JEE Main Maths Previous Year Questions With Solutions

JEE is a common entrance exam for students who wish to pursue their engineering higher studies in India’s most prestigious institutions, such as IITs and NITs.

JEE Main has three sections for BE/B. Tech students are in Mathematics, Physics, and Chemistry. Each section carries 30 questions, which would add up to a total of 90 questions. In that, the candidates are obliged to write 75 questions. The total mark for this examination is 300. 

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Mathematics is one of the sections in JEE Main 2022. The Maths section in JEE will contain 20 Multiple Choice Questions and 10 numerical questions. They are divided into Sections A and B. Every correct answer will be awarded 4 marks, while 1 mark will be deducted for wrong answers. Unattended questions will neither be awarded nor be deducted any mark.

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This article lets us see what maths questions are asked in JEE Main Previous year’s question papers.

Previous Year Questions – JEE Mathematics

Given-below is the most commonly asked questions in previous years’ question papers:

Q1. The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = m x + 1 is also an integer is:

Options:

• 1

• 2

• 3

• 5

Answer: Option B – 2

Q2. Choose the correct statement about two circles whose equations are given below:

x2 + y2 – 10 x – 10 y + 41 = 0

x2 + y2 – 22 x – 10 y + 137 = 0

Options:

• circles have the same centre

• circles have no meeting point

• circles have only one meeting point

• circles have two meeting points

Answer: Option C – circles have only one meeting point

Q3. Let   be the real roots of the equation, x3 + ax2 + bx + c = 0, (a, b, c  R and a, b  0). If the system of equations (in, u, v,w) given by u +  v +  w = 0,   u +  v +  w = 0;  u +  v +  w = 0 has non-trivial solution, then the value of 2 a b is:

Options:

1. 4
2. 3
3. 2
4. 1

Answer: Option B – 3

Q4. The equation of one of the straight lines which passes through the point (1,3) and makes an angles (2) with the straight line, y+1=3 2 x is:

Options:

1. 4 2 x + 5 y – 15 + 42 = 0
2. 5 2 x + 4 y – 15 + 42 = 0
3. 4 2 x + 5 y – 4 2= 0
4. 4 2 x – 5 y – 5 + 42 = 0

Answer: Option A – 4 2 x + 5 y – 15 + 42 = 0

Q5. If x  – x 3x3 is equal to L, then the value of (6L + 1) is

Options:

1. 4
2. 1/6
3. 3/7
4. 2

Answer: Option D – 2

Q6. A vector a has components 3p and 1 with respect to a rectangular Cartesian system. This system has been rotated through a certain angle (about its origin) in the anticlockwise direction. If, with respect to the new system, a has components p + 1 and 10, then a value of p is equal to:

Options:

1. 3
2. – 4
3. 12
4. – 1

Answer: Option D – – 1

Q7. For the four circles M, N, O and P, given below are the four equations :

Circle M: x2 + y2 = 1

Circle N: x2 + y2 – 2 x = 0

Circle O: x2 + y2 – 2x – 2y + 1 = 0

Circle P: x2 + y2 – 2y = 0

If the centres of the M and N circles are joined together, further centres of the circles N and O are joined together. Moreover, the centres of the circles O and P are joined together. Finally, the centres of the circles P and M are joined together; then, these lines form the sides of a:

Options:

1. Rhombus
2. Square
3. Parallelogram
4. Rectangle

Answer: Option B – Square

Q8. If , are natural numbers such that 100 α – 199 β = 100 100 + 99 101 + 98 102 + … + 1 (199), then will be the slope of the line passing through () and origin?

Options:

1. 510
2. 550
3. 560
4. 590

Answer: Option B – 550

Q9. The real-valued function f x=cosec-1 xx-x, where [x] indicates the greatest integer less than or equal to x, is defined for all x belonging to:

Options:

1. all reals except integers
2. all non-integers except the interval [– 1, 1]
3. all integers except 0, – 1, 1
4. all reals except the interval [– 1, 1]

Answer: Option B – all non-integers except the interval [–1, 1]

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Q10. If the functions are defined as f x = x and as g x = 1 -x, then identify the common domain of the below-specified functions:

ƒ + g,  ƒ  – g, ƒg, gƒ,  g – ƒ where (ƒ ± g) (x) = ƒ (x) ± g(x),  ƒg(x) f xg x

Options:

1. 0 ≤x ≤1
2. 0 ≤x <1
3. 0 <x <1
4. 0 <x ≤1

Answer: Option C – 0 <x <1

Q11. What will be the sum of all the 4-digit distinct numbers formed with the digits 1, 2, 2 and 3?

