Explore topic-wise InterviewSolutions in Current Affairs.

Let Z = ax + by is a linear objective function. Variables x and y are called ……… variables.

If x = a (a > 0) divides the area bounded by x axis, part of $x^2(y–1)=8$and the ordinates x = 2, x = 4 into two equal parts then a _____

Let $P$ be a square matrix satisfying $P^2=I-P,$ where $I$ is identity matrix. If $P^n=5I-8P,$ then the value of $n$ is

If $p=\left|\begin{array}{cc}x& 1\\ 1& x\end{array}\right|$ and $Q=\left|\begin{array}{ccc}x& 1& 1\\ 1& x& 1\\ 1& 1& x\end{array}\right|$ then $\frac{dQ}{dx}$=.......

Which one of the following is not a function ?

(a) $\left\{\right(x,y):x,yϵR,x^2=y\}$
(b) $\left\{\right(x,y):x,yϵR,y^2=x\}$
(c) $\left\{\right(x,y):x,yϵR,x=y^3\}$
(d) $\left\{\right(x,y):x,yϵR,y=x^3\}$

if A=5+ 2 root 6 find the value of rootA + 1/root A

$\frac{d}{dx}\left[lo{g}_a^x\right]=$

If $3ta{n}^{-1}x+co{t}^{-1}x=\pi ,$ then x equals to

(a) 0 (b) 1 (c) $-1$ (d) $\frac{1}{2}$

If l, m, n are the direction cosines of any line, then sum of the squares of the direction cosines of the line is always

For any set A , (A')' is equal to

Let f(x) is a real valued function defined by $f\left(x\right)=x^2+x^2{\int }_{-1}^{1}tf\left(t\right)dt+x^3{\int }_{-1}^{1}f\left(t\right)dt$, then

Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e., the angle between the bounding radii) is

If tan(A+B) =3tanA

then show that sin(2A +2B)+sin2A=2sin²B

Consider a parabola with its axis along the Y-axis. The corresponding function is __-

A body radiates energy 5 W at a temperature of ${127}^{o}C$ . If the temperature is increased to ${927}^{O}C$, then it radiates energy at the rate of

If the equation $z^4+a_1{z}^3+a_2{z}^2+a_{3}z+a_4=0$ where $a_1,a_2,a_3,a_4$ are real coefficients different from zero, has a pure imaginary root, then the expression $\frac{a_3}{a_1{a}_2}+\frac{a_1{a}_4}{a_2{a}_3}$ has the value equal to

The number of common tangents to the following pairs of circles $x^2+y^2+4x-6y-3=0$ and $x^2+y^2+4x-2y+4=0$ is

Find gof and fog, if
(i) f(x) =|x| and g(x) =|5x-2|

$\left(ii\right)f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$.

If the equations $x^2+2\lambda x+{\lambda }^2+1=0,\lambda ϵRanda{x}^2+bx+c=0$ where a, b, c are lengths of sides of triangle have a common root, then the possible range of values of $\lambda$ is

Find the ratio of the length of the tangents from any point on the circle $15x^2+15y^2-48x+64y=0$ to the two circles $5x^2+5y^2-24x+32y+75=0,$ $5x^2+5y^2-48x+64y+300=0.$

The initial temperature of a body is 80 ^oC. Its temperature falls to 64 ^oC in 5 minutes and to 52 ^oC in next 10 minutes. If the temperature of surrounding is 7n ^oC, value of n is

Let the lines $(2–i)z=(2+i)\overline{z}$ and $(2+i)z+(i–2)\overline{z}–4i=0,$ $($here $i^2=–1$$)$ be normal to a circle $C$. If the line $iz+\overline{z}+1+i=0$ is tangent to this circle $C$, then its radius is :

If the function y=sin(f(x)) is monotonic for all values of x (where f(x)is continuous), then the maximum value of the difference between the maximum and minimum value of f(x) is

P is a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, N is the foot of the perpendicular from P on the transverse axis.The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

A car goes 5 km east, 3km south, 2km west and 1km north. The magnitude of the resultant displacement will be ___ km at an angle of $ta{n}^{-1}$(- / -) with the positive x-axis (where x axis is in the east direction) in the clock wise direction.

I alternately toss a fair coin and toss a fair die until I either toss a head or throw a 2. If I toss the coin first ,the probability that I throw a 2 before I toss a head is

Let A = {a, b, {c, d}, e}. Which of the following are false and why ?

(i) {c, d} $\subset$ A (ii) {c, d} $ϵ$ A (iii){{c, d}$ϵ$ A }

(iv) a $ϵ$ A (v) a $\subset$ A (vi) {a, b, e} $\subset$ A

(vii) {a, b, e} $ϵ$ A (viii) {a, b, c} $ϵ$ A (ix) $\varphi$$ϵ$ A (x) { $\varphi$ } $\subset$ A

Let $L$ is distance between two parallel normals of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b,$ then maximum value of $L$ is:-

P and Q are partners sharing profits in 2 : 1 ratio. They admitted R into partnership giving him $\frac{1}{5}$ share which he acquired from P and Q in 1 : 2 ratio. Calculate the new profit sharing ratio.

${lim}_{x\to 1}\frac{1-x^2}{sin\pi x}$

Consider a curve $(2x+y-1{)}^2=5(x-2y-3)$ then the possible coordinates of foci are

If $|x|\ge 6,$ then $x$ can be represented on the number line by

Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$In\Delta ABC,ifa=8,b=10,c=12andC=\lambda A,\text{find the value of}\lambda .$

A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white ball, 4 red balls and 5 black balls. If one ball is drawn from each of the boxes $B_1,B_2$ and $B_3$, the probability that all three drawn balls are of the same colour is

If a hyperbola has one focus at the origin and its eccentricity is $\sqrt{2}$ . One of the directrices is $x+y+1=0.$ Then the equations to its asymptotes are

There are three values of t for which the following system of equations has non-trivial solutions.

(a-t) x+by + cz=0

bx + (c - t) y +az=0

cx + ay + (b-t) z=0

We can express the product of the three values of t in the form of determainant as

If three dice are throw simultaneously, then the probability of getting a score of 5 is

The area of an equilateral triangle inscribed in the circle $x^2+y^2-6x-8y-25=0$ is

Prove that:

$co{s}^{6}A-si{n}^{6}A=cos2A(1-\frac{1}{4}si{n}^{2}2A)$

The population of cattle in a farm increases so that the difference between the population in year n+2 and that in year n is proportional to the population in n + 1. If the populations in years 2010, 2011 and 2013 were 39, 60 and 123, respectively, then the population in 2012 was

If $|x|<1$ and $y=1+x+x^2+x^3+....,$ then write the value of $\frac{dy}{dx}$.

Prove that:

$co{s}^2\frac{\pi }{8}+co{s}^2\frac{3\pi }{8}+co{s}^2\frac{5\pi }{8}+co{s}^2\frac{7\pi }{8}=2$

Find the vector which acts like the angle bisector for the vectors $2\hat{i}+2\hat{j}+\hat{k}and2\hat{i}+4\hat{j}+\sqrt{5}\hat{k}$