NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

1. Let X be the set of all persons living in Delhi. The persons a and b in X are said to be related if the difference in their ages is at most 5 years. The relation is

Correct Answer: (d) retlexive and symmetric but not transitive
Solution:a - b ≤ 5
Let b - c ≤ 5
so a - c ≤ 10
as (a - b) ∈ R and ( b ∼ c) ∈ R
but (a - c) ∈ R
So it is not a transitive relation.
By considering all the options, we come to the conclusion that only option (d) is correct.

2. Solve the following equation

Correct Answer: (a)
Solution:


3. Solve the following equation

Correct Answer: (b) is greater than -8
Solution:

⇒ a(bc - 1) - (c - 1) + 1(1 - b) > 0
⇒ abc - a - c + 1 + 1 - b > 0
⇒ abc 2 - (a + b + c) > 0
⇒ abc > (a + b + c) - 2
Then; 0 > - 2 [which is correct]
Hence, abc =0
∴ After considering all the option; (b) is correct option.

4. Consider the following statements in respect of the determinant

Correct Answer: (c) Both 1 and 2
Solution:

5. What is (1000000001)₂ -(0.0101)₂ equal to ?

Correct Answer: (b) (512.6875)₁₀
Solution:

6. Solve the following equation

Correct Answer: (d)
Solution:

7. If z₁ and z₂ are complex numbers with |z₁| = |z₂| then which of the following is/are correct?

1. z₁ = z₂
2. Real part of z₁ = Real part of z₂
3. Imaginary part of z₁ = Imaginary part of z₂

Select the correct answer using the code given below :

Correct Answer: (d) None
Solution:

8. Solve the following equation


1. A and B commute.
2. AB is a null matrix.

Select the correct answer using the code given below:

Correct Answer: (b) 2 only
Solution:

9. The number of real roots of the equation x² - 3|x| + 2 = 0 is

Correct Answer: (a) 4
Solution:x² - 3|x| + 2 = 0
Case (i) when x ≥ 0
x² - 3x + 2 = 0
(x - 1) (x - 2) = 0
x = 1, 2(both roots satisfy the condition x ≥ 0 )
Case (ii) when x < 0
x² + 3x + 2 = 0
(x + 1) (x + 2) = 0
x = - 1, -2 (both roots satisfy the condition x < 0 )
So no. of real roots is 4.

10. If the sum of the roots of the equation ax² + bx + c = 0 is equal to the sum of their squares, then

Correct Answer: (c) ab + b² = 2ac
Solution: