JEE Main 2024 Question Paper & Answers
The official JEE Main 2024 question papers, with the official answer key. Attempt as a real timed exam (with negative marking) or switch to practice mode for instant per-question answers and explanations.
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Official PYQ
JEE Main 2024 - April 4 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 4 Shift 1
1Let be given by where . If is continuous at , then is equal to: (reconstructed from a badly garbled scan; final answer trusted from source)
- A) 48
- B) 12
- C) 3
- D) 6
Answer: B
2Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black; and 6 red, 6 black balls, respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is:
- A)
- B)
- C)
- D)
Answer: B
3The vertices of a triangle are , and . A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to the origin is:
- A)
- B)
- C)
- D)
Answer: C
4If the solution of the differential equation satisfies , then is equal to:
- A) 0
- B)
- C)
- D)
Answer: C
5Let the sum of the maximum and the minimum values of the function be , where . Then is equal to:
- A) 182
- B) 217
- C) 195
- D) 201
Answer: D
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Official PYQ
JEE Main 2024 - April 4 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 4 Shift 2
1
- A) 968
- B) 1152
- C) 746
- D) 1250
Answer: B
2
- A) 25
- B) 20
- C) 50
- D) 40
Answer: A
3
- A)
- B)
- C)
- D)
Answer: B
4
- A) Only (II) is correct.
- B) Only (I) is correct.
- C) Both (I) and (II) are correct.
- D) Neither (I) nor (II) is correct.
Answer: B
5Let three real numbers a,b,c be in arithmetic progression and , b, be in geometric progression. If a > 10 and the arithmetic mean of a,b and c is 8, then the cube of the geometric mean of a,b and c is
- A) 120
- B) 312
- C) 316
- D) 128
Answer: A
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Official PYQ
JEE Main 2024 - April 5 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 5 Shift 1
1
- A) 72
- B) 69
- C) 75
- D) 78
Answer: C
2Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let a and b be the sides of the rectangle PQRS when its area is maximum. Then (a + b)2 is equal to :
- A) 72
- B) 60
- C) 80
- D) 64
Answer: A
3
- A) 44
- B) 48
- C) 46
- D) 42
Answer: C
4
- A)
- B)
- C)
- D)
Answer: B
5
- A) only (I) is true.
- B) only (II) is true.
- C) neither (I) nor (II) is true.
- D) both (I) and (II) are true.
Answer: D
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Official PYQ
JEE Main 2024 - April 5 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 5 Shift 2
1
- A) 6
- B) 3
- C) 4
- D) 5
Answer: C
2The differential equation of the family of circles passing the origin and having center at the line y = x is :
- A)
- B)
- C)
- D)
Answer: C
3
- A)
- B)
- C)
- D)
Answer: D
4
- A)
- B)
- C) 1
- D)
Answer: D
560 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th word is :
- A) word is : (1) OBBHJ
- B) HBBJO
- C) OBBJH
- D) JBBOH
Answer: C
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Official PYQ
JEE Main 2024 - April 6 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 6 Shift 1
1
- A)
- B)
- C)
- D)
Answer: B
2
- A)
- B)
- C)
- D)
Answer: A
3
- A)
- B)
- C)
- D)
Answer: C
4The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is
- A)
- B) 1.8
- C)
- D) 1.94
Answer: C
5
- A) both one-one and onto.
- B) onto but not one-one.
- C) neither one-one nor onto.
- D) one-one but not onto.
