Question 1 :
If <em>X</em> and <em>Y</em> are two sets, then <em>X</em> ∩ (<em>Y</em> ∪ <em>X</em>)′ equals

Question 2 :
Let <em>A</em> and <em>B</em> have 3 and 6 elements respectively. What can be the minimum number of elements in <em>A</em> ∪ <em>B</em>?

Question 4 :
<p>A relation between two persons is defined as follows:</p> <p>aRb ⇔ <em>a</em> and <em>b</em> born in different months. Then, <em>R</em> is</p>

Question 5 :
The relation “is a factor of” on the set <em>N</em> of all natural numbers is not

Question 6 :
Let <em>E</em> = {1, 2, 3, 4} and <em>F</em> = {1, 2}. Then the number of onto functions from <em>E</em> to <em>F</em> is

Question 7 :
If <em>A</em> = {1, 2, 3, 4}, then the number of subsets of set <em>A</em> containing element 3, is

Question 9 :
The relation <em>R</em> defined in <em>N</em> as <em>a</em> <em>R</em> <em>b</em> ⇔ <em>b</em> is divisible by <em>a</em> is

Question 10 :
If <em>A</em> and <em>B</em> are two sets, then <em>A</em> ∩ (<em>A</em> ∪ <em>B</em>) equals

Question 11 :
Statement-1: The range of {tex} f ( x ) = \frac { e ^ { x } - e ^ { - x } } { e ^ { x } + e ^ { - x } } {/tex} defined on {tex} [ 0 , \infty ) {/tex} is {tex} [ 0 , \infty ) {/tex} Statement- 2: Range of {tex} e ^ { x } {/tex} defined {tex} \mathbf { R } {/tex} is {tex} [ 0 , \infty ) {/tex}

Question 12 :
Let f₁ : (–∞, 0) → R, f₂ : (–∞, 0) → R and f₃ : (1, ∞) → R be functions defined by<br>f₁(x) = e^x – <img style='object-fit:contain' style="vertical-align: middle" alt="Image not present" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f47666a277e3d5ccb76941f">, f₂(x) = <img style='object-fit:contain' style="vertical-align: middle" alt="Image not present" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f47666a277e3d5ccb76941f"> + |x| and f₃(x) = e^1–x – <img style='object-fit:contain' style="vertical-align: middle" alt="Image not present" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f47666b11a01e5cb9495bf5">. Then choose the correct option(s)

Question 13 :
Let {tex} g ( x + y ) , g ( x ) \cdot g ( y ) {/tex} and {tex} g ( x - y ) {/tex} are in A.P. For all {tex} x , y {/tex} and {tex} g ( 0 ) \neq 0 . {/tex} Then

Question 15 :
Statement-1: The period of the function{tex} f(x) = sin \frac{\pi}{4} [x] + cos \frac{\pi}{2} x + cot\frac{\pi}{4} [x] is 24 <br>Statement-2: The period of sinx, cosx is 2{tex}\pi{/tex} and period (f(x) + g(x)) = 1.c.m (period of f(x), period of g(x))

Question 16 :
The set of all values of {tex} { } ^ { \prime } a ^ { \prime } ( a > 0 ) {/tex} for which the function {tex} f: [ - 3,3 ] \rightarrow \mathbf { R } {/tex} defined by {tex} f ( x ) = {/tex} {tex} \left[ x ^ { 2 } / a \right] \operatorname { cosec } a x + \sec a x {/tex} is an even function contains

Question 17 :
The domain of the function <em>f</em>(<em>x</em>) = log_{3 + <em>x</em>}(<em>x</em>² − 1) is

Question 18 :
If <em>f</em>(<em>x</em>+<em>f</em>(<em>y</em>)) = <em>f</em>(<em>x</em>) + <em>y</em> ∀ <em>x</em>, <em>y</em> ∈ <em>R</em> and <em>f</em>(0) = 1, then the value of <em>f</em>(7) is

Question 19 :
Let {tex} f ( x ) = \cos ( \pi / x ) {/tex} and {tex} D _ { + } = \{ x: f ( x ) > 0 \} . {/tex} Then {tex} D _+{/tex} contains

Question 20 :
If [cos^− 1<em>x</em>] + [cos^− 1<em>x</em>] = 0, where [.] denotes the greatest integer function, then the complete set of values of <em>x</em> is

Question 21 :
From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is

Question 22 :
If <em>f</em>(<em>x</em>+1) + <em>f</em>(<em>x</em>−1) = 2<em>f</em>(<em>x</em>) and <em>f</em>(0) = 0, then <em>f</em>(<em>n</em>), <em>n</em> ∈ <em>N</em>, is

Question 23 :
The values of <em>b</em> and <em>c</em> for which the identity <em>f</em>(<em>x</em>+1) − <em>f</em>(<em>x</em>) = 8<em>x</em> + 3 is satisfied, where <em>f</em>(<em>x</em>) = <em>b</em><em>x</em>² + cx + <em>d</em>, are

Question 24 :
Let <em>f</em>(<em>x</em>) = sin <em>x</em> and <em>g</em>(<em>x</em>) = log_<em>e</em>|<em>x</em>|. If the ranges of the composition function fo<em>g</em> and <em>g</em>of are <em>R</em>₁ and <em>R</em>₂, respectively, then

Question 25 :
If <em>A</em> = {1, 2, 3}, <em>B</em> = {<em>a</em>, <em>b</em>}, then <em>A</em> × <em>B</em> mapped <em>A</em> to <em>B</em>is