List of practice Questions

The number of common terms in the progressions 4, 9, 14, 19, ...,up to 25th term and 3, 6, 9, 12, ..., up to 37th term is:

On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed ?

Identify major product "X" formed in the following reaction :

Compare the energies of following sets of quantum numbers for multielectron system.
(A) n = 4, 1 = 1
(B) n= 4, l = 2
(C) n = 3, l = 1
(D) n = 3, l = 2
(E) n = 4, 1 = 0
Choose the correct answer from the options given below :

What is the structure of C ?

The electronic configuration of Cu(II) is 3d⁹ whereas that of Cu(I) is 3d¹⁰. Which of the following is correct ?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The total number of geometrical isomers shown by [Co(en)$_2$Cl$_2$]$^+$ complex ion is three.
Reason (R): [Co(en)$_2$Cl$_2$]$^+$ complex ion has an octahedral geometry.
In the light of the above statements, choose the most appropriate answer from the options given below:

The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is :

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Both rhombic and monoclinic sulphur exist as S$_8$ while oxygen exists as O$_2$.
{Reason (R): Oxygen forms $p\pi$-$p\pi$ multiple bonds with itself and other elements having small size and high electronegativity like C, N, which is not possible for sulphur.
In the light of the above statements, choose the most appropriate answer from the options given below:

For the given compounds, the correct order of increasing $pK_a$ value :

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): SN$_2$ reaction of C$_6$H$_5$CH$_2$Br occurs more readily than the SN$_2$ reaction of CH$_3$CH$_2$Br.
Reason (R): The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring.
In the light of the above statements, choose the most appropriate answer from the options given below:

Relative stability of the contributing structures is :

Given below are two statements:
Statement (I): The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of electron gain enthalpy consideration from other atoms in the molecule.
Statement (II): $p\pi$-$p\pi$ bond formation is more prevalent in second period elements over other periods.
In the light of the above statements, choose the {most appropriate answer from the options given below:

In which one of the following pairs the central atoms exhibit sp$^2$ hybridization?

The F$^-$ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula:

If $ A $ denotes the sum of all the coefficients in the expansion of $ (1 - 3x + 10x^2)^n $ and $ B $ denotes the sum of all the coefficients in the expansion of $ (1 + x^2)^n $, then:

In the following sequence of reaction, the major products B and C respectively are :

If $ (a, b) $ be the orthocenter of the triangle whose vertices are $ (1, 2) $, $ (2, 3) $, and $ (3, 1) $, and $ I_1 = \int_a^b x \sin(4x - x^2) dx $, $ I_2 = \int_a^b \sin(4x - x^2) dx $, then $ 36 \frac{I_1}{I_2} $ is equal to:

Let $ x = x(t) $ and $ y = y(t) $ be solutions of the differential equations $ \frac{dx}{dt} + ax = 0 $ and $ \frac{dy}{dt} + by = 0 $ respectively, $ a, b \in \mathbb{R} $. Given $ x(0) = 2 $, $ y(0) = 1 $, and $ 3y(1) = 2x(1) $, the value of t for which $ x(t) = y(t) $, is:

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is:

The molar conductivity for electrolytes A and B are plotted against C^1/2as shown below. Electrolytes A and B respectively are :

Methods used for purification of organic compounds are based on :

While measuring the diameter of a wire using a screw gauge, the following readings were noted: Main scale reading is $ 1 \, \text{mm} $ and circular scale reading is equal to 42 divisions. Pitch of the screw gauge is $ 1 \, \text{mm} $, and it has 100 divisions on the circular scale. The diameter of the wire is $ \frac{x}{50} \, \text{mm} $. The value of $ x $ is:

The distance of the point $ (7, -2, 11) $ from the line $ \frac{x - 6}{1} = \frac{y - 4}{0} = \frac{z - 8}{3} $ along the line $ \frac{x - 5}{2} = \frac{y - 1}{-3} = \frac{z - 5}{6} $, is: