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


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8 Questions MCQ Test Maths 35 Years JEE Main & Advanced Past year Papers | 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 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers 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 2022 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.
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Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 1

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

The expression is equal to (1980)

Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 2

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

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

The standard deviation of 17 numbers is zero. Then  (1980)

Detailed Solution for Test: Single Correct MCQs: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced - Question 4

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

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

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

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

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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