JEE Main 2023 Mathematics April 10 Shift 1 Question Paper PDF Download with Solutions

JEE Main 2025 preparation with the official JEE Main 2023 Mathematics April 10 Shift 1 Question Paper—available for free download in PDF format, complete with detailed Solutions and Answer Key! The JEE Main 2023 Mathematics Question Paper for April 10 Shift 1 is structured into two key sections: Section A, comprising 20 Multiple Choice Questions (MCQs), and Section B, featuring 10 numerical-type questions, of which candidates need to attempt only 5. This format mirrors the latest JEE Main exam pattern, making it an invaluable tool for understanding question types, difficulty levels, and time management.

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JEE Main 2023 Mathematics Question Paper With Solutions

Question 1:

An arc PQ of a circle subtends a right angle at its centre O. The midpoint of the arc PQ is R. If →O P = →u, O→R = →v and →OQ = →αu+ →βv, then α, β² are the roots of the equation:

3x² − 2x − 1 = 0
3x² + 2x − 1 = 0
x² − x − 2 = 0
x² + x − 2 = 0

Correct Answer: (3) x² − x − 2 = 0
View Solution

Question 2:

A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in cm²) is equal to:

800
1025
900
675

Correct Answer: (1) 800
View Solution

Question 3:

Let O be the origin and the position vector of the point P be −̂i−2ĵ+3k̂. If the position vectors of A, B, and C are −2̂i+ ĵ−3k̂, 2̂i+4ĵ−2k̂, and −4̂i+2ĵ−k̂ respectively, then the projection of vector O⃗P on a vector perpendicular to vectors A⃗B and A⃗C is:

¹⁰⁄₃
⁸⁄₃
⁷⁄₃
3

Correct Answer: (4) 3
View Solution

Question 4:

If A is a 3×3 matrix and |A| = 2, then |3adj(|3A|A²)| is equal to:

3¹² × 6¹⁰
3¹¹ × 6¹⁰
3¹² × 6¹¹
3¹⁰ × 6¹¹

Correct Answer: (2) 3¹¹ × 6¹⁰
View Solution

Question 5:

Let two vertices of a triangle ABC be (2, 4, 6) and (0,−2,−5), and its centroid be (2, 1,−1). If the image of the third vertex in the plane x + 2y + 4z = 11 is (α, β, γ), then αβ + βγ + γα is equal to:

Correct Answer: (2) 74
View Solution

Question 6:

The negation of the statement (p ∨ q) ∧ (q ∨ (∼ r)) is:

((∼ p) ∨ r) ∧ (∼ q)
((∼ p) ∨ (∼ q)) ∧ (∼ r)
((∼ p) ∨ (∼ q)) ∨ (∼ r)
(p ∨ r) ∧ (∼ q)

Correct Answer: (1) ((∼ p) ∨ r) ∧ (∼ q)
View Solution

Question 7:

The shortest distance between the lines x + 2 / 1 = y / −2 = z − 5 / 2 and x − 4 / 1 = y − 1 / 2 = z + 3 / 0 is:

Correct Answer: (4) 9
View Solution

Question 8:

If the coefficient of x⁷ in (ax − 1 / bx²)¹³ and the coefficient of x⁻⁵ in (ax + 1 / bx²)¹³ are equal, then a⁴b⁴ is equal to:

Correct Answer: (1) 22
View Solution

Question 9:

A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius γ. Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius:

2λ / 3
√19λ / 7
3λ / 5
√19λ / 5

Correct Answer: (4) √19λ / 5
View Solution

Question 10:

For the system of linear equations 2x − y + 3z = 5, 3x + 2y − z = 7, 4x + 5y + αz = β, which of the following is NOT correct?

