List of practice Questions

Two identical conducting spheres with negligible volume have 2.1 nC and –0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ________ $\times$ 10⁻⁹ N. [Given : $4\pi\epsilon_0 = \frac{1}{9 \times 10^9}$ SI unit]

Which of the following reaction/s will not give \(p-\) aminoazobenzene?

If an emitter current is changed by $4 mA ,$ the collector current changes by $3.5 mA$. The value of $\beta$ will be

Four identical particles of equal masses $1 kg$ made to move along the circumference of a circle of radius $1 m$ under the action of their own mutual gravitational attraction. The speed of each particle will be :

Given below are two statements : Two photons having equal linear momenta have equal wavelengths. If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.

Let $R =\{( P , Q ) | P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of (1,-1) is the set:

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be _________ Hz.

Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equations
\(x+y+z=5\)
\(x+2y+3z=\mu\)
\(x+3y+\lambda z=1\)
is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is __________ N.
(take g=10 ms\(^{-2}\))
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An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is \(0.9\) and that of the second unit is \(0.8\). The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is \(p\), then \(98p\) is equal to \dots\dots.

A free electron of 2.6 eV energy collides with a \(H^+\) ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (\(h = 6.6 \times 10^{-34}\) J s)

The sum of first 4 terms of a G.P. is 65/12 and sum of their reciprocals is 65/18. If product of first 3 terms is 1 and the 3rd term is α, then 2α is _________

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m/s.]

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

According to Bohr's atomic theory :- (A) Kinetic energy of electron is $\propto \frac{ Z ^{2}}{ n ^{2}}$. (B) The product of velocity (v) of electron and principal quantum number (n), 'vn' $\propto Z ^{2}$. (C) Frequency of revolution of electron in an orbit is $\propto \frac{ Z ^{3}}{ n ^{3}}$. (D) Coulombic force of attraction on the electron is $\propto \frac{ Z ^{3}}{ n ^{4}}$. Choose the most appropriate answer from the options given below:

Complete combustion of $1.80 g$ of an oxygen containing compound $\left( C _{ x } H _{ y } O _{2}\right)$ gave $2.64 g$ of $CO _{2}$ and $1.08 g$ of $H _{2} O$. The percentage of oxygen in the organic compound is:

Out of the following, which type of interaction is responsible for the stabilisation of $\alpha$ -helix structure of proteins?

(A) $HOCl + H _{2} O _{2} \rightarrow H _{3} O ^{+}+ Cl ^{-}+ O _{2}$
(B) $I _{2}+ H _{2} O _{2}+2 OH ^{-} \rightarrow 2 I ^{-}+2 H _{2} O + O _{2}$
Choose the correct option.

Which of the following equation depicts the oxidizing nature of $H _{2} O _{2} ?$

Given below are two statements : Statement I : Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame. Statement II : Cuprous metaborate is obtained by heating boric anhydride and copper sulphate in a non-luminous flame. In the light of the above statements, choose the most appropriate answer from the options given below.