Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2008 › Q57
2 marksMathematics › Sets, relations and functions › Sets and set operationsHardabout 4 min

DSE 2008 Question 57: Sets, relations and functions

For each positive integer a=1,2,3,…a=1,2,3,\ldotsa=1,2,3,…, let SaS_{a}Sa​ be the set of points on the curve y=1/xay=1/x^{a}y=1/xa for all positive real x. Then the intersection ⋂a=1∞Sa\bigcap_{a=1}^{\infty}S_{a}⋂a=1∞​Sa​ is

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

For each positive integer a=1,2,3,…, let Sₐ be the set of points on the curve y=1/x^a for all positive real x. Then the intersection ⋂ₐ₌₁^∞Sₐ is (A) a set with infinitely many points (B) a set having a single point (C) a set having exactly 2 points (D) a set having more than 2, but a finite number of points

Also written as: For each positive integer a=1,2,3,..., let S_a be the set of points on the curve y=1/x^a for all positive real x. Then the intersection intersection_(a=1)^(inf)S_a is

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on Sets and set operations, part of Sets, relations and functions in Mathematics.

Unions, intersections, complements and differences of sets, and the identities that connect them.

TestStop has 25 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q26For S₁, S₂ ⊂ ℝ define S₁ - S₂ = {x ∈ S₁, x ∉ S₂}. Let P = {x ∈ ℝ: x² - 2x - 3 ≤ 0} and Q = {x ∈ ℝ: log₅(1 +…
Practise Sets, relations and functionsMore on Sets and set operations

Similar questions from other papers

  • CUET-PG 2023 Shift 1 · Q46Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): Assertion (A): The inverse of y = f(x) = e^x exists for all x…
  • CUET-PG 2023 Shift 2 · Q61The inverse of a function: x = √(3y+9) is
  • UGC-NET 2023 · Q55Which of the following are correct in the case of the theory of sets? A. (AUB')n(A'UC)n(BUC') = (AnBnC)U(AUBUC). B. (AUB')n(A'UC)n(BUC') = (AnBnC)U(AUBUC)'. C. AU(BnC)…
  • CUET-PG 2022 · Q45For the set A = {3, 4}, find Power Set P(A)
  • IIT JAM 2022 · Q13Let f:[0,∞)→ℝ be defined by f(x) = (x+1)/(x+2) for all x in the domain. Then f is

Question from the DSE 2008 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.