Answer: C
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Official PYQ
JEE Main 2024 - April 6 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 6 Shift 2
1Let ABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABC and the same process is repeated infinitely many times. If P is the sum of perimeters and Q is be the sum of areas of all the triangles formed in this process, then:
- A)
- B)
- C)
- D)
Answer: A
2
- A) 24
- B) 23
- C) 25
- D) 26
Answer: C
3If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is:
- A)
- B)
- C)
- D)
Answer: A
4
- A)
- B)
- C)
- D) 2
Answer: C
5If the locus of the point, whose distances from the point (2, 1) and (1, 3) are in the ratio 5 : 4, is , then the value of is equal to:
- A) 5
- B)
- C) 37
- D) 437
Answer: C
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Official PYQ
JEE Main 2024 - April 8 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 8 Shift 1
1
- A) 10
- B) 8
- C) 14
- D) 7
Answer: D
2
- A)
- B) log8(6)
- C)
- D)
Answer: C
3
- A) 110
- B) 130
- C) 125
- D) 145
Answer: B
4
- A)
- B)
- C)
- D)
Answer: A
5
- A) 2
- B) 0
- C) 1
- D) 3
Answer: A
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - April 8 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 8 Shift 2
1If the image of the point (-4, 5) in the line lies on the circle ()2 + (), then r is equal lo :
- A) 1
- B) 2
- C) 75
- D) 3
Answer: B
2
- A) 27
- B) 25
- C) 25
- D) 21
Answer: B
3
- A) 2
- B) 3
- C) 0
- D) 1
Answer: C
4
- A) 96
- B) 78
- C) 91
- D) 84
Answer: C
5The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to :
- A) 175
- B) 181
- C) 177
- D) 179
Answer: D
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Official PYQ
JEE Main 2024 - April 9 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 9 Shift 1
1
- A)
- B)
- C)
- D)
Answer: B
2The parabola divides the area of the circle in two parts. The area of the smaller part is equal to :
- A)
- B)
- C)
- D)
Answer: A
3
- A)
- B)
- C)
- D)
Answer: A
4
- A) 80
- B) 90
- C) 60
- D) 70
Answer: D
5
- A) 25
- B) 24
- C) 27
- D) 22
Answer: A
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Official PYQ
JEE Main 2024 - April 9 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - April 9 Shift 2
1
- A) e
- B)
- C) 0
- D)
Answer: A
2
- A) 3
- B) 5
- C) 4
- D) 6
Answer: A
3
- A) 1
- B) 2
- C)
- D)
Answer: A
4
- A) 12
- B)
- C) 10
- D) 8
Answer: A
5The area (in square units) of the region enclosed by the ellipse in the first quadrant below the line y = x is :
- A)
- B)
- C)
- D)
Answer: B
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - February 1 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - February 1 Shift 1
1A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:
- A)
- B)
- C)
- D)
Answer: B
2
- A)
- B)
- C)
- D)
Answer: C
3
- A) 243
- B) 729
- C) 27
- D) 891
Answer: B
4
- A) C
- B)
- C)
- D)
Answer: A
5If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:
- A) 47
- B) 53
- C) 51
- D) 43
Answer: C
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - February 1 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - February 1 Shift 2
1
- A) 5
- B) 2
- C) 0
- D) 3
Answer: D
2
- A)
- B) 9
- C)
- D) 8
Answer: A
3
- A) 1
- B) 3
- C) 2
- D) 0
Answer: D
4
- A) 0
- B) 1
- C) 2
- D)
Answer: A
5
- A)
- B)
- C)
- D)
Answer: D
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - January 27 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 27 Shift 1
1The value(s) of for which can hold (for suitable ) is given by the range:
- A) or
- B)
- C)
- D)
Answer: A
2The distance of the point from the line , measured along a line parallel to , is:
- A) 12
- B) 14
- C) 18
- D) 21
Answer: B
3Let and be solutions of the differential equations and respectively, . Given that , and , the value of for which is:
- A)
- B)
- C)
- D)
Answer: D
