NDA II - Mathematics Question Paper 2017 - NDA MCQ

If Sn = nP   , where S_n denotes the sum of the first n terms of an AP, then the common difference is

The roots of the equation (q − r)x² + (r − p)x + (p − q) = 0 are

If E is the universal set and A = B ∪ C, then the set
E − (E − (E − (E − (E − A)))) is same as the set

If A={x:x is a multiple of 2},B={x:x is a multiple of 5} and C={x:x is a multiple of 10}, then A∩(B∩C) is equal to 

If α and β are the roots of the equation 1 + x + x² = 0 , then the matrix product  is equal to?

If |a| denotes the absolute value of an integer, then which of the following are correct?
I.|ab| = |a||b|
II. |a + b| ≤ |a| + |b|
III. |a − b| ≥ |a| − |b|

Q. Select the correct answer using the code given below.

How many different permutations can be made out of the letters of the word “PERMUTATION”?

If A =  and k =1/2i, where i = 
√−1 , then kA is equal to

The sum of all real roots of the equation
|x − 3|² + |x − 3| − 2 = 0 is

If is given that the roots of the equation x² − 4x − log₃ P = 0 are real. For this, the minimum value of P is

If A is a square matrix, then the value of adj A^T − (adj A)^T is equal to

The value of the product
 … up to infinite terms is

The value of the determinant

for​all values of θ, is

The number of terms in the expansion of (x + a)¹⁰⁰ + (x − a)¹⁰⁰ after simplification is

In the expansion of (1 +)⁵⁰ , the sum of the coefficients of odd powers of x is

If a, b, c are non-zero real numbers, then the inverse of the matrix

A person is to count 4500 notes. Let a_n denote the number of notes he counts in the nth minute.
If a₁ = a₂ = a₃ = . . = a₁₀ = 150 , and
a₁₀ , a₁₁ , a₁₂ . .. are in AP with the common difference −2 , then the time taken by him to count all the notes is

The smallest positive integer n for which
 n = 1 , is

If we define a relation R on the set N × N as (a, b) R (c, d) ⟺ a + d = b + c for all (a, b), (c, d) ∈ N × N, then the

If y = x + x2 + x3 + ⋯ up to infinite terms, where x < 1 , then which of the following is correct?

If α and β are the roots of the equation 3x² + 2x + 1 = 0 , then equation whose roots are α + β⁻¹ and β + α⁻¹ is

The value of

Up to infinite terms is

A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is

The system of equation kx + y + z = 1,
x + ky + z = k and x = y + kz = k2 has nosolution if k equals

If 1.3 + 2.3² + 3.3³ + ⋯ + n. 3ⁿ 
Then a and b are respectively

In △ PQR, ∠R  are the roots of the equation ax² + bx + c = 0, then which one of the following is correct?

If , then the maximum value of |z| is equal to