Mathematics Question Paper of NDA(National Defence Academy & Naval Academy) Exam (II), 2009

1. If

(1 + 3 + 5 + ... + p) + (1 + 3 + 5 + ... + q)
                                              = (1 + 3 + 5 + ... + r)

where each set of parentheses contains the sum of consecutive odd integers as shown, what is the smallest possible value of (p + q + r) where p > 6?

(a) 12    

(b) 21    

(c) 45    

(d) 54

Ans: (b)

2. Let A = {x| x < 9, x ε N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?

(a) 12

(b) 21

(c) 27

(d) 30

Ans: (d)

3. Let A = {-1, 2, 5, 8}, B = {0,1,3,6,7} and R be the relation 'is one less than' from A to B, then how many elements will R contain?

(a) 2

(b) 3

(c) 5

(d) 9

Ans: (b)

4. A mapping f : R → R which is defined as f(x) = cos x; x εR is

(a) One-one only

(b) Onto only

(c) One-one onto

(d) Neither one-one nor onto

Ans: (d)

5. If a is a complex number such that a² + a + 1 = 0, then what is a ³¹ equal to?

(a) a

(b) a²

(c) 0

(d) 1

Ans: (a)

Download Mathematics Paper of NDA Exam II 2009