List of practice Questions

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).

If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = \(\frac{3}{7}\) AB and P lies on the line segment AB.

Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B ?

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)

Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units?

If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).

Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

Find the coordinates of the points of trisection of the line segment joining (4, − 1) and (− 2, − 3).

Express the following in the scientific notation:
(i) 0.0048
(ii) 234,000
(iii) 8008
(iv) 500.0
(v) 6.0012

What do you mean by significant figures?

What is the SI unit of mass? How is it defined?

Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below:
\(1\text{Pa} = 1\text{N m}^{–2} \)
If mass of air at sea level is \(1034\, \text{g cm}^{–2}\), calculate the pressure in pascal.

If the density of methanol is \(0.793\, \text{kg L}^{–1}\), what is its volume needed for making 2.5 L of its 0.25 M solution?

In three moles of ethane \((\text{C}_2\text{H}_6)\), calculate the following:
(i) Number of moles of carbon atoms.
(ii) Number of moles of hydrogen atoms.
(iii) Number of molecules of ethane.

A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range : α\(_{steel}\)= 1.20 × 10\(^{-5}\) K\(^{-1}\).

Calculate the atomic mass (average) of chlorine using the following data:
% Natural Abundance Molar Mass
\(^{35}\text{Cl}\) 75.77 34.9689
\(^{37}\text{Cl}\) 24.23 36.9659

A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is 27.0 °C ? Coefficient of linear expansion of steel = 1.20 × 10\(^{-5}\) K\(^{-1}\).

How much copper can be obtained from 100 g of copper sulphate \((\text{CuSO}_4)\)?

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made :

Temperature	Pressure thermometer A	Pressure thermometer B
Triple-point of water	1.250 × 10\(^5\) Pa	0.200 × 10\(^5\) Pa
Normal melting point of sulphur	1.797× 10\(^5\) Pa	0.287 × 10\(^5\) Pa

What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B?
What do you think is the reason behind the slight difference in answers of thermometers A and B ? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?