(Mathematics) NDA/NA Solved Paper 2017-I

Total Questions: 50

1. Let S be the set of all persons living in Delhi. We say that x, y in S are related ifthey were born in Delhi on the same day.

Which one of the following is correct?

Correct Answer: (a) The relation is an equivalent relation
Solution:

S= {All persons living in Delhi}
A relationship is said to be equivalence relation if it is reflexive, symmetric and transitive.
⇒ Here, (x, y) ∈ R ⇒ reflexive relation.
⇒ Since, x є y are born on the same day,
x R y ⇒ y R x
So, it is symmeitric relation.
⇒ x R y, y R Z ⇒  x R Z (Date of births are same)
So, it is transitive relation.
So, the given relation is an equivalent relation.

2. Let A= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing two or three elements is

Correct Answer: (c) 165
Solution:

3. The value of i²ⁿ+ i²ⁿ⁺¹+i²ⁿ⁺²+i²ⁿ⁺³, where i =√-I, is 

Correct Answer: (a) 0
Solution:

4. If the difference between the roots of the equation 𝓍²+ kx +1 = 0 is strictly less than √5, where | k | ≥2, then k can be any element of the interval

Correct Answer: (a) [-3,-2] ᑌ [2, 3]
Solution:


5. If the roots of the equation 𝓍²+ p𝓍 + q = 0 are in the same ratio as those of the equation 𝓍² + lx + m = 0, then which one of the following is correct?

Correct Answer: (a) p²m= l²q
Solution:

6. The value of

where n is not a multiple of 3 and i= √-1, is

Correct Answer: (b) -1
Solution:

7. Three-digit numbers are formed from the digits 1, 2 and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?

Correct Answer: (d) 1332
Solution:

8. What is the sum of the series 0.3+0.33+0.333+ .... n terms?

Correct Answer: (a)
Solution:


9. If 1, ω, ω² are the cube roots of unity, then (1 + ω) (1 + ω²) (1 + ω³) (1 + ω + ω²) is equal to 

Correct Answer: (c) 0
Solution:

(1+ω) (1+ω²)(1 + ω³) (1+ω+0²).
So, (1+ω) (I+ω²)(1+ω³) (0) =0.

10. If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is

Correct Answer: (d) -(m+n)
Solution:

Given, Sₘ = n and Sₙ =m
This is direct formula
Sₘ₊ₙ = -(m+n)