List of practice Questions

Consider a weak base $B$ of $pK_b = 5.699$. $x$ mL of $0.02$ M HCl and $y$ mL of $0.02$ M weak base $B$ are mixed to make $100$ mL of a buffer of pH $=9$ at $25^\circ\text{C}$. The values of $x$ and $y$ respectively are

Regarding the hydrides of group 15 elements $EH_3$ $(E = N, P, As, Sb)$, select the correct statement(s):
[A.] The stability of hydrides decreases down the group.
[B.] The basicity of hydrides decreases down the group.
[C.] The reducing character increases down the group.
[D.] The boiling point increases down the group. Choose the correct answer:

At temperature $T$ K, $2$ moles of liquid $A$ and $3$ moles of liquid $B$ are mixed. The vapour pressure of the ideal solution formed is $320$ mm Hg. At this stage, one mole of $A$ and one mole of $B$ are added to the solution. The vapour pressure is now measured as $328.6$ mm Hg. The vapour pressures (in mm Hg) of pure $A$ and pure $B$ respectively are:

Consider the reaction: \[ \text{Ph–CH=CH}_2 \xrightarrow[\text{peroxide}]{\text{HBr}} \text{Product} \] Which of the following statements are correct?
[A.] The reaction proceeds through a more stable radical intermediate.
[B.] The role of peroxide is to generate $\mathrm{H^\bullet}$ radical.
[C.] During this reaction, benzene is formed as a byproduct.
[D.] $1$-Bromo-$2$-phenylethane is formed as a minor product.
[E.] The same reaction in absence of peroxide proceeds via a carbocation intermediate. Choose the correct answer.

The figures below show: Which of the following points in Figure 2 most accurately represents the nodal surface shown in Figure 1?

Given below are the four isomeric compounds $P, Q, R, S$:
$P$: Aromatic compound containing an $-\mathrm{OH}$ group
$Q$: Aromatic compound containing an $-\mathrm{CHO}$ group (aldehyde)
$R$: Aromatic compound containing a ketone group
$S$: Aromatic compound containing a ketone group Identify the correct statements from below:
[A.] $Q, R$ and $S$ will give precipitate with $2,4$-DNP.
[B.] $P$ and $Q$ will give positive Baeyer’s test.
[C.] $Q$ and $R$ will give sooty flame.
[D.] $R$ and $S$ will give yellow precipitate with $I_2/\mathrm{NaOH}$.
[E.] $Q$ alone will deposit silver with Tollens’ reagent. Choose the correct option.

In the given pentapeptide, find out an essential amino acid ($Y$) and the sequence present in the pentapeptide.
Choose the correct answer from the options given below:

500 mL of $1.2$ M KI solution is mixed with 500 mL of $0.2$ M $ \mathrm{KMnO_4} $ solution in basic medium. The liberated iodine is titrated with standard $0.1$ M $ \mathrm{Na_2S_2O_3} $ solution in the presence of starch indicator till the blue colour disappears. The volume (in L) of $ \mathrm{Na_2S_2O_3} $ consumed is ________ (nearest integer).

Consider the dissociation equilibrium of the following weak acid: \[ \mathrm{HA \rightleftharpoons H^+(aq) + A^-(aq)} \] If the $pK_a$ of the acid is $4$, then the pH of a $10\ \text{mM}$ HA solution is ________ (Nearest integer). (Given: The degree of dissociation can be neglected with respect to unity)

$X$ is the number of geometrical isomers exhibited by $[\mathrm{Pt(NH_3)(H_2O)BrCl}]$.
$Y$ is the number of optically inactive isomer(s) exhibited by $[\mathrm{CrCl_2(ox)_2}]^{3-}$.
$Z$ is the number of geometrical isomers exhibited by $[\mathrm{Co(NH_3)_3(NO_2)_3}]$. Find the value of $X + Y + Z$. }

The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16\,\mu\text{T}$. The magnetic field at a distance $x=\sqrt{3}R$ on its axis from the centre is ____ $\mu\text{T}$.

Let $z=(1+i)(1+2i)(1+3i)\cdots(1+ni)$, where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to

Let $(h,k)$ lie on the circle $C:x^2+y^2=4$ and the point $(2h+1,\,3k+2)$ lie on an ellipse with eccentricity $e$. Then the value of $\dfrac{5}{e^2}$ is equal to

If $f(x)$ satisfies the relation \[ f(x)=e^x+\int_0^1 (y+x e^x)f(y)\,dy, \] then $e+f(0)$ is equal to

Let $S$ be a set of $5$ elements and $P(S)$ denote the power set of $S$. Let $E$ be the event of choosing an ordered pair $(A,B)$ from $P(S)\times P(S)$ such that $A\cap B=\varnothing$. If the probability of the event $E$ is $\dfrac{3^p}{2^q}$, where $p,q\in\mathbb{N}$, then $p+q$ is equal to

The binding energy for the following nuclear reactions are expressed in MeV.
\[ {}^{3}_{2}\text{He} + {}^{1}_{0}\text{n} \rightarrow {}^{4}_{2}\text{He} + 20 \text{ MeV} \] \[ {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} \rightarrow {}^{5}_{2}\text{He} - 0.9 \text{ MeV} \] If $ X_3, X_4, X_5 $ denote the stability of $ {}^{3}_{2}\text{He}, {}^{4}_{2}\text{He} $ and $ {}^{5}_{2}\text{He} $, respectively, then the correct order is:

The velocity ($v$) – distance ($x$) graph is shown in the figure. Which graph represents acceleration ($a$) versus distance ($x$) variation of this system?

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $ \frac{5}{x} $. The value of $ x $ is ________.

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector is increased by 8 times, the intensity will

Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance ($u$) and image distance ($v$) using same convex lens having power $+5$ D as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement.

In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_0$. The distance between two slits is $2\,\text{mm}$. The distance of screen from slits is $10\,\text{m}$. The wavelength of light is $6000\,\text{\AA}$. The intensity of light on the screen in front of one of the slits is ________.

A soap bubble of surface tension $0.04\,\text{N/m}$ is blown to a diameter of $7\,\text{cm}$. If $(15000 - x)\,\mu\text{J}$ of work is done in blowing it further to make its diameter $14\,\text{cm}$ $(\pi = 22/7)$, then the value of $x$ is ________.

In a meter bridge experiment to determine the value of unknown resistance, first the resistances $2\,\Omega$ and $3\,\Omega$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance $l$ cm from the left end. Now, when an unknown resistance $x\,\Omega$ is connected in parallel to $3\,\Omega$, the null point is shifted by $10\,\text{cm}$ to the right. The value of $x$ is ________ $\Omega$.

In the group analysis of cations, Ba$^{2+}$ & Ca$^{2+}$ are precipitated respectively as

``X'' is an oxoanion of the lightest element of group 17 (in the periodic table). The metal is in +6 oxidation state in ``X''. The color of the potassium salt of X is