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Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Each question contains statements given in two columns, which have to be matched. The statements in Column-I are labelled A, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in ColumnII. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example :

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s then the correct darkening of bubbles will look like the given.

Q. Match the statements given in Column-I with the intervals/union of intervals given in Column-II.             (2011) 

Column-I                                                                                                                        Column-II

(A) The set Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE: z is a complex number, |z| = 1 z ≠ ± 1}is                          (p) (-∞, - 1) ∪ (1,∞)

(B) The domain of the function f (x) =Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                                        (q) (-∞, - 0) ∪ (0,∞)

(C) If  Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEthen the set   Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                                 (r) [2, ∞)

                                                                                                                                        (s) (-∞, -1]U[1,∞) 

(D) If f (x) = x3/2 (3x – 10), x ≥ 0 then f (x) is increasing in                                         (t) (-∞, 0]∪ [2,∞)

Ans. Sol. A → (s), B → (t), C → (r) D → (r)

et z = x + iy where and x2 +  y2 = 1 and x ≠ ± 1

Then ReMatrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE = ReMatrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEMatrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

where Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE ∴ A  → s

(B) For the domain of f (x) Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

We should have

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Let 3x = t thenMatrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEand  Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEand  Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Also t = 3x can not be – ve
∴ t ∈ (0, 3) ∪ [9,∞) and t ∈ (0,1] ∪ [3,∞)
Þ x ∈ (-∞,1) ∪ [2,∞) and x ∈ (-∞, 0] ∪ (1,∞)
Combining the two, we get x ∈ (-∞, 0] ∪ [2,∞)

∴ B → t

(C) 

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ C → r

(D) f (x) = x3/2 (3x - 10),x ≥ 0

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

For f(x) to be increasing f'(x) ≥ 0

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematica | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE but x ≥ 0 ⇒ x ≥ 2

∴ f (x) is incresing on [2,∞) ∴ D → r.

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