The system is inconsistent for α = −5 and β = 8
The system has infinitely many solutions for α = −6 and β = 9
The system has a unique solution for α ≠ −5 and β = 8
The system has infinitely many solutions for α = −5 and β = 9

Correct Answer: (2) The system has infinitely many solutions for α = −6 and β = 9
View Solution

Question 11:

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these terms is equal to:

Correct Answer: (3) 231
View Solution

Question 12:

Let P be the point of intersection of the line x+3/3 = y+2/1 = 1−z/2 and the plane x + y + z = 2. If the distance of the point P from the plane 3x − 4y + 12z = 32 is q, then q and 2q are the roots of the equation:

x² + 18x − 72 = 0
x² + 18x + 72 = 0
x² − 18x − 72 = 0
x² − 18x + 72 = 0

Correct Answer: (4) x² − 18x + 72 = 0
View Solution

Question 13:

Let f be a differentiable function such that x²f(x) − x = 4∫₀ˣ tf(t) dt, f(1) = 2/3. Then 18f(3) is equal to:

Correct Answer: (4) 160
View Solution

Question 14:

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2N < N! is m/n, where m and n are coprime, then 4m − 3n is equal to:

Correct Answer: (2) 8
View Solution

Question 15:

If I(x) = ∫e^sin²xcosx(sin2x − sinx)dx and I(0) = 1, then I(π/3) is equal to:

e³⁄₄
−e³⁄₄
1/2e³⁄₄
−1/2e³⁄₄

Correct Answer: (3) 1/2e³⁄₄ View Solution

Question 16:

96 cos(π/33) cos(2π/33) cos(4π/33) cos(8π/33) cos(16π/33) is equal to:

Correct Answer: (3) 3
View Solution

Question 17:

Let the complex number z = x + iy be such that (2z − 3i) / (2z + i) is purely imaginary. If x + y² = 0, then y⁴ + y² − y is equal to:

Correct Answer: (4) 3/4
View Solution

Question 18:

If f(x) = [(tan 1°)x + log_e(123)] / [x log_e(1234) − (tan 1°)], x > 0, then the least value of f(f(x)) + f(f(4/x)) is:

Correct Answer: (2) 4
View Solution

Question 19:

The slope of the tangent at any point (x, y) on a curve y = y(x) is (x² + y²) / (2xy), x > 0. If y(2) = 0, then a value of y(8) is:

4√3
−4√2
−2√3
2√3

Correct Answer: (1) 4√3
View Solution

Question 20:

Let the ellipse E: x² + 9y² = 9 intersect the positive x- and y-axes at the points A and B respectively. Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle with vertices A, P, and the origin O is m/n, where m and n are coprime, then m − n is equal to:

Correct Answer: (4) 17
View Solution

Question 21:

Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple is in a match, is 840, then the total number of persons who participated in the tournament is:

Correct Answer: 16
View Solution

Question 22:

The number of elements in the set {n ∈ Z : |n² − 10n + 19| < 6} is:

Correct Answer: 6
View Solution

Question 23:

The number of permutations of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is:

Correct Answer: 4898
View Solution

Question 24:

Let f(x) be defined as:
f(x) = x⌊x⌋, −2 < x < 0, and f(x) = (x − 1)⌊x⌋, 0 ≤ x < 2. If m and n are the number of points in (−2, 2) where y = |f(x)| is not continuous and not differentiable, then m + n is equal to:

Correct Answer: 4
View Solution

Question 25:

Let a common tangent to the curves y² = 4x and (x − 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to:

Correct Answer: 32
View Solution

Question 26:

If the mean of the frequency distribution is 28, then its variance is:

Correct Answer: 151
View Solution

Question 27:

The coefficient of x⁷ in (1 − x + 2x³)¹⁰ is:

Correct Answer: 960
View Solution

Question 28:

If y = p(x) is the parabola passing through points (−1, 0), (0, 1), and (1, 0), and the area of the region {(x, y) : (x + 1)² + (y − 1)² ≤ 1, y ≤ p(x)} is A, then 12(π − 4A) is equal to:

Correct Answer: 16
View Solution

Question 29:

Let a, b, c be three distinct positive real numbers such that (2a)^log_ea = (bc)^log_eb and b log₂(e^a) = a log_e(c). Then 6a + 5bc is equal to:

Correct Answer: Bonus
View Solution

Question 30:

The sum of all terms of the arithmetic progression 3, 8, 13, ..., 373, which are not divisible by 3, is:

Correct Answer: 9525
View Solution

JEE Main 2023 Mathematics Paper Analysis April 10 Shift 1

JEE Main 2023 Mathematics Paper Analysis for the exam scheduled on April 10 Shift 1 is available here. Candidates can check subject-wise paper analysis for the exam scheduled on April 10 Shift 1 here along with the topics with the highest weightage.

