JEE mains practice set-1| Competative exam

 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.