7 April JEE Main Mathematics Question Paper 2025 OUT with Answer Key Session 2

1

If x |x - 3| + 3 |x - 2| + 1 = 0, then the number of real solution is

1

2

is a circle of radius r and centre (a, b), then 15ab/r ² is equal to

0

3

3 + 2√2

4

Let f(x) = x-5/x ² -3x+2', if range of f(x) is (−∞, α) U (β, ∞). There α ² + β ² equals to

194

5

If a box contains 19 unbiased coins and 1 biased coin with both faces head. If a coin is randomly chosen out of this box and tossed. If the head appears, then the probability that the unbiased coin was selected

19/21

6

If f(θ) = tan(tan θ) - tan(sin θ)/tan θ-sin θ is continuous at θ = 0, then the value of f(θ) at θ = 0 is equal to

1

7

Let y = y(x) and (1 + x ² )y' – 2xy = (x ⁴ + 2x ² + 1) cosx. If y(0) = 1, then ∫ ³ _-3 y(x)dx equals to

24

8

The sum of series ² C ₁ • (1 × 2) + ³ C ₂ • (2 x 3) + ⁴ C ₃ • (3 × 4) + ... + ¹⁹ C ₁₈ • (18 x 19) is S, then S/295 is equal to

114

1

The remainder when 64 ^{64 64} is divided by 7 is equal to

1

2

Let A be a set defined as A = {2. 3, 6, 9}. Find the number of singular matrices of order 2 * 2 such that elements are from the set A.

36

3

Area bounded by the curves y = 4 - x ² /4 and y = x - 4/2 (in square units) is

125/3

4

If X ₁ , X ₂ , X ₃ , X ₄ are in GP, then we subtract 2, 4, 7, 8 from X ₁ , X ₂ , X ₃ , X ₄ respectively, then the resultant numbers are in AP, then the value of 1/24 (X ₁ . X ₂ . X ₃ . X ₄ ) is

2 ³ /3 ⁹

5

If f(x) = (x ² /2) - [√x] ∀ x ∈ [0, 4], where [.] denotes the greatest integer function, then number of points of discontinuity of f(x) is

8

6

π(π + 6)/3√3

7

If α and ẞ are negative real roots of the quadratic equation x ² – (p + 2)x + (2p + 9) = 0 and pe ε (α, β). Then the value of ẞ ² – 2α is

13

8

Let the straight line AB: x + y − 2 = 0, AC: 3y – x = 2 intersects x-axis at B and C respectively. If P is the orthocentre of the triangle ABC, then area of the triangle CPB is

6 sq. units

9

Statement 1: If (z+i/z-i) is purely real, then there are exactly 2 complex numbers z.
Statement 2: If (z+1/z-1) is purely imaginary, then there are infinite such complex numbers z.
Then,

Statement 2 is true.

10

The value of the limit

5 ³ /3 ⁷

Shift 1

7 April JEE Main Mathematics Question Paper 2025 Shift 1 PDF

Shift 2

7 April JEE Main Mathematics Question Paper 2025 Shift 2 PDF

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Vedantu

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Aakash

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Resonance

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