List of practice Questions

If A and B are two events such that \(P(A)=\frac1{3},P(B)=\frac1{5}\) and \(P(A∪B)=\frac1{2}\) then \(P(\frac{A}{B'}) + P(\frac{B}{A'})\) is equal to

A common tangent T to the curves
\(C_1:\frac{x^2}{4}+\frac{y^2}{9} = 1\)
and
\(C_2:\frac{x^2}{4^2}\frac{-y^2}{143} = 1\)
does not pass through the fourth quadrant. If T touches C₁ at (x₁, y₁) and C₂ at (x₂, y₂), then |2x₁ + x₂| is equal to ______.

Match List I with List II.

List-I	List-II
A. Benzene sulphonyl chloride	I. Test for primary amines
B. Hoffmann bromamide reaction	II. Anti Saytzeff
C. Carbylamine reaction	III. Hinsberg reagent
D. Hoffmann orientation	IV. Known reaction of Isocyamates

Choose the correct answer from the options given below:

20 mL of 0.02 M K₂Cr₂O₇ solution is used for the titration of 10 mL of Fe²⁺ solution in the acidic medium. The molarity of Fe²⁺ solution is ______×10^–2 M. (Nearest integer)

2NO + 2H₂ → N₂ + 2H₂O
The above reaction has been studied at 800 °C. The related data is given in the table below.
The order of the reaction with respect to NO is ___.

2sin(\(\frac{\pi}{22}\))sin(\(\frac{3\pi}{22}\))sin(\(\frac{5\pi}{22}\))sin(\(\frac{7\pi}{22}\))sin(\(\frac{9\pi}{22}\)) is equal to

Amongst the following, the number of oxide(s) which are paramagnetic in nature is
Na₂O, KO₂, NO₂, N₂O, ClO₂, NO, SO₂, Cl₂O

The molar heat capacity for an ideal gas at constant pressure is 20.785 J K^–1 mol^–1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is _____. (Nearest integer)
(Given : R = 8.314 JK-1mol-1).

According to MO theory, number of species/ions from the following having identical bond order is ___.
CN-, NO+, O2, O+2, O2+2

At 310 K, the solubility of CaF₂ in water is 2.34 ×10^–3 g/100 mL. The solubility product of CaF₂ is _____ × 10^–8 (mol/L)³.
(Given molar mass : CaF₂ = 78 g mol^–1).

The conductivity of a solution of complex with formula CoCl₃(NH₃)₄ corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is ______.

In the titration of KMnO₄ and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is _____.

Optical activity of an enantiomeric mixture is +12.6° and the specific rotation of (+) isomer is +30°. The optical purity is _______%.

Let \(\vec a\)=\(\hat i\)−\(\hat j\)+2\(\hat k\) and \(\vec b\) be a vector such that
\(\vec a\)×\(\vec b\)=2\(\hat i\)−\(\hat k\) and \(\vec a\)⋅\(\vec b\)=3.
Then the projection of \(\vec b\) on the vector \(\vec a\)−\(\vec b\) is :

Let \(\overset{→}a = \hat{i}- \hat{J}+2\hat{K}\) and \(\overset{→}b\) be a vector such that \(\overset{→}a×\overset{→}b=2\hat{i}−\hat{k} \) and \(\overset{→}a⋅\overset{→}b=3\). Then the projection of \(\overset{→}b\) on the vector \(\overset{→}a-\overset{→}b\) is :

In the following reaction,
the % yield for reaction I is 60% and that of reaction II is 50%. The overall yield of the complete reaction is _______%. [Nearest integer].