List of practice Questions

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17 0C. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of N₂ = 28.0 u).

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at – 20 °C ? (atomic mass of Ar = 39.9 u, of He = 4.0 u).

A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball ?

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules ? Is the root mean square speed of molecules the same in the three cases? If not, in which case is v_rms the largest ?

Estimate the average thermal energy of a helium atom at (i) room temperature (27 °C), (ii) the temperature on the surface of the Sun (6000 K), (iii) the temperature of 10 million kelvin (the typical core temperature in the case of a star).

The ceiling of a long hall is 25 $\text m$ high. What is the maximum horizontal distance that a ball thrown with a speed of 40$\text m \;\text s^{-1}$ can go without hitting the ceiling of the hall ?

An air bubble of volume 1.0 cm³ rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C ?

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m³ at a temperature of 27 °C and 1 atm pressure.

An oxygen cylinder of volume 30 litre has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol^–1 K^–1, molecular mass of O₂ = 32 u).

A police van moving on a highway with a speed of 30 $\text {km}\;\text h^{-1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 $\text {km}\;\text h^{-1}$. If the muzzle speed of the bullet is 150 $\text {m}\;\text s^{-1}$, with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

The inequality $\dfrac{2x − 1}{3} ≥\dfrac{3x − 2}{4} −\dfrac{(2 − x)}{5}$ holds for $x $ belonging to

Show how will you synthesize:(i) 1-phenyl ethanol from a suitable alkene.
(ii) cyclohexyl methanol using an alkyl halide by an SN₂ reaction.
(iii) pentane-1-ol using a suitable alkyl halide?

Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.(ii) 5 pencils and 7 pens together cost Rs50, whereas 7 pencils and 5 pens together cost Rs46. Find the cost of one pencil and that of one pen.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i)$\dfrac{1}{4} , 1$ (ii) $\sqrt 2 , \dfrac{1}{3}$ (iii) $0, \sqrt5$ (iv) $1, 1$ (v) $-\dfrac{1}{4} ,\dfrac{1}{4}$(vi) $4, 1$

Show that the points (5, –1, 1), (7, – 4, 7), (1 – 6, 10) and (–1, – 3, 4) are the vertices of a rhombus.

Find the following integral: $\int (2x^2+e^x)dx$

If $\frac{2}{11}$ is the probability of an event, what is the probability of the event ‘not A’

A coin is tossed twice, what is the probability that atleast one tail occurs?