Mathematics Question Paper of NDA(National Defence Academy & Naval Academy) Exam (II), 2006

Directions :

The following four (4) items consist of two statements, one labelled as the ' Assertion (A)' and the other as 'Reason (R)'. You are to. examine these two statements carefully and select the answers to these items using the code given below :

Code:

(a) Both A and R are individually true and R is the correct explanation af A

(b) Both A and R are individually true but R is not the correct explanation of A

(c) A is true but R is false

(d) A is false but R is true

1. Assertion (A) : The number of triangles that can be formed by joining the mid-points of any three adjacent faces of a cube is 20.

Reason (R) : If there are 11 points on a plane and none of them are collinear, then the number of triangles that can be formed is C (n, 3).

Ans: (a)

2. Assertion (A) : The number of selections of 20 distinct things taken 8 at a time is same as that taken 12 at a time.

Reason (R) : C (n, r) = C (n, s), if n = r + s.

Ans: (a)

3. Assertion (A) : 1/8, log_a²a, log_aa² are in GP but not in AP

Reason (R) : x, y, z are in AP as well as in GP if x = y = z.

Ans: (a)

4. Assertion (A) : If Z₁ = 3 + √-4, and Z₂ = 3 + √-25, Z₁/Z₂ is a complex number.

Reason (R) : If Z₁, Z₂ are complex numbers, then Z₁/Z₂ is always a complex number.

Ans: (a)

5. An aircraft has. three engines A, Band C. The aircraft crashes if all the three engines fail. The probabilities of failure are 0.03, 0.02 and 0.05 for engines. A, Band C respectively. What is the probability that the aircraft will not crash?

(a) 0.00003    

(b) 0.90

(c) 0.99997    

(d) 0.90307

Ans: (c)

Download Mathematics Paper of NDA Exam II 2006