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Mathematics - Basic of Mathematics

Practise 20 JEE Main previous year questions on Basic of Mathematics, compiled from papers spanning 2002 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Basic of Mathematics has been asked in 10 of the 25 years of JEE Main papers analysed (2002–2026), with 20 questions in all. 40% of them were easy, 50% moderate and 10% tough. Most of its questions came from 2021, with 5 questions that year. In the last three years (2024–2026) it had 2 questions across 49 papers, about 0 per paper.

The chapter's 2 topics are not weighted equally: Inequalities (11 questions, 55%) and Logarithm (9 questions, 45%) have been asked the most. Inequalities has also led over the last five years, with 5 questions. Inequalities has produced the most tough questions (2).

  1. 1The sum of squares of all the real solutions of the equation is equal to ________.08 Apr, 2026 (E)Logarithm
  2. 2If the set of all solutions of is , then is equal to:04 Apr, 2026 (M)Inequalities
  3. 3The number of the real solutions of the equation: is24 Jan, 2026 (M)Inequalities
  4. 4The product of all solutions of the equation , is :22 Jan, 2025 (M)Logarithm
  5. 5The number of integral solution x of log x + 7 2 x - 7 2 x - 3 2 0 is11 Apr, 2023 (M)Inequalities
  6. 6Let a , b , c be the three distinct positive real numbers such that 2 a log e a = b c log e b and b log e 2 = a log e c Then 6 a + 5 b c is 10 Apr, 2023 (M)Logarithm
  7. 7If the solution of the equation log cos x cot x + 4 log sin x tan x = 1 , x 0 , 2 is sin - 1 + 2 , where , are integers, then + is equal to:30 Jan, 2023 (M)Logarithm
  8. 8Let S = x - 6 , 3 - - 2 , 2 : x + 3 - 1 x - 2 0 and T = x Z : x 2 - 7 x + 9 0 . Then the number of elements in S T is28 Jul, 2022 (E)Inequalities
  9. 9Let A = x R : x + 1 2 and B = x R : x - 1 2 . Then which one the following statements is NOT true?25 Jun, 2022 (E)Inequalities
  10. 10The sum of the roots of the equation, x + 1 - 2 log 2 3 + 2 x + 2 log 4 10 - 2 - x = 0 , is :31 Aug, 2021 (E)Logarithm
  11. 11If A = { x R : | x - 2 | 1 } , B = x R : x 2 - 3 1 , C = { x R : | x - 4 | 2 } and Z is the set of all integers, then the number of subsets 27 Aug, 2021 (M)Inequalities
  12. 12The number of solutions of the equation log ( x + 1 ) 2 x 2 + 7 x + 5 + log ( 2 x + 5 ) ( x + 1 ) 2 - 4 = 0 , x 0 , is20 Jul, 2021 (E)Logarithm
  13. 13If for x 0 , 2 , log 10 sin x + log 10 cos x = - 1 and log 10 sin x + cos x = 1 2 log 10 n - 1 , n 0 , then the value of n is equal to :16 Mar, 2021 (M)Logarithm
  14. 14The number of solutions of the equation log 4 x - 1 = log 2 x - 3 is ______.26 Feb, 2021 (M)Logarithm
  15. 15The number of distinct solutions of the equation, log 1 2 sin x = 2 - log 1 2 cos x in the interval 0 , 2 , is ________09 Jan, 2020 (M)Logarithm
  16. 16If A = x R : x 2 and B = x R : x - 2 3 ; then09 Jan, 2020 (E)Inequalities
  17. 17Let S = x R : x 0 2 x - 3 + x x - 6 + 6 = 0 . Then S :08 Apr, 2018Inequalities
  18. 18The least integral value of such that , satisfies :23 Apr, 2013 (Online)Inequalities
  19. 19Statement - 1: For every natural number . Statement : For every natural number .2008Inequalities
  20. 20If are distinct real numbers and then is2002Inequalities

Frequently Asked Questions

1.How many questions are available for Basic of Mathematics?

This chapter includes 20 questions compiled from JEE Main papers spanning 2002 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Basic of Mathematics chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Basic of Mathematics an important chapter for JEE Main Mathematics?

Basic of Mathematics has appeared in 10 of the 25 years of JEE Main papers covered here, with 20 questions across 20 papers - about one per paper it appears in.

4.What is the difficulty level of Basic of Mathematics questions in JEE Main?

Of the 20 questions analysed for this chapter, 40% are easy, 50% moderate and 10% tough. 2021 had the most, with 5 questions.

5.Which topics in Basic of Mathematics should I focus on?

These topics have carried the most weightage in Basic of Mathematics:

  • Inequalities - 11 questions (55%)
  • Logarithm - 9 questions (45%)
  • Inequalities has produced the most tough questions (2).
6.Is Basic of Mathematics's weightage in JEE Main going up or down?

Across all 20 papers analysed, Basic of Mathematics has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.