^2{)}^2+(1-\omega +{\omega }^2{)}^2+1$ is

A line is such that its segment beween the straight lines 5x - y - 4 = 0 and 3x + 4y - 4 = 0 is bisected at the point (1, 5). Obtain its equation.

If A+B+C=180°, prove that

tan(A/2)tan(B/2)+ tan(B/2)tan(C/2)+ tan(C/2)tan(A/2)= 1

Study the following information carefully and answer the questions given below:

P, Q, R, S, T, V and W are seven students of a college. Each of them has a favourite subject from Physics, Chemistry, English, Biology, History, Geography and Philosophy, not necessarily in the same order. Each of them also has a favourite sport from Football, Cricket, Hockey, Volleyball, Badminton, Table Tennis and Basket ball not necessarily in the same order.
R likes Philosophy and his favourite sport is Hockey. The one who likes Football likes English. T’s favourite sport is not Badminton or Table Tennis. V does not like either History or Biology. The one whose favourite sport is Basketball does not like Physics. W likes Chemistry and his favourite sport is Volleyball. S likes Geography. Q’s favourite sport is Badminton. V does not like English and his favourite sport is not Basketball. P’s favourite sport is Cricket. The one whose favourite sport is Badminton does not like Biology.

Which subject does T like?

If the straight line $(a-1)x-by+4=0$ is normal to the hyperbola $xy=1$ then which of the followings does not hold?

If $\frac{1+3p}{3},\frac{1-p}{4}$ and $\frac{1-2p}{2}$ are probabilities of mutually exclusive events of a random experiment, then the range of $p$ is

If f(x) be a function defined on the closed interval [a, b] and graph of the function f(x) is a curve above X-axis, the area bounded by the curve f(x) and the ordinates x = a, x = b and X-axis is:

For $\Delta ABC$, if $A={\tan }^{-1}2,B={\tan }^{-1}3$, then $C=$

Evaluate the following:

$\left(i\right)(\sqrt{x+1}+\sqrt{x-1}{)}^6+(\sqrt{x+1}-\sqrt{x-1}{)}^6$

$\left(ii\right)(x+\sqrt{x^2-1}{)}^6+(x-\sqrt{x^2-1}{)}^6$

$\left(iii\right)(1+2\sqrt{x}{)}^5+(1-2\sqrt{x}{)}^5$

$\left(iv\right)(\sqrt{2}+1{)}^6+(\sqrt{2}-1{)}^6$

$\left(v\right)(3+\sqrt{2}{)}^5-(3-\sqrt{2}{)}^5$

$\left(vi\right)(2+\sqrt{3}{)}^7+(2-\sqrt{3}{)}^7$

$\left(vii\right)(\sqrt{3}+1{)}^5-(\sqrt{3}-1{)}^5$

$\left(viii\right)(0.99{)}^5+(1.01{)}^5$

$\left(ix\right)(\sqrt{3}+\sqrt{2}{)}^6-(\sqrt{3}-\sqrt{2}{)}^6$

$\left(x\right)\{a^2+\sqrt{a^2-1}{\}}^4+\{a^2-\sqrt{a^2-1}{\}}^4$

Find three numbers in G.P. whose sum is 38 and their product is 1728.

If A and B are two matrices, then AB is defined only if

The equation $2{\tan }^{2}x-5\sec x=1$ holds true for exactly eleven distinct values of $x\in [0,\frac{n\pi }{2}],n\in N$. The greatest value of $n$ is

Let A={1,2,3}. Then, the number of relation containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is
(a)1
(b)2
(c)3
(d)4

How many 5 digit even numbers can be made from the digits 1,2,3,4,5 if repetition is not allowed?

cos^{​​​​-1} (3/5) + sec^{​​​​-1} (x) = tan^{​​​​-1} (1/2) , then x=?

