Explore topic-wise InterviewSolutions in Current Affairs.

By using properties of determinants

$\left|\begin{array}{ccc}y+k& y& y\\ y& y+k& y\\ y& y& y+k\end{array}\right|=k^2(3y+k)$

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$

Find the number of solutions for $cosx=x$.

If P and x are real, then $e^{2\pi co{t}^{-1}x}{\left(\frac{1+ix}{ix-1}\right)}^p=$

(a) From the given figure find the value of 'x'. [4 MARKS]



(b) In the figure below, x = ${30}^{\circ }$. The value of (6y – 3x) is ___.

If a < 0 then the inequality $a{x}^2$-2x + 4 > 0 has the solution represented by

$f\left(x\right)=\{\begin{array}{cc}|x-a|sin\frac{1}{x-a},& ifx\ne 0\\ 0,& ifx=a\end{array}atx=a$

Check if f(x) is continuous at x=a.

Maximise the function Z =11x +7y, subject to the constraints $x\le 3,y\le 2,x\le 0$ and $y\le 0$

If $\left|\begin{array}{cc}x& 2\\ 18& x\end{array}\right|=\left|\begin{array}{cc}6& 2\\ 18& 6\end{array}\right|$, then x is equal to
a) 6
b) $\pm 6$
c) -6
d) zero

Domain of 1/1+x²

Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to

A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand-operated. It takes 4 minutes on the automatic and 6 minutes on the hand-operated machines to manufacture a packet of screws 'A' while it takes 6 minutes on the automatic and 3 minutes on the hand-operated machine to manufacture a packet of screws 'B'. Each machine is available for at most 4 hours on any day. The manufacturer can sell all the screws 'A' at a profit of 70 paise and screws 'B' at a profit of Rs1. Assuming that he can sell all the screws he manufactures, how many packets of each type should the factory owner produce in a day in order to maximize his profit ? Formulate the above LPP and solve it graphically and find the maximum profit.

The equation of circle which has radius of $6$ units and is centred at $(5,8),$ is

Find the equation of the tangent to the circle $x^2+y^2=a^{2}at(acos\alpha ,asin\alpha )$.

If $f\left(x\right)=30-2x-x^3$, then the number of positive integral value(s) of $x$ satisfying $f\left(f\right(f\left(x\right)\left)\right)>f\left(f\right(-x\left)\right)$ is
(correct answer + 1, wrong answer - 0.25)

In how many ways can five keys be put in a ring?

What is the vertex of the quadratic function y = $x^2-6x+12$?

a+ b = 5, ab = 2 find $a^3$ + $b^3$

Number of words that can be formed by using the $4$ letters of the word $MISSISSIPPI$ is

$\text{Write the length of the latus-rectum of the hyperbola}16x^2-9y^2=144$

In how many ways can an examinee answer a set of ten true/false type questions?

A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initial A (for Adenine), C (for Cytosine), C (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?

The sum of 0.2+0.004+0.00006+0.0000008+....... to $\infty$ is

Find $\frac{dy}{dx}$ of each of the functions expressed in parametric form.
$x=t+\frac{1}{t},y=t-\frac{1}{t},$

Find the area of the region bounded by the parabola $y^2=2px$, and $x^2=2py$.

If $z_1\ne 0$ and $z_2$ be two complex numbers such that $\frac{z_2}{z_1}$ is a purely imaginary number, then the value of $\left|\frac{2z_1+3z_2}{2z_1-3z_2}\right|$ is

Show that $5–\sqrt{3}$ is irrational.

In how many ways we can select a committee of 6 persons from 6boys and 3girls ,if at least two boys and at least two girls must be in the committe

Solution set of $lo{g}_{0.25}(x^2+2x-8{)}^2-lo{g}_{0.5}(10+3x+x^2)=1$

If $x^2$ + x + 1 =0 is a factors of 15$x^3$ + Ax + B , Find ( A, B)

A woman has $11$ close friends. The number of ways in which she can invite $5$ of them to dinner, if two particular of them are not on speaking terms and will not attend together, is

The equation of a circle whose radius is $8$ units and which touches both $x-$axis and $y-$axis is

tan inverse x^2 + y^2 = a^2 find dy/dx

Let $p,q,r\in R^{+}$ such that $27pqr\ge (p+q+r{)}^3$ and $3p+4q+5r=12.$ Then the value of $p+q+r$ is

The number of real values of $x$, that satisfy the equation $x^{{\log }_{\sqrt{x}}2x}=4$ is

Evaluate $\left|\begin{array}{cc}\cos {15}^{\circ }& \sin {15}^{\circ }\\ \sin {75}^{\circ }& \cos {75}^{\circ }\end{array}\right|$

If (-2,5) is the centre of the circle which touches y-axis, then the equation of the circle is

There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

If $ta{n}^{-1}\left(\frac{1}{4}\right)+ta{n}^{-1}=\left(\frac{2}{9}\right)=\frac{1}{2}co{s}^{-1}x,$ then x is equal to

${lim}_{x\to 1}\frac{1-x^2}{sin2\pi x}$

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

If the sides $a,b,c$ of a triangle $ABC$ form successive terms of G.P. with common ratio $r(>1)$ then which of the following is correct?