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Mathematics - Binomial Theorem

Practise 16 KVPY previous year questions on Binomial Theorem, compiled from papers spanning 2010 to 2020. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KVPY tests.

  1. 1Let r be the remainder when 2021 2020 is divided by 2020 2 . Then r lies between2020 (SA)
  2. 2Let M = 2 30 - 2 15 + 1 , and M 2 be expressed in base 2 . The number of 1 s in this base 2 representation of M 2 is2020 (SB/SX)
  3. 3The least value of a natural number such that , where , is19 Nov, 2017 (SA)
  4. 4Consider the following statements. For any integer , I. is never divisible by 17 . II. is never divisible by 17 . Then19 Nov, 2017 (SA)
  5. 5Among the inequalities below, which ones are true for all natural numbers n greater than 1000 ? I. II. III. IV.19 Nov, 2017 (SB/SX)
  6. 6Let be an integer and define a polynomial where are integers. Suppose we know that . If , then19 Nov, 2017 (SB/SX)
  7. 7The number of all 2 -digit numbers such that is equal to the sum of the square of digit in its tens place and the cube of the digit in units2016 (SA)
  8. 8The number of digits in the decimal expansion of is2016 (SA)
  9. 9Let and let Then2015 (SB/SX)
  10. 10The coefficient of in is -2012 (SB/SX)
  11. 11The number of distinct prime divisors of the number is2011 (SA)
  12. 12If , where is a real variable and is a positive integer, then the value of is2011 (SB/SX)
  13. 13Arrange the expion of in decreasing powers of . Suppose the coefficient of the first three terms form an arithmetic progression. Then the nu2010 (SB/SX)
  14. 14The number of natural numbers in the interval for which the polynomial divides the polynomial is-2010 (SB/SX)
  15. 15Let and for . Then the remainder obtained dividing aco ob by 11 is-2010 (SB/SX)
  16. 16Suppose are positive integers such that The value of the expression is-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 16 questions compiled from KVPY papers spanning 2010 to 2020.

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

These are KVPY questions specifically for the Binomial Theorem chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Binomial Theorem an important chapter for KVPY Mathematics?

Binomial Theorem has appeared in 7 of the 11 years of KVPY papers covered here, with 16 questions across 10 papers - about 2 per paper it appears in.