Explore topic-wise InterviewSolutions in Current Affairs.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cccc}2& -3& 3& \\ 2& 2& 3& \\ 3& -2& 2& \end{array}\right]$, if it exists.

The number of ways in which one or more balls can be selected out of $10$ white, $9$ green and $7$ black balls is

If,
show that f o
f(x)
= x, for
all.
What is the inverse of f?

At what temperature will the rate of effusion of $N_2$ be 1.625 times that of $S{O}_2$ at ${50}^{\circ }$ C?

If $\alpha ,\beta ,\gamma ,\delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k, then the value of $4sin\frac{\alpha }{2}+3sin\frac{\beta }{2}+2sin\frac{\gamma }{2}+sin\frac{\delta }{2}$ is equal to

The corner points of the feasible region determined by the system of linear constraints are $(0,10),(5,5),(15,15),(0,20).$ Let $z=px+qy$ where $p,q>0.$ Condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(15,15)$ and $(0,20)$ is

If $m$ is a non-zero number and $\int \frac{x^{5m-1}+2.x^{4m-1}}{(x^{2m}+x^m+1{)}^3}dx=f\left(x\right)+c,$ then $f\left(x\right)$ is

Let $f\left(x\right)=\frac{x-2}{x+2},$ then the value of $c$ that satisfy the mean value theorem for the function on the interval $[-1,2]$ is:

From the adjoining venn diagram, find $(A\cup B)\cap C$

If $y=\tan (x^{\circ }+{45}^{\circ }),$ then $\frac{dy}{dx}=$

The distance of the point P (3,8,2) from the line $\frac{1}{2}(x-1)=\frac{1}{4}(y-3)=\frac{1}{3}(z-2)$ measured parallel to the plane $3x+2y-2z+15=0is$

Find


:

x

In a factory 70% of the workers like oranges and 64% likes apples. What is the maximum percentage of people who can like both?

The radius of the circle S is same as the radius of $x^2+y^2-2x+4y-11=0$ and the centre of S is the centre of $x^2+y^2-2x-4y+11=0$ . Find the equation of S.

If $\int \frac{dx}{x^3(1+x^6{)}^{2/3}}=xf\left(x\right)(1+x^6{)}^{1/3}+C$, then the function $f\left(x\right)$ is equal to

(where $C$ is constant of integration)

Assume that a bag contains 4 red squares, 3 red rectangles, 5 blue squares and 4 blue circles. An object is taken out from the bag. What is the probability of taking out a blue square?

Find equation of the line through the point (0, 2) making an angle with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Let $\ast ,\square \in \{\wedge ,\vee \}$ be such that Boolean expression $(p\ast \sim q)\Rightarrow \left(p\square q\right)$ is a tautology. Then:

sec square theta - cos square theta =sin square ( sec square+1)

The number of integers satisfying the inequality $||x-1|-2|<5,$ is

If $\underset{x\to 0}{lim}\frac{{\sin }^{-1}x-{\tan }^{}-1}{3x^3}$ is equal to $L,$ then the value of $(6L+1)$ is:

If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is inscribed in a rectangle whose length to breadth ratio is $2:1$ in such a manner that it touches the sides of rectangle, then the area of the rectangle is

Write the first five terms of the sequences whose $n^{th}$ term is :

$a_n=(-1{)}^{n-1}.5^{n+1}$

1. 5

If ${\sin }^{-1}\frac{1}{3}+{\sin }^{-1}\frac{2}{3}={\sin }^{-1}x,$ then $x$ is equal to

Differentiate the given functions w.r.t. x.

$(logx{)}^{cosx}$

Let ABCD be a square of side length l, and $\Gamma$ a circle passing through B and C, and touching AD. The radius of $\Gamma$ is

The logical statement $\sim (\sim p\to q)\vee (p\wedge \sim q)$ is equivalent to

The Fibonacci sequence is defined by $1=a_1=a_2$ and $a_n=a_{n-1}+a_{n-2},n>2$
Find $\frac{a_{n+1}}{a_n},forn=1,2,3,4,5$

Let $f\left(x\right)=\frac{2{\sin }^{2}x-1}{\cos x}+\frac{\cos x(2\sin x+1)}{1+\sin x}.$ Then $\int e^x\left(f\right(x)+f^{\prime }(x\left)\right)dx$ equals

(where $C$ is the constant of integration)

A dip circle is kept in such a way that its plane makes an angle of ${30}^{\circ }$ with the magnetic meridian. The measured value of the angle of dip is ${45}^{\circ }$. What will be its true value at that place?