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 …
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 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 Exam Solved Question Paper (Topic-wise) Physics | Current and Electricity Capacitor Series and Parallel Circuits Mathematics Trigonometry Quadratic Equation
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 …
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 …
Q1. Deficit Financing means (a) Difference of total expenditure and income by revenue from all sources. (b) Government spends in excess of revenues so that a budget deficit is incurred which is financed by the borrowings. (c) Difference in borrowing and external and internal resources. (d) Capital expenditure on items of public construction, public enterprises …
Q1. Ilbert Bill was prepared for abolishing judicial disqualification based on racial distinction. The bill was vehemently criticised by the Europeans living in India. Who was the Governor-General at that time ? (a) Lord Ripon (b) Lord Dalhousie (c) Lord Curzon (d) Lord Chelmsford (UPSC Prelims 1987) Answer: (a) Lord Ripon Explanation: The Ilbert Bill …
Q1. ‘Ghadar party’ in U.S.A. was formed by (a) V. D. Savarkar (b) Lala Har Dayal (c) Swami Varma (d) Raja Pratap Singh (UPSC Prelims 1987) Answer: (b) Lala Har Dayal Explanation: The Ghadar Party, founded in 1913 in the U.S.A., was led by Lala Har Dayal to promote Indian independence through revolutionary activities. It …
Q1. Which of the following statements is not correct for economically underdeveloped countries ? (a) Involvement of a very little proportion of labour in primary occupations (b) Lower percentage of literacy (c) Mass unemployment (d) High birth rate Answer: (a) Involvement of a very little proportion of labour in primary occupations Explanation: In economically underdeveloped …
In 1924, a young French physicist named Louis de Broglie proposed one of the most revolutionary ideas in modern physics: if light could behave as both a wave and a particle, why couldn’t matter do the same? The Central Idea He proposed that every particle with momentum possesses a wavelength, now called the de …