List of practice Questions

Calculate the mass of sodium acetate $(\text{CH}_3\text{COONa})$ required to make 500 mL of 0.375 molar aqueous solution. Molar mass of sodium acetate is $82.0245\, \text{g mol}^{–1}.$

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of $\frac 14$ m and a tread of $\frac 12$ m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace.

Calculate the mass per cent of different elements present in sodium sulphate $(\text{Na}_2\text{SO}_4)$.

Calculate the molar mass of the following:
(i) $\text{H}_2\text{O}$ (ii) $\text{CO}_2$ (iii) $\text{CH}_4$

Answer the following :

The triple-point of water is a standard fixed point in modern thermometry. Why ? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale) ?
There were two fixed points in the original Celsius scale as mentioned above which were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?
The absolute temperature (Kelvin scale) T is related to the temperature $t_c$ on the Celsius scale by
$t_c$ = T – 273.15
Why do we have 273.15 in this relation, and not 273.16 ?
What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale ?

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law :
R = $R_0$ [1 + α (T – $T_0$)]
The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω ?

Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between $T_A \space and \space T_B$ ?

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.

Which term of the AP: 121, 117, 113, ..... is its first negative term?

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.

A triangle ABC is circumscribed a circle of radius 4 cm — **Fig. 10.14**

Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?

A family uses 8 kW of power.
(a) Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square meter. If 20% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?
(b) Compare this area to that of the roof of a typical house.

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
(a) How much work does she do against the gravitational force ?
(b) Fat supplies 3.8 × 10$^7$J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

If $y = \cot^{-1} \, (x^2)$, then the value of $ \frac{dy}{dx}$ is equal to

For the following APs, write the first term and the common difference:
(i) 3, 1, − 1, − 3 …
(ii) − 5, − 1, 3, 7 …
(iii) $\frac{1}{3}, \frac{5}{3},\frac{9}{3},\frac{13}{3}$ ,…
(iv) 0.6, 1.7, 2.8, 3.9 …

In which of the following situations, does the list of numbers involved make as arithmetic progression and why?
(1) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.
(2) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.
(3) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre.
(4) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum.

Write first four terms of the A.P. when the first term a and the common difference d are given as follows
(1) a = 10, d = 10
(2) a = − 2, d = 0
(3) a = 4, d = − 3
(4) a = − 1 d =$\frac{1}{2}$
(5) a = − 1.25, d = − 0.25

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article. [Use $\pi =\frac{22 }{7}$]