NDA NDA 1 2024 Mathematics Solved PYQ Paper

Let A and B be matrices of order 3 × 3. If |A| = 1/2² and |B| = 1/729,

then what is the value of

|2B[adj(3A)]| ?

If z is any complex number and iz³ + z² − z + i = 0,

where i = √(−1), then what is the value of

(|z| + 1)² ?

What is the sum of all four digit numbers formed by using all digits 0, 1, 4, 5 without repetition of digits?

If x, y and z are the cube roots of unity, then what is the value of xy + yz + zx?

A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man’s relatives and 3 of them are his wife’s relatives?

A triangle PQR is such that 3 points lie on the side PQ, 4 points on QR and 5 points on RP respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?

If log_ba = p, log_dc = 2p and log_fe = 3p, then what is (ace)^1/p equal to?

If −√2 and √3 are roots of the equation

a₀ + a₁x + a₂x² + a₃x³ + x⁴ = 0,

where a₀, a₁, a₂, and a₃ are integers, then which one of the following is correct?

Let z₁ and z₂ be two complex numbers such that

(z₁z₂̅) / (z₁̅z₂) = 1,

then what is the value of

Re[(z₁/z₂) + 1] ?

If 26! = n8^k, where k and n are positive integers, then what is the maximum value of k?