JEE Main 2023 · 8 Apr 2023 Shift 1

Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A × B each having at least 3 and at most 6 elements is :

1. A792
2. B772
3. C752
4. D782

If for z = α+iβ, |z+2| = z+4(1+i), then α + β and αβ are the roots of the equation

1. Ax² + 3x − 4 = 0
2. Bx² + 7x + 12 = 0
3. Cx² + 2x − 3 = 0
4. Dx² + x − 12 = 0

Let α, β, γ be the three roots of the equation x³ + bx + c = 0. If βγ = 1 = −α, then b³ + 2c³ − 3α³ − 6β³ − 8γ³ is equal to

1. A169/8
2. B155/8
3. C19
4. D21

Let A = ⎡2 1 0; 1 2 −1; 0 −1 2⎤. If |adj(adj(adj 2A))| = (16)ⁿ, then n is equal to

1. A10
2. B8
3. C12
4. D9

Let P = ⎡√3/2 1/2; −1/2 √3/2⎤, A = ⎡1 1; 0 1⎤ and Q = PAPᵀ. If PᵀQ²⁰⁰⁷P = ⎡a b; c d⎤, then 2a + b − 3c − 4d equal to

1. A2004
2. B2005
3. C2006
4. D2007

The number of arrangements of the letters of the word “INDEPENDENCE” in which all the vowels always occur together is

1. A14800
2. B33600
3. C16800
4. D18000

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is

1. A126(5!)²
2. B7(360)²
3. C7(720)²
4. D720

If the coefficients of three consecutive terms in the expansion of (1 + x)ⁿ are in the ratio 1 : 5 : 20, then the coefficient of the fourth term is

1. A1827
2. B3654
3. C5481
4. D2436