JEE Main 2023 · 10 Apr 2023 Shift 1

If f(x) = ((tan 1°)x + logₑ(123))/(x logₑ(1234) − (tan 1°)), x > 0, then the least value of f(f(x)) + f(f(4/x)) is

1. A0
2. B2
3. C4
4. D8

Let the complex number z = x + iy be such that (2z − 3i)/(2z + i) is purely imaginary. If x + y² = 0, then y⁴ + y² − y is equal to:

1. A2/3
2. B3/2
3. C3/4
4. D4/3

For the system of linear equations 2x − y + 3z = 5 3x + 2y − z = 7 4x + 5y + αz = β, which of the following is NOT correct?

1. AThe system is inconsistent for α = −5 and β = 8
2. BThe system has a unique solution for α ≠ −5 and β = 8
3. CThe system has infinitely many solutions for α = −5 and β = 9
4. DThe system has infinitely many solutions for α = −6 and β = 9

If A is a 3 × 3 matrix and |A| = 2, then |3 adj (|3A| A²)| is equal to

1. A3¹² · 6¹¹
2. B3¹² · 6¹⁰
3. C3¹⁰ · 6¹¹
4. D3¹¹ · 6¹⁰

If the coefficient of x⁷ in (ax − 1/(bx²))¹³ and the coefficient of x⁻⁵ in (ax + 1/(bx²))¹³ are equal, then a⁴b⁴ is equal to:

1. A11
2. B22
3. C33
4. D44

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

1. A231
2. B220
3. C210
4. D241

A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in cm²) is equal to

1. A675
2. B1025
3. C900
4. D800

If I(x) = ∫ e^(sin² x) (cos x sin 2x − sin x) dx and I(0) = 1, then I(π/3) is equal to

1. A−e^(3/4)
2. Be^(3/4)
3. C−(1/2)e^(3/4)
4. D(1/2)e^(3/4)