Boolean algebra forms the mathematical foundation of digital electronics and computer systems. Understanding Boolean algebra and logic gates is crucial for analyzing and designing digital circuits, which are at the heart of modern computing devices. 1. Introduction to Boolean Algebra Definition: Boolean algebra is a branch of algebra that deals with binary variables and logical …

Boolean Algebra and Logic Gates Read More »

Q1. “Khilafat” movement subsided because of the (a) Concessions given to Muslims by the British (b) Amity achieved between Congress and Muslim League (c) Accession of Kamal Pasha on the throne of Turkey (d) None of the above (UPSC Prelims 1979) Answer: (c) Accession of Kamal Pasha on the throne of Turkey Explanation: The Khilafat …

UPSC Prelims PYQ | Khilafat Movement Read More »

Q1. The chemical name for urea is (a) Aneurin (b) Chloroethene (c) Carbamide (d) None of these (UPSC Prelims 1987) Answer: (c) Carbamide Explanation: Urea, a nitrogen-rich compound used in fertilizers, is chemically known as carbamide. It is synthesized from ammonia and carbon dioxide, and plays a key role in agriculture and medicine. Q2. Azolla …

UPSC Prelims PYQ | Fertilizers and Pesticides Read More »

Mathematics 1. Evaluate the expression: $\csc 10^\circ – \sqrt{3} \sec 10^\circ$ a) 8 b) 6 c) 4 d) 2 (JEE Main 2026 | Exam Date: 21.01.2026 | Shift I) Answer: (c) 4 Solution: Convert the terms into sine and cosine: $$\frac{1}{\sin 10^\circ} – \frac{\sqrt{3}}{\cos 10^\circ} = \frac{\cos 10^\circ – \sqrt{3} \sin 10^\circ}{\sin 10^\circ \cos 10^\circ}$$ …

JEE Main 2026 Solved Question Paper | Exam Date 21.01.2026 | Shift I Read More »

1. The sum of all roots of the equation $(x – 1)^2 – 5|x – 1| + 6 = 0$ is: a) 4 b) 1 c) 5 d) 3 (JEE Main 2026 | Exam Date: 21.01.2026 | Shift I) Answer: (a) 4 Solution: Let $|x – 1| = t$. The equation becomes $t^2 – 5t …

JEE Main PYQ | Quadratic Equation Read More »

1. Evaluate the expression: $\csc 10^\circ – \sqrt{3} \sec 10^\circ$ a) 8 b) 6 c) 4 d) 2 Answer: (c) 4 Solution: Convert the terms into sine and cosine: $$\frac{1}{\sin 10^\circ} – \frac{\sqrt{3}}{\cos 10^\circ} = \frac{\cos 10^\circ – \sqrt{3} \sin 10^\circ}{\sin 10^\circ \cos 10^\circ}$$ Multiply and divide the numerator by 2: $$\frac{2\left(\frac{1}{2}\cos 10^\circ – \frac{\sqrt{3}}{2}\sin …

JEE Main PYQ | Trigonometry Read More »

JEE Main Exam Solved Question Paper (Year-wise) JEE Main 2026 Solved Question Paper | Exam Date: 21.01.2026 | Shift I JEE Main 2026 Solved Question Paper | Exam Date: 22.01.2026 | Shift I JEE (Main) 2026 | Phase-2 | Exam Date: 02-04-2026 | Morning Shift JEE Main Exam Solved Question Paper (Topic-wise) Physics | Current …

JEE Main Exam Read More »

Q1. “Monalisa” – the famous painting was recently in the news because (a) Its fifth centenary was celebrated (b) The colour of the painting changed due to chemical preservatives (c) It was auctioned at high prices (d) It was stolen from the museum where it was placed (UPSC Prelims 1987) Answer: (b) The colour of …

UPSC Prelims PYQ | Painting Read More »

Q1. India is a federal state because of (a) Dual Citizenship prevalent here (b) Dual judiciary (c) Share of power between the Centre and the States (d) Written Constitution (UPSC Prelims 1987) Answer: (c) Share of power between the Centre and the States Explanation: India’s federal structure is defined by the division of powers between …

UPSC Prelims PYQ | Federal Structure of India Read More »