List of practice Questions

The [H\(^+\)] of 0.1 N acetic acid solution is $1.33 \times 10^{-3}$. The pH of the solution (correct to two decimal places) is ..........

The positive root of the equation $x^4 + x^2 - 2 = 0$ is ...........

$\displaystyle \int_{0}^{1} x\,dx + \int_{1}^{2} (2-x)\,dx = ...........$

One gram of radioactive nuclei with a half-life of 300 days is kept in an open container. The weight of nuclei remaining after 900 days (correct to 1 decimal place) is .............. mg.

Two sources P and Q produce electromagnetic waves of wavelengths $\lambda$ and $2\lambda$, respectively. Source P ejects a photon with maximum kinetic energy 4.0 eV from a metal with work function 2.0 eV. The maximum kinetic energy (eV) of a photon ejected by source Q from the same metal is .............

The population of a bacterial culture increases from one thousand to one billion in five hours. The doubling time of the culture (correct to 1 decimal place) is ............ min.

A linear DNA contains five restriction sites for EcoRI and three restriction sites for BamHI. The number of fragments that will be generated after digestion with EcoRI is .............

The electric field and capacitance of a capacitor in the absence of dielectric material are $E$ and $C$, respectively. When the capacitor is filled with a dielectric material, the electric field and capacitance become $E'$ and $C'$, respectively. Which of the following is(are) correct?

Antigen and antibody interaction is shown by the following scheme
\[ \text{Ab} + \text{Ag} \; \xrightleftharpoons[k_{-1}]{k_{1}} \; \text{Ab-Ag} \] Where Ab is antibody, Ag is antigen and Ab–Ag is antigen–antibody complex. The values of $k_{1}$ and $k_{-1}$ are $5 \times 10^{5}\ \mu\mathrm{M}^{-1}\mathrm{s}^{-1}$ and $2 \times 10^{-2}\ \mathrm{s}^{-1}$ respectively. The dissociation constant for the complex is .............. nM.

The elements with atomic numbers 19, 37 and 55

Fehling’s solution

Which of the following point(s) lies(lie) on the plane $2x + 3y + z = 6$?

Kinetic theory of an ideal gas is based upon the following assumption(s)

Which of the following organs are correctly paired with their function?

The $\Delta G^\circ$ for homolactic fermentation converting glucose to lactate is –196 kJ mol$^{-1}$. If $\Delta G^\circ$ for the formation of ATP is +30.5 kJ mol$^{-1}$, then

Bacterial plasmid genes of non-chromosomal origin are associated with

Two inductors P and Q having inductance ratio 1:2 are connected in parallel in an electric circuit. The energy stored in the inductors P and Q are in the ratio

A body X of mass $M$ moving with velocity $v$ hits a stationary body Y of mass $m$. If $M \gg m$ and X moves with velocity $v'$ after the collision, then the velocity of Y after an elastic collision is

The cells involved in allergic reactions and containing surface receptors of IgE antibodies and histamine are

Which of the following is(are) INCORRECT in the regulation of the trp operon?

If one of the diameters of a circle has end points $(2,0)$ and $(4,0)$, then the equation of that circle is

If $P = \{1, 2, -1, 3\}$, $Q = \{0, 4, 1, 3\}$ and $R = \{1, 6, 7\}$, then $P \cap (Q \cup R)$ =

The position of a particle along the y-axis is $y = P t^4 + Q$. For dimensional consistency, the dimension of $P$ in terms of length [L] and time [T] is

In metal–carbonyl complexes, the $\pi$-back bonding is

If $u(x)$ and $v(x)$ are differentiable at $x=0$, and if $u(0)=5$, $u'(0) = -3$, $v(0) = -1$ and $v'(0) = 2$, then the value of $\dfrac{d}{dx}\left(uv + \frac{u}{v}\right)$ at $x = 0$ is