Exam (elaborations) jee

JEE (Advanced) 2024 Paper 2


SECTION 1 (Maximum Marks: 12)

• This section contains FOUR (04) questions.
• Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correct
answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −1 In all other cases.


Q.1 Considering only the principal values of the inverse trigonometric functions, the value of

 3  2 
tan  sin −1   − 2cos −1  
 5  5 
is

7 −7
(A) (B)
24 24
−5 5
(C) (D)
24 24




Q.2

Let S = ( x, y)   
: x  0, y  0, y 2  4 x, y 2  12 − 2 x and 3 y + 8 x  5 8 . If the area
of the region S is  2, then  is equal to

17 17 17 17
(A) (B) (C) (D)
2 3 4 5



Q.3 2
Let k  . If lim
x →0 +
(sin(sin kx) + cos x + x ) x = e6 , then the value of k is


(A) 1 (B) 2 (C) 3 (D) 4




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,JEE (Advanced) 2024 Paper 2

Q.4 Let f : → be a function defined by
 2  
 x sin  2  , if x  0,
f ( x) =  x 
 if x = 0.
 0,
Then which of the following statements is TRUE?

 1 
(A) f ( x) = 0 has infinitely many solutions in the interval  10 ,   .
10 
1 
(B) f ( x) = 0 has no solutions in the interval  ,   .
 
 1 
(C) The set of solutions of f ( x) = 0 in the interval  0,  is finite.
 1010 
 1 1
(D) f ( x) = 0 has more than 25 solutions in the interval  2 ,
 
.





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, JEE (Advanced) 2024 Paper 2


SECTION 2 (Maximum Marks: 12)

• This section contains THREE (03) questions.
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is (are) correct answer(s).
• For each question, choose the option(s) corresponding to (all) the correct answer(s).
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 ONLY if (all) the correct option(s) is(are) chosen;
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen;
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of
which are correct;
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option;
Zero Marks : 0 If unanswered;
Negative Marks : −2 In all other cases.
• For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct
answers, then
choosing ONLY (A), (B) and (D) will get +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2marks;
choosing ONLY (B) and (D) will get +2 marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option(s) (i.e. the question is unanswered) will get 0 marks and
choosing any other option(s) will get −2 marks.



Q.5 Let S be the set of all ( ,  )   such that
 1 
sin( x 2 )(log e x) sin  2 
lim  x  = 0.
x → 
x (log e (1 + x)) 
Then which of the following is (are) correct?

(A) (−1, 3)  S
(B) (−1, 1)  S
(C) (1, − 1)  S
(D) (1, − 2)  S




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