List of practice Questions

f : R $\to$ R and g : [0, $\infty$) $\to$ R is defined by f(x) = $x^2$ and g(x) = $\sqrt{x}$ . Which one of the following is not true?

A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is :

A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be :
(Take g = 10 m/s\(^2\))

An organic compound $X\left( C _{7} H _{7} Cl \right)$ when reacted with $KCN / C _{2} H _{5} OH$ gave major product $Y . Z$ is formed when $Y$ is reduced with $LiAlH _{4}$. What are $Y$ and $Z$ ?

An emf of $15\, V$ is applied to a circuit containing $5\, H$ inductance and $10\, \Omega$ resistance. The ratio of currents at time $t = \infty$ and $t = 1\, s$ is

At $T( K )$, copper (atomic mass $=63.5\, u$ ) has fcc unit cell structure with edge length of $x \mathring {A}$. What is the approximate density of $Cu$ in $g \,cm ^{-3}$ at that temperature? $\left(N_{A}=6.0 \times 10^{23} mol ^{-1}\right)$

Chlorine oxidises sulphur dioxide in the presence of water to give an oxyacid $A$. Chlorine also oxidises iodine in the presence of water to give an oxyacid $B$. The oxidation states of $S$ and $I$ in $A$ and $B$ are respectively

$CuSO_4$ solution is electrolysed for $15$ minutes to deposit $0.4725\, g$ of copper at the cathode. The current in amperes requited is (Faraday = $96.500 \,C\,mol^{-1}$. atomic weight of copper = $63$)

For a particle executing simple harmonic motion, the displacement-time $(x - t)$ graph is as shown in the figure. The acceleration of the particle at $t = \frac{4}{3} s$ is

$\ce{H_2C = CH_2 + O_2 ->[Aqueous \; medium] Ch_3CHO}$ What is the catalyst used in the above green reaction?

Identify the set of acidic oxides.

Identify $Z$ in the following sequence of reactions. $\ce{ C_2 H_4 Br_2 ->[(i) Alc.KOH][(ii) NaNH_2] X ->[Red\, hot][Fe \,tube\, 873 K] Y ->[(CH_3CO)_2 O/\Delta][Anhyd. AlCl_3] Z}$

If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$

In the first order thermal decomposition of $C _{2} H _{5} I (g) \longrightarrow C _{2} H _{4}(g)+ HI (g)$, the reactant in the beginning exerts a pressure of $2$ bar in a closed vessel at $600 \,K$. If the partial pressure of the reactant is $0.1$ bar after $1000$ minutes at the same temperature the rate constant in $\min ^{-1}$ is $(\log 2=0.3010)$

In a nuclear reactor the activity of a radioactive substance is $2000 / s$. If the mean life of the products is $50$ minutes, then in the steady power generation, the number of radio nuclides is

In a $p$ - type semiconductor the donor level is at $50 \,meV$ above the valence band. To produce one electron, the maximum wavelength of light photon required is (Planck's constant, $h=6.6 \times 10^{-34} \,Js$ and speed of light in vacuum, $c=3 \times 10^{8} \,ms ^{-1}$ )

Potential energy of a body of mass $1\, kg$ free to move along X-axis is given by $U(x) = \left( \frac{x^2}{2} - x \right) J .$ If the total mechanical energy of the body is $2\, J$. then the maximum speed of the body is (Assume only conservative force acts on the body)

Sodium nitrite is reacted with $H_2SO_4$ to form $NaHSO_4, HNO_3$, water and $X$. Gold is dissolved in aqua-regia to form water, $AuCl^{-}_4$ and $Y. X$ and $Y$ are respectively

The average translational kinetic energy of a molecule in a gas becomes equal to $0.69\, eV$ at a temperature about [Boltzmann constant = $1.38 \times 10^{-23} \; J \; K^{-1}$]

The copper (II) halide which does not exist is

The electric field intensity at a point on the axis of an electric dipole in ah is $4 \; NC^{-1}$. Then the electric field intensity at a point on the equitorial hue which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant $4$ is

The non-biodegradable waste formed in fertilizer industries is

The number of moles of solute present in the solutions of $I, II$ and $III$ is respectively I. $500 \,mL$ of $0.2\, M\, NaOH$ II. $200 \,mL$ of $0.1 \,N \,H _{2} SO _{4}$ II. $6 g$ of urea in $1 \,kg$ of water

The pair of metals refined by "vapour phase refining" is

The velocity of an object moving in a straight line path is given as a function of time by $v = 6t - 3t^2$. where $v$ is in $ms^{-1} , t $ is in $s$. The average velocity of the object between $t = 0$ and $t = 2s$ is