List of practice Questions

If a cone of height h and a sphere have same radii r and same volume, then r:h will be:

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$ in the fig, then $\angle POA$ is equal to :

If the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is $30^\circ$, then the height of the tower is :

If the perimeter of a circle is equal to that of a square, then find the ratio of their areas.

The length of an arc of a circle of radius 12 cm is $10\pi$. Find the central angle of this arc.

To draw a pair of tangents to a circle which are inclined to each other at an angle of $ 50^\circ $, it is required to draw tangents at end points of those two radii of the circle. What should be the angle between these two radii?

If $\sec(7^\circ - 2\alpha) = \csc(5\alpha - 7^\circ)$, then the value of $\alpha$ is:

The angle of elevation of a 15 m high tower from a point 15 m away from its foot is:

(a) Explain the meaning of the statement ‘electric charge of a body is quantised’.
(b) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?

Using the standard electrode potentials given below ,predict if the reaction between the following is feasible:
(a) Fe³⁺(aq) and I^- (aq)
(b) Ag⁺ (aq) and Cu(s)
(c) Fe³⁺ (aq) and Cu(s)
(d) Ag(s) and Fe³⁺(aq)
(e) Br₂(aq) and Fe²⁺(aq)

The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

“When a people are enslaved, as long as they hold fast to their language it is as if they had the key to their prison.”
Can you think of examples in history where a conquered people had their language taken away from them or had a language imposed on them?

List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
(ii) B = {x: x is an $\frac{-1}{2} < x <\frac{ 9}{2}$ integer,}
(iii) C = {x: x is an $x^2 ≤ 4 $ integer,
(iv) D = {x: x is a letter in the word “LOYAL“}
(v) E = {x: x is a month of a year not having 31 days}
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.

Had he earned any money before that? In what way?

Figure shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.

Calculate the capacitance and the rate of charge of potential difference between the plates.
Obtain the displacement current across the plates.
Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.