Explore topic-wise InterviewSolutions in Current Affairs.

If $\alpha ,\beta ,\gamma$ are the roots of $x^3-x^2-1$ = 0, then the value of $\frac{1+\alpha }{1-\alpha }+\frac{1+\beta }{1-\beta }+\frac{1+\gamma }{1-\gamma }$ is equal to:

If a, b, c and d are in G.P. show that
.

Find x and y, if 2$\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$

The derivative of ${\tan }^{-1}\left(\frac{\sin x-\cos x}{\sin x+\cos x}\right),$ with respect to $\frac{x}{2},$ where $(x\in (0,\frac{\pi }{2}))$ is:

Find the adjoint of the given matrix.

$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

If the coefficient of x in ${(x^2+\frac{\lambda }{x})}^5$ is 270, then $\lambda =$

Question 76

One or more outcomes of an experiment make an event ?

Which of the following limit is equal to 0?

Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done ?

Verify the Rolle's theorem for $f\left(x\right)=x(x-1{)}^{2}in[0,1]$

If $\underset{0}{\overset{\pi }{\int }}\frac{dx}{a-\cos x}=\frac{\pi }{\sqrt{a^2-1}}$, then the value of $\underset{0}{\overset{\pi }{\int }}\frac{dx}{(\sqrt{10}-\cos x{)}^3}$ is equal to (where $|a|>1$)

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that :

(i) one is red and two arc white

(ii) two are blue and one is red

(iii) one is red.

Construct
a 2 ×
2 matrix,,
whose elements are given by:

(i)

(ii)

(iii)

Given
examples of two functions f: N → N and g:
N → N such that gof is onto but f
is not onto.

(Hint:
Consider f(x) = x + 1 and

The number of terms which are identical in the sequence $2,5,8,11,\dots \text{upto}60\text{terms}$ and $3,5,7,9,\dots \text{upto}50\text{terms}$, is

$\int e^x\left[\frac{x^3+x+1}{(1+x^2{)}^{3/2}}\right]dx$ is equal to

If $3x+5y+17=0$ is polar for the circle $x^2+y^2+4x+6y+9=0$, then the pole is

The range of $f\left(x\right)=|x|+5$ is

The value of integral $\int \sqrt{\frac{x-2}{x-3}}dx$ is equal to

(Where $C$ is integration constant)

The value of integral $\underset{0}{\overset{\pi /2}{\int }}\frac{\sin x-\cos x}{1+\sin x\cos x}dx$ is

In
the matrix,
write:

(i) The
order of the matrix (ii) The number of elements,

(iii) Write
the elements a₁₃,
a₂₁,
a₃₃,
a₂₄,
a₂₃

Solve the equation of x,y, z and t, if $2\left[\begin{array}{cc}x& z\\ y& t\end{array}\right]+3\left[\begin{array}{cc}1& -1\\ 0& 2\end{array}\right]=3\left[\begin{array}{cc}3& 5\\ 4& 6\end{array}\right]$

Write the total number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}.$

$\overrightarrow{C}$ is the sum of two vectors $\overrightarrow{A}and\overrightarrow{B}$ and $\overrightarrow{D}$ is the cross product of vectors $\overrightarrow{A}and\overrightarrow{B}$.

If $\overrightarrow{a},\overrightarrow{b},$ and $\overrightarrow{c}$ are unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}+2\overrightarrow{c}=\overrightarrow{0},$ then $|\overrightarrow{a}\times \overrightarrow{c}|$ is equal to :

The value of $\underset{x\to 1}{lim}\frac{1+\ln x-x}{x^2-1}$ is