Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2013MathematicsSets and Relations

For an integer n let S _ n = n +1, n +2, , n +18 . Which of the following is true for all n 10 ?

Options

  1. AS_ n has a multiple of 19
  2. BS_ n has a prime
  3. CS ₀^ n has at least four multiples of 5
  4. DS_ n ^ n has at most six primes

Correct answer

D. S_ n ^ n has at most six primes

Step-by-step solution

n+1, n+2, n+18 (A) False, if n=19 (C) False if n =15 16 to 33 20,25,30 only three multiples of 5 (D) no. of odd integers in S_ n =9 every third odd integer is multiple of 3 so maximum prime no. =6 .

Practice Sets and Relations on Quantrex Academy →

More from Sets and Relations

Let A and B be two subsets of = 1, 2, 3, -------, 44, 45 such that A = x: x is divisible by 3 and 4 B = x: x is a perfect square number Then n(B - A) equals 2026Given the sets A = 1,2,3 ; B = 2,3,5 and C = 4,5,6 identify Which of the following statements is incorrect . 2026If A = x : x is the first three odd numbers B = 2x + 3 : 0 x true 2026The set expression A (B (A' B')) is equivalent to 2026Let C be the set of all the circles in a plane. If R = (C₁, C₂) C C C₁ and C₂ intersect , then which of the following statements is TRUE? 2026If A = a, b, c, d, e, f , then the number of subsets of A which contains at least 2 elements is 2026If A = 1, 2, 3, 4, , 10 , then the number of non-empty subsets of A containing only even number is 2026If n(A) = 2 and the number of relations from set A to set B is 1024 , then n(B) is 2026 Full Sets and Relations list All KVPY PYQs