List of practice Questions

A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____ cm.
(Velocity of sound in air is 340 ms^–1)

A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ N.
(Take g = 10 ms^–2)

High purity (>99.95%) dihydrogen is obtained by

A car covers AB distance with first one-third at velocity v₁ ms^–1, second one-third at v₂ ms^–1 and last one-third at v₃ ms^–1. If v₃ = 3v₁, v₂ = 2v₁ and v₁ = 11 ms^–1then the average velocity of the car is ____ ms^–1.

The correct order of density is

\(lim_{n→∞} \frac1{2^n}(\frac1{\sqrt{1-1/2^n}} +\frac1{\sqrt{1-\frac2{2^n}}}+\frac1{\sqrt{1-\frac3{2^n}}}+...+\frac1{\sqrt{1-\frac{2^n-1}{2^n}}})\) is equal to

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].

Identify the solar cell characteristics from the following options :

For the below given cyclic hemiacetal (X), the correct pyranose structure is :

Projection of 2\(\hat i\)+4\(\hat j\)−2\(\hat k\) on \(\hat i\)+2\(\hat j\)−α\(\hat k\) is zero. Then, the value of α will be________.