JEE Main 2023 Mathematics Paper Analysis April 10 Shift 1

JEE Main 2023 Mathematics Question Paper Pattern

Feature	Question Paper Pattern
Examination Mode	Computer-based Test
Exam Language	13 languages (English, Hindi, Assamese, Bengali, Gujarati, Kannada, Malayalam, Marathi, Odia, Punjabi, Tamil, Telugu, and Urdu)
Exam Duration	3 hours
Sectional Time Limit	None
Mathematics Marks	100 marks
Total Number of Questions Asked	20 MCQs + 10 Numerical Type Questions
Total Number of Questions to be Answered	20 MCQs + 5 Numerical Type Questions
Marking Scheme	+4 for each correct answer
Negative Marking	-1 for each incorrect answer

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JEE Main 2023 Question Paper: April 10 Shift 1 Mathematics PDF Download With Solutions

Download JEE Main 2023 Mathematics April 10 Shift 1 Question Paper PDF with Solutions

JEE Main 2023 Mathematics Question Paper With Solutions

JEE Main 2023 Mathematics Paper Analysis April 10 Shift 1

JEE Main 2023 Mathematics Question Paper Pattern

JEE Main Previous Year Question Paper

JEE Main Questions

1.
A molecule \( (X) \) with the following structure under mild acidic conditions is hydrolyzed to produce \( (Y) \) and \( (Z) \). Identify the correct statements about \( (Y) \) and \( (Z) \).}

2.
If \(a_1 = 1\) and for all \(n \ge 1\), \[ a_{n+1} = \frac{1}{2}a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2}, \] then the value of \[ \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \] is equal to:

3.
The number of critical points of the function} \[ f(x)= \begin{cases} \dfrac{|\sin x|}{x}, & x\neq0\\ 1, & x=0 \end{cases} \] in the interval \((-2\pi,2\pi)\) is equal to:

4.
If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is

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Download JEE Main 2023 Mathematics April 10 Shift 1 Question Paper PDF with Solutions

JEE Main 2023 Mathematics Question Paper With Solutions

JEE Main 2023 Mathematics Paper Analysis April 10 Shift 1

JEE Main 2023 Mathematics Question Paper Pattern

JEE Main Previous Year Question Paper

JEE Main Questions

1.A molecule \( (X) \) with the following structure under mild acidic conditions is hydrolyzed to produce \( (Y) \) and \( (Z) \). Identify the correct statements about \( (Y) \) and \( (Z) \).}

2.If \(a_1 = 1\) and for all \(n \ge 1\), \[ a_{n+1} = \frac{1}{2}a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2}, \] then the value of \[ \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \] is equal to:

3.The number of critical points of the function} \[ f(x)= \begin{cases} \dfrac{|\sin x|}{x}, & x\neq0\\ 1, & x=0 \end{cases} \] in the interval \((-2\pi,2\pi)\) is equal to:

4.If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is

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1.
A molecule \( (X) \) with the following structure under mild acidic conditions is hydrolyzed to produce \( (Y) \) and \( (Z) \). Identify the correct statements about \( (Y) \) and \( (Z) \).}

2.
If \(a_1 = 1\) and for all \(n \ge 1\), \[ a_{n+1} = \frac{1}{2}a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2}, \] then the value of \[ \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \] is equal to:

3.
The number of critical points of the function} \[ f(x)= \begin{cases} \dfrac{|\sin x|}{x}, & x\neq0\\ 1, & x=0 \end{cases} \] in the interval \((-2\pi,2\pi)\) is equal to:

4.
If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is