List of practice Questions

Elastic strain energy of 10 J is stored in a loaded copper rod of cross-sectional area $2 times 10^{-4} m^2$ and length 0,2 in, Hie Young?? modulus for copper is 125 GPa. The load on the copper rod in kN is

Let $z_1$ and $z_2$ be complex numbers such that $z_1 \neq z_2$ and $| z_1| = | z_2 |$ . If Re $(z_1) > 0$ and $Im (z_2) < 0 $ ,then $\frac{z_1+ z_2}{z_1 - z_2}$ is

The least positive integer $n$ such that $\begin{pmatrix}\cos \frac{\pi}{4}&\sin \frac{\pi}{4}\\ -\sin \frac{\pi}{4}&\cos \frac{\pi}{4}\end{pmatrix} ^{n }$ is an identity matrix of order $2$ is

For $0 \leq p \leq 1$ and for any positive $a, b$ let $I(p) = (a + b)^p, J(p) = a^p + b^p$, then

Let $\vec{\alpha} . \vec{\beta} , \vec{\gamma}$ be three unit vectors such that $\vec{\alpha} . \vec{\beta} = \vec{\alpha} . \vec{\gamma} = 0 $ and the angle between $\vec{\beta}$ and $\vec{\gamma}$ is $30^{\circ}$ . Then $\vec{\alpha} $ is

A body is projected with a speed 'u? at an angle $'\theta'$ with the horizontal. The radius of curvature of the trajectory when it makes an angle $\left(\frac{\theta}{2} \right)$ with the horizontal is (g - acceleration due to gravity)

The solution of $\frac{dv}{dt} +\frac{k}{m}v = -g$ is

Amongst the elements with following electronic configurations, which one of them may have the highest ionization energy?

If $x > 0,$ the $ 1 + \frac{\log_{e^{2}}x}{1!} + \frac{\left(\log_{e^{2}}x\right)^{2}}{2!} + ....=$

Consider the equation of a parabola $y^2 + 4ax = 0$, where $a > 0$ which of the following is/are correct?

If the constraints in a linear programming problem are changed then

\(\int \frac{e^{x^2}\left(2x+x^{3}\right)}{\left(3+x^{2}\right)^{2}} dx\)  is equal to :

Following are colours shown by some alkaline earth metals in flame test. Which of the following are not correctly matched?

Number of solutions of equation $\sin 9 \theta=\sin \theta$ in the interval $[0,2 \pi]$ is

pH of a $0.1\, M$ monobasic acid is found to be $2$. Hence, its osmotic pressure at a given temperature $TK$ is

The rate constant of a reaction is $1.5 \times 10^{-3}$ at $25^{\circ} C$ and $2.1 \times 10^{-2}$ at $60^{\circ} C$. The activation energy is

NASDAQ is an acronym for

Which among the followlng Countries does not have veto power in the UN Security Council?

India is not the member of which of the following organizations?

Where is the headquarters of Organization of Petroleum Exportillg Countries (OPEC) situated?

Deodhar Trophy, Rohinton Baria Trophy and Sheesh Mahal Trophy are associated with___

Approximately what percentage of the total GDP is contributed by the agriculture sector of India?

Which of the following is a pharmaceutical company?

'Kananaskis' was the venue of the G-8 Summit that took place in 2002. This place is located in which of the following countries?

Which of the following represents the expansion of 'T' in C-DOT?