List of practice Questions

In which one of the following reactions, rate constant has the unit mol L^-1 s^-1 ?

Let $y = y(x)$ be a solution curve of the differential equation $$(1 - x^2 y)\,dx = y\,dx + x\,dy.$$ If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$, then a value of $\alpha$ is:

When a 60 W electric heater is immersed in a gas for 100s in a constant volume container with adiabatic walls, the temperature of the gas rises by 5°C. The heat capacity of the given gas is_____J K^-1 (Nearest integer).

A metal crystallises in a body centered cubic lattice with the metallic radius \(\sqrt3 Å\). The volume of the unit cell in m³ is

If 5x+4y=83 and \(\frac{2x}{3y}=1\frac{1}{21}\) then the value of x²-y² is:

Match the column A (type of crystalline solid) with the column B (example for each type) :

A		B
P.	Molecular Solid	i.	SiC
Q.	Ionic Solid	ii.	Mg
R.	Metallic Solid	iii.	H2O
S.	Network Solid	iv.	MgO

Consider the trigonometric equation $ \tan(x) - \tan(y) = 0 $, where $x$ and $y$ are not odd multiples of $ \frac{\pi}{2} $. Then the solution of this equation is:

Dimerisation of solute molecules in low dielectric constant solvent is due to :

A 30% solution of hydrogen peroxide is

If 'a' stands for the edge length of the cubic systems - The ratio of radii in simple cubic, body centered cubic and face centered cubic unit cells is

What is the oxidation number of S in H₂S₂O₈ ?

Which one of the following gases converts haemoglobin into carboxy haemoglobin ?

Among the following :

The set which represents aromatic species is

IUPAC name of the compound is

The composition of water gas is

A pair of amphoteric oxides is

Temperature of 25 ºC in Fahrenheit and Kelvin scale respectively are

A mass $m$ is attached to two springs as shown in the figure. The spring constants of the two springs are $K_1$ and $K_2$. For the frictionless surface, the time period of oscillation of mass $m$ is:

A weak acid with pKa 5.9 and weak base with pKb 5.8 are mixed in equal proportions. pH of the resulting solution is

At 500 K, for a reversible reaction \(A_{2_{(g)}}+B_{2_{(g)}}⇌2AB_{(g)}\) in a closed container, K_C = 2 × 10^-5. In the presence of catalyst, the equilibrium is attaining 10 times faster. The equilibrium constant K_C in the presence of catalyst at the same temperature is

Find the value of  $$ \dfrac{\sin^6 15^\circ + \sin^6 75^\circ + 6 \sin^2 15^\circ + \sin^2 75^\circ}{\sin^4 15^\circ + \sin^4 75^\circ + 5 \sin^2 15^\circ \sin^2 75^\circ} $$ 

Which of the following statement is INCORRECT ?

Let $P$ be a square matrix such that $P^2 = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^\alpha + P^\beta = \gamma I - 29P$ and $P^\alpha - P^\beta = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to:

In the situation shown in the diagram, magnitude of q << | Q | and r>>a. The net force on the free charge -q and net torque on it about O at the instant shown are respectively
[ p = 2aQ is the dipole moment ]

Which of the following monomers form biodegradable polymers ?