Mathmatics NDA/NA Solved Paper 2020-I (1-50)

Total Questions: 50

1. What is the modulus of the complex number

Correct Answer: (b) 1
Solution:

2. Consider the proper subsets of {1, 2, 3, 4}. How many of these proper subsets are superset of the set {3} ?

Correct Answer: (c) 7
Solution:

3. Solve the following equation.

Correct Answer: (a) D < 0
Solution:

4. What is the sum of last five coefficients in the expansion of (1+ 𝓍)⁹ when it is expanded in ascending powers of 𝓍 ?

Correct Answer: (a) 256
Solution:

5. Consider the following in respect of a nonsingular matrix of order 3 :

(1) A (adj A) = (adj A) A
(2) |adj A| = |A| Which of the above statements is/are correct ?

Correct Answer: (a) 1 only
Solution:

6. The center of the circle

(x - 2a) (x - 2b) + (y - 2c) (y - 2d) = 0 is

Correct Answer: (c) (a + b, c + d)
Solution:

7. The point (1, -1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then what is the equation of the other diagonal ?

Correct Answer: (c) 2𝓍 - 3y = 5
Solution:

8. Let P(𝓍, y) be any point on the ellipse 25𝓍² + 16y2 = 400. If Q(0, 3) and R(0, - 3) are two points, then what is (PQ + PR) equal to?

Correct Answer: (b) 10
Solution:


9. If the circumcenter of the triangle formed by the lines 𝓍 + 2 = 0, y + 2 = 0 and k𝓍 + y + 2 = 0 is (- 1, - 1), then what is the value of k ?

Correct Answer: (c) 1
Solution:

Equation of two sides of the triangle are 𝓍 + 2 = 0 and y + 2 = 0.
They intersect at right angle.

10. In the parabola, y² = 𝓍, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle θ?

Correct Answer: (b) cosθ . cosec²θ
Solution: