NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

11. What is x - y equal to?

Consider x = 4 tan⁻¹(1/5), y = tan⁻¹(1/70) and z = tan⁻¹(1/99)

Correct Answer: (c) tan⁻¹(8281 / 8450)
Solution:


12. What is x - y + z equal to?

Consider x = 4 tan⁻¹(1/5), y = tan⁻¹(1/70) and z = tan⁻¹(1/99)

Correct Answer: (b) π/3
Solution:

13. What is the circumcentre of the triangle ABC?

Consider the triangle ABC with vertices A(- 2, 3) , B(2, 1) and C (1,2).

Correct Answer: (a) (-2, -2)
Solution:



14. What is the centroid of the tirnalge ABC?

Consider the triangle ABC with vertices A(- 2, 3) , B(2, 1) and C (1,2).

Correct Answer: (b) (1/3, 2)
Solution:

15. What is the foot of the altitude from the vertex A of the triangle ABC?

Consider the triangle ABC with vertices A(- 2, 3) , B(2, 1) and C (1,2).

Correct Answer: (d) (-1, 4)
Solution:

16. Let X be the set of all persons living in a city. Persons x, y in X are said to be related as x < y if y is at least 5 years older than x. Which one of the following is correct?

Correct Answer: (b) The relation is transitive but neither reflexive nor symmetric
Solution:

17. Which one of the following matrices is an elementary matrix?

Correct Answer: (b)
Solution:

18. Consider the following statements in respect of the given equation:

(x² + 2)² + 8x² = 6x(x ² + 2)

1. All the roots of the equation are complex.
2. The sum of all the roots of the equation is 6.

Which of the above statements is/are correct?

Correct Answer: (b) 2 only
Solution:


19. In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds -9 and -1 for roots. The correct equation is

Correct Answer: (a) x² - 10x + 9 = 0
Solution:


20. Solve the following equation

Correct Answer: (c) 7I
Solution: