Explore topic-wise InterviewSolutions in Current Affairs.

The area of the triangle with vertices i, iw, i+iw is (w is cube roots unity)

A line meets x-axis and y-axis at A and B respectively and O is the origin.

$\begin{array}{cccccc}& \text{Column I}& & \text{Column 2}& & \text{Column 3}\\ & & & \text{Equation of AB}& & \text{Area of}\Delta OAB\\ \text{(I)}& \text{Centroid}\Delta OAB\text{is (1, 2)}& \text{(i)}& 2x+y=2& \text{(P)}& \text{6 sq. units}\\ \text{(II)}& \text{Circumcenter of}\Delta OAB\text{is (1, 2)}& \text{(ii)}& 3x+4y=12& \text{(Q)}& \text{9 sq. units}\\ \text{(III)}& \text{Distance of the orthocentre of}\Delta OAB& \text{(iii)}& 2x+y=6& \text{(R)}& \text{1 sq. units}\\ & \text{From A and B is 1 and 2 respectively}& & & & \\ \text{(IV)}& \text{Incenter of}\Delta OAB\text{is (1, 1)}& \text{(iv)}& 2x+y=4& \text{(S)}& \text{4 sq. units}\end{array}$

Which of the following is correct combination?

Find the parametric and symmetric equation of the line passing through the point $(2,3,4)$ and perpendicular to the plane $5x+6y-7z=20$ ?

In Triangle ABC, which of the following is not true:

(a) AB + BC + CA = 0
(b) AB + BC - AC = 0
(c) AB + BC - CA = 0
(d) AB - CB + CA = 0

Find the area of the region bounded by the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1.$

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\frac{\pi }{4}}log(1+tanx)dx.$

Is equation y=f(x-vt) and equation y=f(t-x/v) are same if yes how ?is both these are equation of progressive wave?

Prove that:

$2(si{n}^{6}x+co{s}^{6}x)-3(si{n}^{4}x+co{s}^{4}x)+1=0$

How many three - digit nubmers are there?

The maximum number of points of intersection of five distinct lines and four distinct circles is

If $a{x}^4+b{x}^3+c{x}^2+dx+e=\left|\begin{array}{ccc}{x}^3+3x& x-1& x+3\\ x+1& -2x& x-4\\ x-3& x+4& 3x\end{array}\right|$, then e =

${lim}_{x\to 2}(3-x)$

If AM and GM of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.

If $2p^2-3q^2+4pq-p=0$ and a variable line px + qy =1 always touches a parabola whose axis is parallel to X-axis, then equation of the parabola is

At 3:40, the hour and minute hands of a clock are inclined at

Third term in the expression $(x+a{)}^7$ is

Evaluate the definite integrals.
${\int }_0^2\frac{6x+3}{x^2+4}dx.$

Reflection of the line $\frac{x-1}{-1}=\frac{y-2}{3}=\frac{z-4}{1}$ in the plane x +y +z =7 is :
​

A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is $(a^{\frac{3}{2}}+b^{\frac{2}{3}}{)}^{\frac{3}{2}}$

Let $E_1$ and $E_2$ be two ellipses whose centers are in origin. The major axes of $E_1$ and $E_2$ lies along the $x-$axis and $y-$axis, respectively. Let $S$ be the circle $x^2+(y-1{)}^2=2.$. The straight lin $x+y=3$ touches the curves $S$, $E_1$ and $E_2$ at $P,Q$ and $R,$ respectively. Supoose the $PQ=PR=\frac{2\sqrt{2}}{3}.$If $e_1$ and $e_2$ are the eccentricities of $E_1$ and $E_2$, respectively, then the correct expression(s) is(are)

The equation of a circle which cuts the three circles

$x^2+y^2-3x-6y+14=0,$

$x^2+y^2-x-4y+8=0$

$x^2+y^2+2x-6y+9=0$

orthogonally is $\underset{–}{}$

A function f(x) defined on [a,b] will have a local maximum at x = b if

[ h is a positive quantity tending to zero]

The value of $\underset{x\to \frac{\pi }{2}}{lim}\left[si{n}^{-1}sinx\right]$,[x] is the greatest integer function of x, is

IF A and B are any two events such that P(A) + P(B) - P (A and B ) = P(A), then
(a) $P\left(\frac{B}{A}\right)=1$
(b) $P\left(\frac{A}{B}\right)=1$
(c) $P\left(\frac{B}{A}\right)=0$
(d) $P\left(\frac{A}{B}\right)=0$

The local time of Delhi is 5½ hours ahead of London time and 5 hours behind that of Sydney. If the new York time is 15 hours behind Sydney what is the difference between the local times of new York and London

The number of integral solutions for the equation $x+y+z+t=20,$ where $x,y,z,t$ are all $\ge -1,$ is

cos{3π/2 + x } cos(2π+x) [ cot {3π/2 - z} + cot (2π+x) ] =1

Find the maximum and minimum values of x+sin2x on $[0,2\pi ]$

The value of the integral $\int \frac{dx}{x\sqrt{x^2-a^2}}$ is equal to :

Find the interval(s) in which f(x) = sec(x) is convex.

$\Delta \left(r\right)=\left|\begin{array}{ccc}r& r^2& r^3\\ 1& 2& 4\\ 2& 1& 3\end{array}\right|$ then ${\sum }_{r=1}^5\Delta \left(r\right)$ will be _____

The equation of the director circle of the circle $(x-2{)}^2+(y+3{)}^2=16$ is .

Choose the correct answer
$\int \frac{dx}{si{n}^{2}xco{s}^{2}x}$ is equal to
(a)tan x+cot x +C
(b)tan x-cot x+C
(c)tan xcot x+C
(d)tan x-cot 2x+C

The value(s) of $a$ for which the equation
$2{\log }_{1/25}(ax+28)=-{\log }_5(12-4x-x^2)$ (wherever defined) has coincident roots, is (are)

A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Deterrnine the total number of elementary events associated to this experiment.

Suppose the sum of the first $m$ terms of an arithemetic progression is $n$ and the sum of its first $n$ terms is $m$, where $m\ne n$. Then the sum of the first $(m+n)$ terms of the arithemetic progression is

If the equation $2^{2x}+a\cdot 2^{x+1}+a+1=0$ has roots of opposite sign, then ${}^{\prime }{a}^{\prime }$ lies in the interval

If X and Y are two sets such that X has 40 elements $X\cup Y$ has 60 elements and $X\cap Y$ has 10 elements, how many elements does Y have?

5. If the perimeter of a triangle ABC is 6 times the Arithmetic mean of the sines of its angles. If the side 'a'is 1, then the angle A is?