JEE Main Maths Previous Year Questions (PYQ-Style) — With Solutions
A set of JEE Main-level Mathematics questions in the style of previous-year papers, with answer keys and worked solutions across algebra, calculus, coordinate geometry, vectors, 3D and probability. Attempt each question first, then reveal the solution to check your working.
The sum of the roots of the quadratic equation 2x² − 8x + 6 = 0 is:
- A.3
- B.4
- C.6
- D.−4
The nature of the roots of the equation x² + 4x + 5 = 0 is:
- A.two distinct real roots
- B.two equal real roots
- C.two complex (non-real) roots
- D.exactly one real root
The 10th term of the arithmetic progression 3, 7, 11, 15, … is:
- A.36
- B.39
- C.40
- D.43
The sum of the infinite geometric progression 1 + 1/2 + 1/4 + 1/8 + … is:
- A.3/2
- B.2
- C.3
- D.does not converge
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Unlock all solutions — freeThe number of terms in the binomial expansion of (x + y)¹⁰ is:
- A.9
- B.10
- C.11
- D.12
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Unlock all solutions — freeThe modulus of the complex number 3 + 4i is:
- A.5
- B.7
- C.25
- D.√7
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Unlock all solutions — freeThe value of the limit lim(x→0) (sin x)/x is:
- A.0
- B.1
- C.∞
- D.does not exist
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Unlock all solutions — freeIf f(x) = x³, the value of its derivative f′(x) at x = 2 is:
- A.4
- B.6
- C.8
- D.12
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Unlock all solutions — freeThe derivative of sin x with respect to x is:
- A.cos x
- B.−cos x
- C.−sin x
- D.sec²x
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Unlock all solutions — freeThe function f(x) = x² − 4x + 3 attains its minimum value at x =:
- A.0
- B.1
- C.2
- D.3
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Unlock all solutions — freeThe indefinite integral ∫ 2x dx equals:
- A.x² + C
- B.2x² + C
- C.x²/2 + C
- D.2 + C
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Unlock all solutions — freeThe value of the definite integral ∫₀¹ x² dx is:
- A.1/3
- B.1/2
- C.2/3
- D.1
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Unlock all solutions — freeThe slope of the tangent to the curve y = x² at the point (1, 1) is:
- A.1/2
- B.1
- C.2
- D.3
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Unlock all solutions — freeThe distance between the points (0, 0) and (3, 4) in the plane is:
- A.5
- B.7
- C.√7
- D.25
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Unlock all solutions — freeThe midpoint of the line segment joining the points (2, 3) and (4, 7) is:
- A.(3, 4)
- B.(3, 5)
- C.(6, 10)
- D.(1, 2)
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Unlock all solutions — freeThe slope of the line passing through the points (1, 2) and (3, 6) is:
- A.1/2
- B.1
- C.2
- D.3
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Unlock all solutions — freeThe equation of a straight line with slope 2 that passes through the origin is:
- A.y = 2x
- B.y = x + 2
- C.y = 2
- D.x = 2y
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Unlock all solutions — freeThe centre of the circle x² + y² − 4x − 6y + 9 = 0 is:
- A.(2, 3)
- B.(−2, −3)
- C.(4, 6)
- D.(−4, −6)
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Unlock all solutions — freeThe dot product of the vectors a = î + 2ĵ and b = 2î − ĵ is:
- A.0
- B.2
- C.4
- D.−2
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Unlock all solutions — freeThe magnitude of the vector 2î + 3ĵ + 6k̂ is:
- A.7
- B.11
- C.49
- D.√11
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Unlock all solutions — freeThe distance of the point (1, 2, 2) from the origin in three-dimensional space is:
- A.3
- B.5
- C.9
- D.√5
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Unlock all solutions — freeA fair die is rolled once. The probability of getting an even number is:
- A.1/6
- B.1/3
- C.1/2
- D.2/3
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Unlock all solutions — freeA single card is drawn at random from a standard deck of 52 cards. The probability that it is an ace is:
- A.1/13
- B.1/4
- C.1/52
- D.4/13
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Unlock all solutions — freeTwo fair coins are tossed together. The probability of getting exactly two heads is:
- A.1/4
- B.1/2
- C.3/4
- D.1
Solution locked
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