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JEE Exam  >  JEE Tests  >  35 Years Chapter wise Previous Year Solved Papers for JEE  >  Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - JEE MCQ

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - JEE MCQ


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8 Questions MCQ Test 35 Years Chapter wise Previous Year Solved Papers for JEE - Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced for JEE 2024 is part of 35 Years Chapter wise Previous Year Solved Papers for JEE preparation. The Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced questions and answers have been prepared according to the JEE exam syllabus.The Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced below.
Solutions of Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced questions in English are available as part of our 35 Years Chapter wise Previous Year Solved Papers for JEE for JEE & Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced solutions in Hindi for 35 Years Chapter wise Previous Year Solved Papers for JEE course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced | 8 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study 35 Years Chapter wise Previous Year Solved Papers for JEE for JEE Exam | Download free PDF with solutions
Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 1
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If X and Y are two sets, then X ∩ (X∪Y)c equals. (1979)

Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 1

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 2
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The expression is equal to (1980)

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Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 3
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Select the correct alternative in each of the following. Indicate your choice by the appropriate letter only.Let S be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation of the resulting number is (1980)

Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 3

If each of n observations is multiplied by a constant C, the standard deviation also gets multiplied by C.

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 4
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The standard deviation of 17 numbers is zero. Then  (1980)
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If s. d. = 0, statements like (a) and (b) can not be given.

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 5
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Consider  any set of 201 observations x1, x2, ....x200,  x201.It is given that x1< x2<....< x200 <x201. Then  the mean deviation of this set of observations about  a point k is minimum when k equals (1981 - 2 Marks)
Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 5

Given that x1 < x2 < x3 < ....< x 201

∴ Median of the given observation  th items

= 101th item = x101

Now, deviations will be minimum if taken from the median

∴ Mean deviation will be min if k = x101.

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 6
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If x1, x2,..............., xn are any real numbers and n is any postive integer, then (1982 - 2 Marks)
Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 6

If any of the inequations hold, it must hold for any real numbers x1, x2, ..... xn and any n∈N.

∴ let x1 = 1, x2 = 2, x3 = 3; n = 3 then we can check none of the inequalities (a), (b) or (c) are satisfied.

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 7
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Let S={1, 2, 3, 4} . The total number of unordered pairs of disjoint subsets of S is equal to (2010)
Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 7

S = {1, 2, 3, 4} Let P and Q be disjoint subsets of S
Now for any element a ∈ s, following cases are possible a ∈ P and a∉Q, a ∉P and a ∈ Q, a ∉P and a∉Q
⇒ For every element there are three option
∴ Total options = 34 = 81
Here P ≠Q except when P =Q = φ
∴ 80 ordered pairs (P, Q) are there for which P ≠ Q.
Hence total number of unordered pairs of disjoint subsets ==41

Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 8
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Let P = {θ : sinθ – cosθ = cosθ} and Q = {θ : sinθ + cosθ = sinθ} be two sets. Then (2011)
Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 8

P = {θ : sinθ - cosθ = 2 cosθ}
sinθ = ( 2 + 1) cosθ , tanθ = 2 +1
Q = {θ : sinθ + cosθ = 2 sinθ} cosθ = ( 2 -1) sinθ or  tanθ = 2 +1
∴   P = Q

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