List of practice Questions

“Under the British rule, India underwent systematic economic exploitation with its resources and wealth being diverted to Britain.” Justify the given statement with valid explanation.
What shows that Charley was clumsy and absent-minded? (The Third Level)
If the orthocentre of the triangle formed by the lines $ y = x + 1 $, $ y = 4x - 8 $, and $ y = mx + c $ is at $ (3, -1) $, then $ m - c $ is:
AB and CD are diameters of a circle with centre O and radius 7 cm. If \(\angle BOD = 30^\circ\), then find the area and perimeter of the shaded region.
Explain the role of public facilities for quality of life.
Analyze how Wells employs humour, rhyme, and exaggerated traits to not only entertain, but also educate readers about various wild animals. Explain.
(How to Tell Wild Animals)
Find the focal length of the plano-convex lens of refractive index 1.5 and radius of curvature 10 cm when it is immersed in a liquid of refractive index 1.25.
If $ \tan \theta + \cot \theta = 4 $, then find the value of $ \tan^3 \theta + \cot^3 \theta $.
"We have to use a planned and sustainable manner to conserve our minerals." Support the statement.

A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop

(ii) What is the probability that this defective smartphone was manufactured by company B?

Which part of the human brain is responsible for: 
(a) thinking 
(b) picking up a pencil 
(c) controlling blood pressure 
(d) controlling hunger

Convert Ethanal to But-2-enal

Consider the given figure and choose the correct option:

Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$

The output (Y) of the given logic implementation is similar to the output of an/a  …………. gate.

The current in a solenoid decreases steadily from 6 mA to 2 mA in 50 ms. If an average emf of 0.4 V is induced, find the self-inductance of the solenoid.

‘बाज़ार में कभी–कभी आवश्यकता ही शोषण का रूप धारण कर लेती है।’ — इस कथन को उदाहरण सहित ‘बाज़ार–दर्शन’ पाठ के आधार पर सिद्ध कीजिए। 
 

The pH of a solution is 3. What is the concentration of hydrogen ions in this solution?
A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.

‘चेखव सारे संसार के चहेते लेखक माने जाते हैं।’ – संयुक्त वाक्य में रूपांतरित कीजिए। 
 

(a) Find the point Q on the line \( \frac{2x + 4}{6} = \frac{y + 1}{2} = \frac{-2z + 6}{-4} \) at a distance of \( \frac{\sqrt{5}}{2} \) from the point \( P(1, 2, 3) \).
State the chemical property in each case on which the following uses of baking soda are based upon:
(i) As an antacid
(ii) As a constituent in making baking powder
(iii) In soda-acid fire extinguishers
A capacitor is charged by a battery to a potential difference \( V \). It is disconnected from the battery and connected across another identical uncharged capacitor. Calculate the ratio of total energy stored in the combination to the initial energy stored in the capacitor.
Identify and correct the error in the sentence taken from the article – ‘The Hidden Health Risks of Bread Consumption’:
Health experts worldwide are concerning about the surge in health problems.
Error Correction
Number of functions \( f: \{1, 2, \dots, 100\} \to \{0, 1\} \), that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to: