Here are 30 mathematics questions related to JEE Mains exam:
*Algebra*
1. If α and β are the roots of the equation \[x² + px + q = 0,\] then \[α² + β² \] is equal to:
A) p² - 2q
B) p² + 2q
C) p² - q
D) p² + q
2. The number of solutions of the equation \[|x - 1| + |x - 2| = 1\] is:
A) 1
B) 2
C) 3
D) 4
3. If a, b, c are in AP, then the equation \[ax² + 2bx + c = 0 \] has:
A) Real and distinct roots
B) Real and equal roots
C) Complex roots
D) No roots
*Calculus*
4. The derivative of \[f(x) = x² sin(x) \] is:
A) \[2x sin(x) + x² cos(x)\]
B) \[2x sin(x) - x² cos(x)\]
C) \[x² cos(x) - 2x sin(x)\]
D) \[x² sin(x) + 2x cos(x)\]
5. The value of \[∫(2x + 1) dx\] from x = 0 to x = 1 is:
A) 1
B) 2
C) 3
D) 4
6. The limit of \[\frac{(x² - 4) }{(x - 2) } \] as x approaches 2 is:
A) 0
B) 2
C) 4
D) ∞
*Geometry*
7. The equation of the circle with center (2, 3) and radius 4 is:
A) \[(x - 2)² + (y - 3)² = 16\]
B) \[(x + 2)² + (y + 3)² = 16\]
C)\[ (x - 2)² + (y + 3)² = 16\]
D)\[ (x + 2)² + (y - 3)² = 16\]
8. The distance between the points (1, 2) and (4, 6) is:
A) √10
B) √13
C) √17
D) √20
9. The equation of the line passing through (1, 2) and (3, 4) is:
A) x - y + 1 = 0
B) x + y - 3 = 0
C) x - y - 1 = 0
D) x + y + 1 = 0
*Trigonometry*
10. The value of sin(30°) is:
A) 1/2
B) √3/2
C) 1/√2
D) √3
11. The value of cos(60°) is:
A) 1/2
B) √3/2
C) 1/√2
D) √3
12. The equation \[sin(x) = 1/2 \] has solutions:
A) x = 30°
B) x = 60°
C) x = 30°, 150°
D) x = 60°, 120°
*Miscellaneous*
13. The number of ways to arrange 5 people in a row is:
A) 5!
B) 4!
C) 5! / 2!
D) 5! / 3!
14. The probability of getting a head when a coin is tossed is:
A) 1/2
B) 1/3
C) 2/3
D) 3/4
15. The sum of the first n natural numbers is:
A) n(n + 1)/2
B) n(n - 1)/2
C) n(n + 1)
D) n(n - 1)
16. The equation\[ x² + y² = 4 \] represents:
A) A circle
B) A parabola
C) An ellipse
D) A hyperbola
17. The value of \[∫(1/x) dx\] from x = 1 to x = 2 is:
A) ln(2)
B) ln(1/2)
C) 1/2
D) 2
18. The derivative of \[f(x) = e^x \] is:
A) \[e^x\]
B) \[e^(-x)\]
C)\[ -e^x\]
D) \[-e^(-x)\]
19. The equation of the tangent to the curve \[y = x² \] at (1, 1) is:
A) \[y = 2x - 1\]
B) \[y = 2x + 1\]
C) \[y = x + 1\]
D) \[y = x - 1\]
20. The value of\[ lim (x → 0) (sin(x) / x)\] is:
A) 0
B) 1
C) ∞
D) -1
21. The equation\[ x² - 4x + 4 = 0\] has:
A) Real and distinct roots
B) Real and equal roots
C) Complex roots
D) No roots
22. The sum of the interior angles of a triangle is:
A) 90°
B) 120°
C) 150°
D) 180°
23. The equation of the circle with center (0, 0) and radius 2 is:
A) \[x² + y² = 4\]
B)\[ x² + y² = 2\]
C)\[ x² - y² = 4\]
D)\[ x² - y² = 2\]
24. The value of \[\int_0^1(x² + 1) dx \] is:
A) \[\frac{1}{3}\]
B)\[ \frac{2}{3}\]
C) \[\frac{4}{3}\]
D) \[\frac{5}{3}\]
25. The equation of the line passing through (0, 0) and (1, 1) is:
A)\[ y = x\]
B)\[ y = -x\]
C) \[x + y = 0\]
D)\[ x - y = 0\]
26. The value of \[sin(45°) \] is:
A)\[ 1/2\]
B) \[√3/2\]
C)\[ 1/√2\]
D) \[√3\]
27. The equation \[x² + 2x + 1 = 0 \] has:
A) Real and distinct roots
B) Real and equal roots
C) Complex roots
D) No roots
28. The derivative of \[f(x) = x³ \] is:
A)\[ 2x²\]
B) \[3x²\]
C) \[x²\]
D) \[3x\]
29. The value of \[\int_0^1(e^x) dx \] is:
A)\[ e - 1\]
B) \[e + 1\]
C) \[e\]
D) \[1/e\]
30. The equation of the parabola with vertex (0, 0) and focus (1, 0) is:
A) \[y² = 4x\]
B) \[y² = -4x\]
C) \[x² = 4y\]
D) \[x² = -4y\]
For Answer Please comments.
Some Query:-
1. Which type of question is asked in JEE Mains?
In JEE Main 2026, the exam consists of two types of questions:
Multiple-Choice Questions (MCQs): Candidates select the correct answer from four options.
Numerical Value Questions: Candidates enter the numerical answer in the form of a number.
2. Most Repeated questions in JEE Mains Maths
The most frequently asked, high-yield topics in JEE Main Mathematics include Linear Differential Equations Area Bounded by Curves Vector / Cross Products, and 3D Geometry (specifically shortest distance). Focusing on matrices, sets, functions, and definite integration often yields the highest return due to consistent repetition of question types.
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