List of practice Questions

Injury localized to the hypothalamus would most likely disrupt

The resistances in the two arms of the meter bridge are $5\, \Omega$ and $R\, \Omega$ respectively. When the resistance $R$ is shunted with an equal resistance, the new balance point is at $1.6l_1$. The resistance $R$ is

A conducting sphere of radius $R$ is given a charge $Q$. The electric potential and the electric field at the centre of the sphere respectively are

Fruit colour in squash is an example of

What is the percentage of free space in body centered cubic unit cell?

A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector $ ( \vec{ v_{av}})$ from t = 0 to t = 5 s is .

When the gas expands with temperature using the relation $ V=KT^{2/3} $ for the temperature change of $ 40\,K, $ the work done is

Which quantity is transmitted with propagation of longitudinal waves through a medium?

Mass number of an atom is the sum of

Which of the following relation is called mirror equation?

A car moving on a straight road covers $ 1/3 $ of the distance with $ 25\,km/h $ and rest with $ 75\,km/h $ . The average speed is

All substances that conduct electricity in aqueous solutions are called?

Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $ (2,3,5) $ and $ (5,9,7), $ parallel to the co-ordinate planes?

For transistor the value of $ \beta $ is $50$ then, the value of $\alpha$ is

Light from a point source in air falls on a spherical glass surface ( $ n=1.67 $ and radius of curvature $ =25\,cm $ ). The distance of the light source from the glass surface is $ 95\,cm $ . At what position, the image is formed?

In acidic medium, $H_2O_2 $ changes $ Cr_2O_7^{2-} $ to $CrO_5 $ which has two (-O-O-) bonds. Oxidation state of Cr in $CrO_5 $ is

Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then

Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals

Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is

The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is

The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is

The hydrides of the first elements in groups $15 - 17$, namely $NH_3, H_2O$ and $HF$ respectively show abnormally high values for melting and boiling points. This is due to

The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is

To observe an elevation of boiling point of $0.05^?C$, the amount of solute (Mol. $Wt. = 100$) to be added to $100\, g$ of water $(K_b=0.5)$ is

Metal ion responsible for the Minamata disease is