JEE Main 2024 · 6 Apr 2024 Shift 2

Let f(x) = 1/(7 − sin 5x) be a function defined on R. Then the range of the function f(x) is equal to :

1. A[1/8, 1/5]
2. B[1/7, 1/5]
3. C[1/7, 1/6]
4. D[1/8, 1/6]

Let A = {1, 2, 3, 4, 5}. Let R be a relation on A defined by xRy if and only if 4x ≤ 5y. Let m be the number of elements in R and n be the minimum number of elements from A × A that are required to be added to R to make it a symmetric relation. Then m + n is equal to :

1. A23
2. B24
3. C25
4. D26

If z₁, z₂ are two distinct complex number such that |(z₁ − 2z₂)/(1/2 − z₁z̄₂)| = 2, then

1. Aboth z₁ and z₂ lie on the same circle.
2. Bz₁ lies on a circle of radius 1/2 and z₂ lies on a circle of radius 1.
3. Ceither z₁ lies on a circle of radius 1/2 or z₂ lies on a circle of radius 1.
4. Deither z₁ lies on a circle of radius 1 or z₂ lies on a circle of radius 1/2.

If A is a square matrix of order 3 such that det(A) = 3 and det(adj(−4 adj(−3 adj(3 adj((2A)⁻¹))))) = 2ᵐ 3ⁿ, then m + 2n is equal to :

1. A2
2. B4
3. C3
4. D6

If all the words with or without meaning made using all the letters of the word “NAGPUR” are arranged as in a dictionary, then the word at 315ᵗʰ position in this arrangement is :

1. ANRAGPU
2. BNRAPGU
3. CNRAGUP
4. DNRAPUG

Let 0 ≤ r ≤ n. If ⁿ⁺¹Cᵣ₊₁ : ⁿCᵣ : ⁿ⁻¹Cᵣ₋₁ = 55 : 35 : 21, then 2n + 5r is equal to :

1. A50
2. B55
3. C60
4. D62

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :

1. A150
2. B125
3. C160
4. D180

If the function f(x) = (1/x)²ˣ ; x > 0 attains the maximum value at x = 1/e then :

1. Aeᵖⁱ > πᵉ
2. Beᵖⁱ < πᵉ
3. Ce²ᵖⁱ < (2π)ᵉ
4. D(2e)ᵖⁱ > π²ᵉ