List of practice Questions

Calcium crystallizes in an fcc lattice of unit cell length 5.56 Å and density 1.4848 g cm$^{-3}$. The percentage of Schottky defects (rounded off to one decimal place) in the crystal is ________.
(Given: Atomic mass of Ca = 40 g mol$^{-1}$, $N_A = 6.022 \times 10^{23}$ mol$^{-1}$)

A buffer solution is prepared by mixing 0.3 M NH$_3$ and 0.1 M NH$_4$NO$_3$. If $K_b$ of NH$_3$ is $1.6 \times 10^{-5}$ at 25°C, then the pH (rounded off to one decimal place) of the buffer solution at 25°C is ________.

The dissociation constant of a weak monoprotic acid is $1.6 \times 10^{-5}$ and its molar conductance at infinite dilution is $360.5 \times 10^{-4}$ mho m$^2$ mol$^{-1}$. For 0.01 M solution of this acid, the specific conductance is $n \times 10^{-2}$ mho m$^{-1}$. The value of $n$ (rounded off to two decimal places) is ________.

The functional group(s) in reducing sugar that tests positive with Tollen’s reagent is (are)

The CORRECT Maxwell relation(s) derived from the fundamental equations of thermodynamics is (are)

The total number of optically active isomers of dichloridobis(glycinato)cobalt(III) ion is ________.

The CORRECT statement(s) about the species is (are)

The complex(es) that show(s) Jahn–Teller distortion is (are)

The CORRECT statement(s) about sodium nitroprusside is (are)

The pigment responsible for red color in tomato has one functional group. The CORRECT statement(s) about this functional group is (are)

Hantzsch pyridine synthesis involves several steps. Some of those are

The volume correction factor for a non-ideal gas in terms of critical pressure ($p_c$), critical molar volume ($V_c$), critical temperature ($T_c$), and gas constant ($R$) is

The CORRECT statement regarding the molecules BF$_3$ and CH$_4$ is

Reaction of BCl$_3$ with NH$_4$Cl at 140 °C produces compound P. Further, P reacts with NaBH$_4$ to give a colorless liquid Q. The reaction of Q with H$_2$O at 100 °C produces compound R and a diatomic gas S. Among the following, the CORRECT statement is

The complex that does NOT obey the 18-electron rule is (Given: Atomic numbers of Ti, Mn, Ta and Ir are 22, 25, 73 and 77, respectively)

Hybridization of the central atoms in I$_3^-$, ClF$_3$ and SF$_4$, respectively, are

The decreasing order of C=C bond length in the following complexes is \[ \text{I: [Cl$_3$Pt(CH$_2$=CH$_2$)]}^- \quad \text{II: [Cl$_3$Pt(C(CN)$_2$=C(CN)$_2$)]}^- \quad \text{III: [Cl$_3$Pt(CF$_2$=CH$_2$)]}^- \quad \text{IV: [Cl$_3$Pt(CF$_2$=CF$_2$)]}^- \]

Two sets of quantum numbers with the same number of radial nodes are

A, B and C, a startup business, each investing rs. 20,000. After five months, A withdraw 5000. B rupees 4000 and C invested rupees 6000 more. At the end of the year, a total profit of rs 69900 was recorded. What is the share of B ?

The velocity of blood in a blood vessel of 2.0 cm radius is 30 cm/s. When the blood vessel bifurcates into 2 smaller vessels of radius 1.0 cm each, the velocity of blood in each of the smaller vessels is ______ cm/s. Assume vessel walls are rigid, and blood is incompressible.

The equation $\sin \frac{\theta}{2}\, (\sin \frac{\theta}{2} + \cos \frac{\theta}{2}) = \beta$ has a solution, where $\beta$ is a natural number. Then $\beta$ is ______.

A function $f : D \to \mathbb{R}$ is defined as $f(x) = \dfrac{x^2 + 1}{x^2 + x + 1}$ where $D \subseteq \mathbb{R}$ is the domain. The domain(s) on which the function $f(x)$ is one-to-one is/are