Explore topic-wise InterviewSolutions in Current Affairs.

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$. If $p_k=(\alpha {)}^k+(\beta {)}^k,k\ge 1$, then which one of the following statements is not true ?

The coefficient of$a^3{b}^4{c}^5$ in $(bc+ca+ab{)}^6$ is

Find $(5\sqrt{5}+11{)}^{2n+1}$ - $(5\sqrt{5}-11{)}^{2n+1}$

There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them, there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,$ $i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.



The probability that, on the examination day, the student $S_1$ gets the previously allotted seat $R_1$, and $NONE$ of the remaining students gets the seat previously allotted to him/her is

The condition that the line $\frac{x}{p}+\frac{y}{p}=1$ o be tangent to $\frac{x^z}{a^z}+\frac{y^z}{b^z}=1$ is

The value of $si{n}^{-1}\left\{cot(si{n}^{-1}\sqrt{\left(\frac{2-\sqrt{3}}{4}\right)}+co{s}^{-1}\frac{\sqrt{12}}{4}+se{c}^{-1}\sqrt{2})\right\}$ is:

If (x
+ iy)³ = u + iv, then show that.

Let $f$ be a differentiable function such that
$f\left(1\right)=2$ and $f^{\prime }\left(x\right)=f\left(x\right)$ for all $x\in R$. If $h\left(x\right)=f\left(f\right(x\left)\right)$, then $h^{\prime }\left(1\right)$ is equal to :

Diameter of the circle given by $|(z-\alpha )/(z-\beta )|=k,k\ne 1$ , where $\alpha ,\beta$ are fixed points and $z$ is varying point in argand plane is

$If\alpha ϵ(0,\frac{\pi }{2}),then\sqrt{x^2+x+\frac{ta{n}^2\alpha }{\sqrt{x^2+x}}}$ is always greater than or equal to

The value of ${\sin }^{-1}\left(\sin \left(\frac{17\pi }{4}\right)\right)+{\cos }^{-1}\left(\cos \left(\frac{27\pi }{5}\right)\right)+{\tan }^{-1}\left(\tan \left(\frac{37\pi }{6}\right)\right)$ is

Find the integrals of the functions.
$\int \frac{1}{sinxco{s}^{3}x}dx.$

Considering truth table for $p\to \sim (p\wedge \sim q)$ as follows,
$\begin{array}{ccc}p& q& p\to \sim (p\wedge \sim q)\\ T& T& A\\ T& F& B\\ F& T& C\\ F& F& D\end{array}$
The truth value will be false for which among the following

Equation of the circle inscribed in $|x-2|+|y-5|=4$ is

If one real root of the quadratic equation $81x^2+kx+256=0$ is cube of the other root, then a value of $k$ is :

The coefficient of $x^5$ in the expansion of ${(1+x)}^{21}+{(1+x)}^{22}+\dots +{(1+x)}^{30}$

What does the frequency of an observation in a data set mean? Which observation in the following data has the maximum frequency and which has the minimum frequency?

1, 1, 2, 4, 3, 2, 1, 2, 2, 4

The integrating factor of the differential equation $\frac{dy}{dx}=ytanx-y^{2}secx$ is

[MP PET 1995; Pb. CET 2002]

If the equation, $x^2+bx+45=0(b\in R)$ has conjugate complex roots and they satisfy $|z+1|=2\sqrt{10}$, then:

If A + B + C = $\pi$, Prove that

cos 4A + cos 4B + cos 4C = -1 + 4 cos 2A cos 2B cos 2C.

(99)²is equivalent to

The equation of the tangent to the parabola $y^2=16x$ inclined at an angle of ${60}^{\circ }$ to the positive $x-$axis is

Prove the following by using the principle of mathematical induction for all n ∈ N:

Let $A=[a_{ij}{]}_{4\times 4}$ be a matrix such that $a_{ij}=\{\begin{array}{cc}2,& \text{if}i=j\\ 0,& \text{if}i\ne j\end{array}.$
Then the value of $\left\{\frac{det(adj\left(adjA\right))}{7}\right\}$ is
$\left(\right\{.\}$ represents the fractional part function $)$

If given $g\left(x\right)={\int }_2^{x^2}\frac{1}{ln(1+t^2)}dtthenfind{g}^{\prime }\left(\sqrt{2}\right)$ .

Area under the curve $y=\sqrt{3x+4}$between x=0 and x=4, is

If $\alpha ,\beta$ are roots of the $4x^2+3x+7=0$, then the value of

$\frac{1}{\alpha }+\frac{1}{\beta }$is

The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 which passes through (4,6) is

Total number of six-digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

If $5+55+555+\cdots \text{to}n\text{terms}=\frac{5}{81}({10}^{n+1}+x+yn)$, then the value of $y-x$ is

Write the value of $\frac{d}{dx}\left(x|x|\right).$