4If is the orthocentre of the triangle with vertices , and , and , , then is equal to:
- A) 72
- B) 88
- C) 80
- D) 66
Answer: A
5If denotes the sum of all the coefficients in the expansion of and denotes the sum of all the coefficients in the expansion of , then:
- A)
- B)
- C)
- D)
Answer: A
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Official PYQ
JEE Main 2024 - January 27 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 27 Shift 2
1
- A) More than 2
- B) 1
- C) 2
- D) 0
Answer: B
2
- A) g is continuous but not differentiable at
- B)
- C) g is neither continuous nor differentiable at
- D)
Answer: A
3
- A)
- B)
- C)
- D)
Answer: C
4
- A)
- B)
- C)
- D)
Answer: B
5
- A)
- B)
- C)
- D)
Answer: C
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - January 29 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 29 Shift 1
1If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to
- A) 7
- B) 4
- C) 5
- D) 6
Answer: D
2
- A)
- B)
- C)
- D)
Answer: B
3
- A) (0, 1]
- B) [0, 3)
- C) [0, 1]
- D) [0, 1)
Answer: C
4A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws , is
- A)
- B)
- C)
- D)
Answer: C
5
- A)
- B) 3
- C) 2
- D)
Answer: B
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Official PYQ
JEE Main 2024 - January 29 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 29 Shift 2
1
- A) 26
- B) 27
- C) 66
- D) 23
Answer: A
2Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
- A) 18
- B) 16
- C) 12
- D) 15
Answer: D
3
- A)
- B)
- C)
- D)
Answer: D
4
- A)
- B)
- C)
- D)
Answer: C
5
- A) exactly one point of local minima and no point of local maxima
- B) exactly one point of local maxima and no point of local minima
- C) exactly one point of local maxima and
- D) exactly one point of local minima (4) exactly two points of local maxima and exactly one point of local minima
Answer: C
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - January 30 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 30 Shift 1
1A line passing through the point A(9, 0) makes an angle of 30º with the positive direction of x-axis. If this line is rotated about A through an angle of 15º in the clockwise direction, then its equation in the new position is
- A)
- B)
- C)
- D)
Answer: A
2
- A) 395
- B) 390
- C) 405
- D) 410
Answer: A
3
- A) 9
- B) 1
- C) 4
- D)
Answer: B
4
- A)
- B)
- C)
- D)
Answer: C
5The maximum area of a triangle whose one vertex is at (0, 0) and the other two vertices lie on the curve y = - at points (x, y) and (-x, y) where y > 0 is :
- A) 88
- B) 122
- C) 92
- D) 108
Answer: D
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - January 30 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 30 Shift 2
1
- A)
- B)
- C)
- D)
Answer: D
2
- A)
- B)
- C)
- D) 5
Answer: B
3
- A)
- B)
- C)
- D)
Answer: D
4
- A) 90
- B) 75
- C) 95
- D) 85
Answer: A
5
- A) 600
- B) 392
- C) 608
- D) 108
Answer: C
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - January 31 Shift 1
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 31 Shift 1
1
- A) Both (I) and (II) are true
- B) Neither (I) nor (II) is true
- C) Only (II) is true
- D) Only (I) is true
Answer: A
2
- A) 2 : 1 : 4
- B) 4 : 1 : 4
- C) 1 : 2 : 4
- D) 1 : 1 : 4
Answer: D
3
- A)
- B)
- C)
- D)
Answer: A
4
- A)
- B) 4
- C) 6
- D)
Answer: C
5
- A)
- B)
- C)
- D)
Answer: D
+70 more questions — attempt the full paper to see them all.
Official PYQ
JEE Main 2024 - January 31 Shift 2
180 Mins 300 Marks
75Questions
300Max Marks
Sample questions from JEE Main 2024 - January 31 Shift 2
1The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
- A) 406
- B) 130
- C) 142
- D) 136
Answer: D
2
- A)
- B)
- C)
- D)
Answer: C
3
- A)
- B) 75
- C)
- D)
Answer: B
4
- A) 12
- B) 18
- C) 20
- D) 24
Answer: B
5
- A) 6
- B) 9
- C) 8
- D) 10
Answer: C
+70 more questions — attempt the full paper to see them all.