JEE (Advanced) 2024 Paper 1
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 Let f ( x ) be a continuously differentiable function on the interval (0, ) such that f (1) = 2 and
t10 f ( x) − x10 f (t )
lim =1
t→x t 9 − x9
for each x 0. Then, for all x 0, f ( x ) is equal to
31 9 10 9 13 10
(A) − x (B) + x
11x 11 11x 11
−9 31 10 13 9 10
(C) + x (D) + x
11x 11 11x 11
Q.2 A student appears for a quiz consisting of only true-false type questions and answers all the questions.
The student knows the answers of some questions and guesses the answers for the remaining
questions. Whenever the student knows the answer of a question, he gives the correct answer.
Assume that the probability of the student giving the correct answer for a question, given that he has
1
guessed it, is . Also assume that the probability of the answer for a question being guessed, given
2
1
that the student’s answer is correct, is . Then the probability that the student knows the answer of
6
a randomly chosen question is
1 1 5 5
(A) (B) (C) (D)
12 7 7 12
1/10
,JEE (Advanced) 2024 Paper 1
Q.3 −5
Let x be such that cot x = . Then
2 11
11x 11x
sin ( sin 6 x − cos 6 x ) + cos ( sin 6 x + cos 6 x )
2 2
is equal to
11 − 1 11 + 1
(A) (B)
2 3 2 3
11 + 1 11 − 1
(C) (D)
3 2 3 2
Q.4 x2 y 2
Consider the ellipse + = 1. Let S ( p, q ) be a point in the first quadrant such that
9 4
p2 q2
+ 1. Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one
9 4
end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let
R be the vertex of the ellipse with positive x -coordinate and O be the center of the ellipse. If the
3
area of the triangle ORT is , then which of the following options is correct?
2
(A) q = 2, p = 3 3 (B) q = 2, p = 4 3
(C) q = 1, p = 5 3 (D) q = 1, p = 6 3
2/10
, JEE (Advanced) 2024 Paper 1
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 none of the options is chosen (i.e. the question is 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 +2 marks;
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 (i.e. the question is unanswered) will get 0 marks; and
choosing any other combination of options will get −2 marks.
, T = ( −1 + 2 ) ( ) .
Q.5 n n
Let S = a + b 2 : a, b 1 : n , and T2 = 1 + 2 : n
Then which of the following statements is (are) TRUE?
(A) T1 T2 S
1
(B) T1 0, = , where denotes the empty set.
2024
(C) T2 ( 2024, )
( (
(D) For any given a, b , cos a + b 2 )) + i sin ( ( a + b 2 )) if and only if b = 0,
where i = −1 .
3/10
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 Let f ( x ) be a continuously differentiable function on the interval (0, ) such that f (1) = 2 and
t10 f ( x) − x10 f (t )
lim =1
t→x t 9 − x9
for each x 0. Then, for all x 0, f ( x ) is equal to
31 9 10 9 13 10
(A) − x (B) + x
11x 11 11x 11
−9 31 10 13 9 10
(C) + x (D) + x
11x 11 11x 11
Q.2 A student appears for a quiz consisting of only true-false type questions and answers all the questions.
The student knows the answers of some questions and guesses the answers for the remaining
questions. Whenever the student knows the answer of a question, he gives the correct answer.
Assume that the probability of the student giving the correct answer for a question, given that he has
1
guessed it, is . Also assume that the probability of the answer for a question being guessed, given
2
1
that the student’s answer is correct, is . Then the probability that the student knows the answer of
6
a randomly chosen question is
1 1 5 5
(A) (B) (C) (D)
12 7 7 12
1/10
,JEE (Advanced) 2024 Paper 1
Q.3 −5
Let x be such that cot x = . Then
2 11
11x 11x
sin ( sin 6 x − cos 6 x ) + cos ( sin 6 x + cos 6 x )
2 2
is equal to
11 − 1 11 + 1
(A) (B)
2 3 2 3
11 + 1 11 − 1
(C) (D)
3 2 3 2
Q.4 x2 y 2
Consider the ellipse + = 1. Let S ( p, q ) be a point in the first quadrant such that
9 4
p2 q2
+ 1. Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one
9 4
end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let
R be the vertex of the ellipse with positive x -coordinate and O be the center of the ellipse. If the
3
area of the triangle ORT is , then which of the following options is correct?
2
(A) q = 2, p = 3 3 (B) q = 2, p = 4 3
(C) q = 1, p = 5 3 (D) q = 1, p = 6 3
2/10
, JEE (Advanced) 2024 Paper 1
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 none of the options is chosen (i.e. the question is 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 +2 marks;
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 (i.e. the question is unanswered) will get 0 marks; and
choosing any other combination of options will get −2 marks.
, T = ( −1 + 2 ) ( ) .
Q.5 n n
Let S = a + b 2 : a, b 1 : n , and T2 = 1 + 2 : n
Then which of the following statements is (are) TRUE?
(A) T1 T2 S
1
(B) T1 0, = , where denotes the empty set.
2024
(C) T2 ( 2024, )
( (
(D) For any given a, b , cos a + b 2 )) + i sin ( ( a + b 2 )) if and only if b = 0,
where i = −1 .
3/10
