Mathematics (NDA/NA SOLVED PAPER 2021-I) (51 to 100)

Total Questions: 50

1. f(x + 1) = x²- 3x + 2 then what is f(x) equal to?

Correct Answer: (b) x² - 5x + 6
Solution:

2. If x², x, - 8 are in AP, then which one of the following is correct?

Correct Answer: (c) x ∈ {- 2, 4}
Solution:

3. The third term of a GP is 3. What is the product of its first five terms?

Correct Answer: (b) 243
Solution:

4. The element in the iᵗʰ row and the jᵗʰ column of a determinant of third order is equal to 2(i + j). What is the value of the determinant?

Correct Answer: (a) 0
Solution:

5. With the numbers 2, 4, 6, 8, all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?

Correct Answer: (d) 0
Solution:

6. What is the radius of the circle 4x² + 4y² - 20x + 12y - 15 =0?

Correct Answer: (d) 3.5 units
Solution:

7. A parallelogram has three consecutive vertices (-3, 4), (0,-4) and (5, 2). The fourth vertex is

Correct Answer: (a) (2, 10)
Solution:Let ABCD is a parallelogram as shown in figure.
Point O is the point of intersection of two diagonals.

8. If the lines y + px = 1 and y - qx = 2 are perpendicular, then which one of the following is correct?

Correct Answer: (c) pq - 1 = 0
Solution:Two lines are perpendicular, if a₁ a₂+ b₁b₂ = 0
1 - p . q = 0 ⇒ pq - 1 = 0 .

9. If A, B and C are in AP, then the straight line Ax + 2By + C = 0 will always pass through a fixed point.

The fixed point is

Correct Answer: (d) (1, -1)
Solution:As A, B and C are in A.P.
2B = A + C ⇒ A - 2B + C = 0
From given equation Ax + 2By + C = 0.
For (x, y) = (1,-1), A - 2B + C = 0
Hence, line always passes through (1,-1).

10. If the image of the point (-4, 2) by a line mirror is (4, -2), then what is the equation of the line mirror?

Correct Answer: (b) y = 2x
Solution:Slope of line mirror = 2
and equation of line mirror will slope m = 2 and passes through (0, 0) is y = 2x.