Options:

1. 26664
2. 122664
3. 22264
4. 122234

Answer: Option A – 26664

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Q12. Which of the ones mentioned below is logically equivalent to (p q) ( ~p  q)?

Options:

1. p q
2. (p ^ q)
3. ~p q
4. p ^ ~q

Answer: Option A – p q

Q13. If the coefficient of x7 and x-7 in the expansion of x2 + 1b x11 and x + 1b x211respectively are equal, then what will be the value b:

Options:

1. 1
2. – 1
3. 2
4. 0

Answer: Option A – 1

Q14. If the mean and variance of the following eight observations: 10, 13, 6, 7, a, 12, b, 12 are 9 and 37/4, respectively, what will be the value of a-b2?

Options:

1. 20
2. 54
3. 16
4. 49

Answer: Option C – 16

Q15. If α and β are the roots of the equation x2 – 2014 x + 512 = 0, then the value of 8 + 8 is equal to:

Options:

1. 25
2. 50
3. 75
4. 100

Answer: Option B – 50

Q16. Let n be a 2-digit natural number. If n is selected at random, what will be the probability that 2n – 2 is a multiple of 3?

Options:

1. 1/3
2. 2/3
3. 1/2
4. 0

Answer: Option C – 1/2

Q17. If tangents to the circle x – 12 + y – 32 = 22 are drawn from the point (–1, 1) such that the tangents’ points of contact are A and B. Also, if a point P lies on the circle such that AB = AP, what will be the area of ΔABP?

Options:

1. 2
2. 1/4
3. 4
4. 7

Answer: Option C – 4

Q18. If sec y  dydx = sin  (x + y)  + (x – y) ; y 0 = 0, then what will be value of 5 y‘ 2?

Options:

1. 4
2. 3
3. 2
4. 1

Answer: Option C – 2

Q19. A circle with a centre (2, 3) passes through the origin. A diameter MN is such that it is perpendicular to the line that joins the centre of the circle and its origin. What are the coordinates of points M and N?

Options:

1. (– 1, 5) & (5, 1)
2. (– 2, 5) & (– 5, 1)
3. (3, 6) & (5, 1)
4. (– 1, 1) & (5, – 1)

Answer: Option A – (– 1, 5) & (5, 1)

Q20. The area bounded by the curve y = x2 and the line y – x = 2 is:

Options:

1. 7/2
2. 9/2
3. 6/5
4. 4/3

Answer: Option B – 9/2

Q21. A circle that touches the y-axis at (0, 6) and contains an x-intercept equal to 6 5, what will be the circle’s radius?

Options:

1. 2
2. 4
3. 9
4. 19

Answer: Option C – 9

Q22. Three vectors a, b,  and c with magnitudes 2, 1 and 2 respectively follow the given relation a= b*b* c. The acute angle between the vectors b & c is θ. What will be the value of (1+tan )?

Options:

1. 2
2. 4
3. 9
4. 13

Answer: Option A – 2

Q23. If two sides of a parallelogram are given as: 4x + 5y = 0 and 7x + 2y = 0. If one of the diagonals is 11x + 7y = 9, then what will be the other diagonal pass through the point?

Options:

1. 13, –43
2. 1, 1
3. 12,14
4. 2, 3

Answer: Option B – (1, 1)

Q24. The point P a, b undergoes the below-mentioned transformation to a new coordinate P‘ – 12, 72

• Reflection about y = x
• Translation through 2 units in the +ve direction of the x-axis
• Rotation through an angle 4 in an anticlockwise sense about the origin

Options:

1. 2
2. 1
3. 4
4. 9

Answer: Option D – 9

Q25. For an ellipse E, the centre lies at the point (3, – 4), one of the vertices is at (5, – 4) and one of its foci is at (4, – 4). If the equation of tangent on the ellipse E is m x – y = 4 (m > 0), what is the value of 5 m2?

Options:

1. 3
2. 5
3. 7
4. 9

Answer: Option A – 3

Conclusion

To secure maximum marks in the Maths section of the JEE examination, it is essential to go through and solve the problems given in previous years’ question papers. It will help the candidates enhance their time-management and problem-solving skills. 

In this article, we have given 25 questions that were asked in previous year’s papers along with their answers. The students can make use of it while they prepare for their examinations.

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