2 April 2025 JEE Main Mathematics Question Paper (Available) with Answer Key

1

Total number of terms in an A.P are even. Sum of odd terms is 24 and sum of even terms is 30. Last term exceeds the first term by 21/2. Find the total number of terms.

8

2

If the domain of the function f(x) = 1/√3x+10-x ² + 1/√x+|x| is (a, b) then (1+a) ² + b ² is equal to:

26

3

Find the eccentricity of ellipse in which length of minor axis is equal to one-fourth of the distance between foci.

4/√17

4

If dy/dx + 2ysec ² x = 2sec ² x + 3tanx . sec ² x and f(0)= 5/4. Then the value of 12(y(π/4) - 1/e ² ) equals to:

21

5

Evaluate ∫ ² _-2 9x ² /1+5x dx

24

6

If the mean and variance of eight observations a, b, 8, 12, 10, 6, 4, 15, is 9 and 9.25, respectively. Then a + b + ab is equal to

93

7

10

8

If y = cos (π/3 + cos ^-1 (x/2)), then which of the following is true.

x ² - 2xy + 4y ² = 3

9

2 - √2 - ln (√2 + 1)

10

The image of the point (1, 0, 3) about the line passing through →a = 3î + 2ĵ – k̂ and whose direction ratio are →r = 4î + 2ĵ – k̂ is

(-23/21, 20/21, -73/21)

11

If the curve x ² = 4y intersects the line y = 2(x + 6) at (a, b) in 2nd quadrant, then ∫ ^b _a x ⁴ /1 + 5 ^x dx is

1024/5

12

If the sum of series is m/n, where m and n are natural coprime numbers, then (m + n) is

276

13

In the given figure, number of ways to fill a, b, c, d and e into boxes such that no row empty and at most one letter is filled in one box, is

76

17

1

Find the maximum value of n such that 50! is divisible by 3 ⁿ .

22

2

Let P _n = α ⁿ + β ⁿ , P ₁₀ = 123, P ₉ = 76, P ₈ = 47 and P ₁ = 1, the quadratic equation whose roots are 1/α and 1/β.

x ² + x - 1 = 0

3

The total number of 10 digits sequences formed by only {0, 1, 2} where 1 should be used at least 5 times and 2 should be used exactly three times, is

2892

4

Let a ₁ , a ₂ , a ₃ ,.... is an A.P. and ∑ ¹² _k = ₁ a2 _k-1 = -72/5 a ₁ and ∑ ⁿ _k=1 a _k =0. Then the value of n is

11

5

6

Let the system of equations, 3x – y + ẞz = 3, 2x + αy + z = -3 and x + y + 4z = 4 has infinite solutions, then 22ẞ – 9α equals to

8

9

If then α +2ẞ + γ is equal to:

11

The term independent of x in the binomial expression of is:

12

Let E be an ellipse such that E: x ² /18 + y ² /9 = 1. Let point P lies on E such that S and S ' are foci of ellipse. Then, find the sum of min (PS . PS ' ) + max (PS . PS ' ).

13

14

Let θ∈ [−2π, 2π] satisfying 2cos ² θ – sinθ - 1 =0. Then the number of solutions of equation is

6

15

If Q and R are two points on line L: x-1/-1 = y-2/3 = z-3/5 such that QR = 5. If P(0, 2, 3) be any point, then the area of ΔPQR is

√85/14

16

Let sin x cos y (f(2x + 2y) − f(2x – 2y)) = cos x sin y f(2x + 2y) + f(2x – 2y)) ∀ x, y ∈ R and f ' (0) = 1/2. If f(x) is differentiable function, then f ''' (2π/3) is -

-1/16

17

For a tetrahedron ABCD, the area of triangular face ABC, ACD and ABD is 5, 6 and 7 sq. units, respectively. If AB, AC and AD are mutually orthogonal, then the area of triangular face BCD is

√110 sq. units

18

If 2 + k ² z/k + kz̅ = z, k ≠ 0, such that z = x + i y and y ≠ 0 and |z - 1 + 2i| = 1, then find the maximum distance of point (k + k ² i) from the given circle on which z lies

19

Let C ₁ and C ₂ are circle passing through (–9, 4), both are in contact with x + y = 3 nd x - y = 3 (tangent lines). If r ₁ and r ₂ are radius of C ₁ and C ₂ respectively, then |r ² ₁ - r ² ₂ | equals to

768

20

If (I + A) = , then find the value of det ((a + 1) adj ((a - 1)A))

4a ² (a - 1) ³ (a ² - 1) ³

21

Given A = {1, 2 ..., 40}. Three numbers are randomly selected from set A. Then, the probability that the terms form an increasing G.P. is

1/494