JEE Main 2024 · 4 Apr 2024 Shift 2

Let a relation R on N × N be defined as: (x₁, y₁) R (x₂, y₂) if and only if x₁ ≤ x₂ or y₁ ≤ y₂. Consider the two statements: (I) R is reflexive but not symmetric. (II) R is transitive Then which one of the following is true?

1. AOnly (I) is correct.
2. BOnly (II) is correct.
3. CBoth (I) and (II) are correct.
4. DNeither (I) nor (II) is correct.

The area (in sq. units) of the region S = {z ∈ C : |z − 1| ≤ 2; (z + z̄) + i(z − z̄) ≤ 2, Im(z) ≥ 0} is

1. A3π/2
2. B7π/3
3. C7π/4
4. D17π/8

Let A = [1 2; 0 1] and B = I + adj(A) + (adj A)² + ... + (adj A)¹⁰. Then, the sum of all the elements of the matrix B is:

1. A22
2. B−110
3. C−124
4. D−88

If the coefficients of x⁴, x⁵ and x⁶ in the expansion of (1 + x)ⁿ are in the arithmetic progression, then the maximum value of n is:

1. A7
2. B14
3. C21
4. D28

The value of (1 × 2² + 2 × 3² + ... + 100 × (101)²)/(1² × 2 + 2² × 3 + ... + 100² × 101) is

1. A31/30
2. B305/301
3. C32/31
4. D306/305

Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the arithmetic mean of a, b and c is 8, then the cube of the geometric mean of a, b and c is

1. A128
2. B312
3. C120
4. D316

Let f(x) = 3√(x − 2) + √(4 − x) be a real valued function. If α and β are respectively the minimum and the maximum values of f, then α² + 2β² is equal to

1. A24
2. B38
3. C44
4. D42

If the function f(x) = { (72ˣ − 9ˣ − 8ˣ + 1)/(√2 − √(1 + cos x)), x ≠ 0; a logₑ 2 logₑ 3, x = 0 } is continuous at x = 0, then the value of a² is equal to

1. A746
2. B968
3. C1152
4. D1250