If $\alpha ,\beta$ are the roots of the equation $x^2-px+q=0and\alpha$ > $0,\beta$ >$0$ , then the value of ${\alpha }^{\frac{1}{4}}+{\beta }^{\frac{1}{4}}is{(p+6\sqrt{q}+4q^{\frac{1}{4}}\sqrt{p+2\sqrt{q}})}^k$ , where k is equal to

A student appears for tests $I,II$ and $III$. The student is successful if he passes in tests $I,II$ or $I,III$. The probabilities of the student passing in tests $I,II$ and $III$ are respectively $p,q$ and $\frac{1}{2}$ . If the probability of the student to be successful is $\frac{1}{2}$. Then

Circles are drawn on chords of the rectangular hyperbola $xy=4$ parallel to the line $y=x$ as diameters. All such circles pass through two fixed points whose coordinates are

The shortest distance from (1, 1, 1) to the line of intersection of the pair of planes $xy+yz+xz+y^2=0$is

Total number of solutions to the system of linear equations 2x + 3y + z = 1, 4X + 6y + 2z = 3, 6x + 9y + 3z = 2 is ___

If A and B are two sets such that n(A)=27, n(B)=35 and$n(A\cup B)=50$, find $n(A\cap B)$.

The lines $x+y=10,2x-y-6=0\text{and}x+2y=k$ are concurrent if $k=$

A Tennis tournament is to be played by $10$ pairs of students and each pair is to play with every other pair one set. If four sets are played each day then the number of days required for the tournament is

The number of 5 digit numbers in which no two consecutive digits are identical

Q33. Statements

1. Some mysteries are movies.

2. No toys are plays.

3. Some toys are mysteries.

Conclusions:

I. Some toys are movies.

II. Some mysteries are plays.

III. Some toys are not movies.

IV. Some mysteries are not plays.

Find the magnetic induction at the origin in the figure shown

Find the sum of all natural numbers lying between 100 and 500 which are divisible by 8

In a beauty contest, half the number of experts voted for Miss $A$ and two-third voted for Miss $B$, $10$ voted for both and $6$ did not vote for either. Then how many experts were there?

if X sin^3A + Y cos^3A = (sinA)(cosA) and X sinA = Y cosA , prove that X^2 + Y^2 = 1

If $\begin{array}{c}R\left(t\right)=\left[\begin{array}{cc}cost& sint\\ -sint& cost\end{array}\right]\end{array}$

then R(s).R(t) = [Roorkee1981]

Let P(6,3) be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

If the normal at the point P intersects the x-axis at (9,0), then the eccentricity of hyperbola is,

The period of $si{n}^2\theta$ is

A man starts from the point $p(-3,4)$ and will reach the point $Q(0,1)$ touching the line $2x+y=7$ at $R$ the coordinates $R$ on the line so that he will travel in the shortest distance is
A) $(\frac{84}{50},\frac{9}{25})$
B) ($\frac{91}{25},\frac{42}{25}$)
C) ($\frac{42}{25},\frac{91}{25}$)
D) ($\frac{42}{25},0)$

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. On these subjects, the student has a $75\%$ chance of passing in at least one, a $50\%$ chance of passing in at least two and a $40\%$ chance of passing in exactly two. Which of the following relations are true.

The locus of the mid-point of the chord of a circle $x^2+y^2=4$ such that the segment intercepted by the chord on the curve $x^2-2x–2y=0$ subtends a right angle at the origin is

Angle between the common tangents of the hyperbolas $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

The value of ${}_{-x}^{\pi }\frac{co{s}^{2}x}{1+a^x}dx,a>0,is$ [IIT Screening 2001; AIEEE 2005]

The equation of diameter which bisects the chord $3x+y+5=0$ of the circle $x^2+y^2=16$ is

If the A.M. of two positive numbers a and b(a > b) is twice their geometric mean.

Prove that : $a:b=(2+\sqrt{3}):(2-\sqrt{3})$.

The area bounded by the x-axis, the curves y=f(x) and the lines x=1, x=b is equal to $\sqrt{b^2+1}-\sqrt{2}$ for all $b>1$, then f(x) is

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three vectors such that $|\overrightarrow{a}|=|\overrightarrow{c}|=1;|\overrightarrow{b}|=4$ and $|\overrightarrow{b}\times \overrightarrow{c}|=\sqrt{15}$. If $\overrightarrow{b}-2\overrightarrow{c}=\lambda \overrightarrow{a}$ then a value of $\lambda$ is

Write last two digits of the number $3^{400}$

A straight line passes through the point $(\alpha ,\beta )$ and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is $\frac{x}{2\alpha }+\frac{y}{2\beta }=1.$