JEE Main Sets, Relations, Functions & Trigonometry – Topic Test

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Difficulty: 15 medium · 15 hard

Sets, Relations, Functions & Trigonometry MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

1. Q1. In a group of 100 people, 72 like tea and 65 like coffee. The least possible number of people who like both tea and coffee is:

   100 लोगों के समूह में, 72 लोग चाय पसंद करते हैं और 65 लोग कॉफी पसंद करते हैं। चाय और कॉफी दोनों पसंद करने वाले लोगों की न्यूनतम संभव संख्या है:

   • A. 35
   • B. 28
   • C. 37
   • D. 42
   Solution

   Since n(T ∪ C) ≤ 100, n(T ∩ C) = n(T) + n(C) − n(T ∪ C) ≥ 72 + 65 − 100 = 37, and this minimum is attainable.

   चूँकि n(T ∪ C) ≤ 100, अतः n(T ∩ C) = n(T) + n(C) − n(T ∪ C) ≥ 72 + 65 − 100 = 37, और यह न्यूनतम मान प्राप्त किया जा सकता है।

2. Q2. The domain of the real function f(x) = √(x − 1) + 1/√(5 − x) is:

   वास्तविक फलन f(x) = √(x − 1) + 1/√(5 − x) का प्रांत (domain) है:

   • A. [1, 5)
   • B. (1, 5]
   • C. (1, 5)
   • D. [1, 5]
   Solution

   The first term needs x − 1 ≥ 0, i.e. x ≥ 1, while the second needs 5 − x > 0 (strict, as it is in a denominator), i.e. x < 5, giving [1, 5).

   पहले पद के लिए x − 1 ≥ 0, अर्थात् x ≥ 1 आवश्यक है, जबकि दूसरे पद के लिए 5 − x > 0 (हर में होने के कारण कड़ाई से), अर्थात् x < 5 आवश्यक है, जिससे [1, 5) प्राप्त होता है।

3. Q3. Among the following functions from R to R, three share a common structural property while one does not. Which is the odd one out?

   R से R में निम्नलिखित फलनों में से, तीन एक समान संरचनात्मक गुणधर्म साझा करते हैं जबकि एक नहीं। कौन-सा भिन्न (odd one out) है?

   • A. f(x) = x|x|
   • B. f(x) = sin x
   • C. f(x) = x²
   • D. f(x) = x³
   Solution

   sin x, x³ and x|x| are all odd functions, whereas x² is an even function, making it the odd one out.

   sin x, x³ और x|x| सभी विषम फलन हैं, जबकि x² एक सम फलन है, जो इसे भिन्न बनाता है।

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