NTA Mathematics 1 — Questions and Answers
Question 1: Which of the following is the derivative of sin(x)?
- cos(x) (Correct answer)
- -cos(x)
- -sin(x)
- tan(x)
Correct answer: cos(x)
The derivative of sin(x) with respect to x is cos(x).
Question 2: What is the value of ∫₀¹ x² dx?
- 1/3 (Correct answer)
- 1/2
- 1/4
- 2/3
Correct answer: 1/3
Integrating x² gives x³/3, evaluated from 0 to 1 equals 1/3.
Question 3: If A is a 3×3 matrix and det(A) = 5, what is det(2A)?
- 40 (Correct answer)
- 10
- 20
- 5
Correct answer: 40
For an n×n matrix, det(kA) = kⁿ·det(A), so det(2A) = 2³×5 = 40.
Question 4: The sum of the series 1 + 1/2 + 1/4 + 1/8 + … (infinite geometric series) is:
- 2 (Correct answer)
- 1
- 3/2
- 4/3
Correct answer: 2
For an infinite geometric series with first term a=1 and ratio r=1/2, the sum is a/(1-r) = 1/(1-1/2) = 2.
Question 5: Which conic section is represented by the equation x²/9 + y²/4 = 1?
- Ellipse (Correct answer)
- Circle
- Parabola
- Hyperbola
Correct answer: Ellipse
An equation of the form x²/a² + y²/b² = 1 with a ≠ b represents an ellipse.
Question 6: What is the number of ways to arrange the letters of the word 'EXAM'?
- 24 (Correct answer)
- 12
- 48
- 6
Correct answer: 24
The word EXAM has 4 distinct letters, so the number of arrangements is 4! = 24.
NTA Mathematics 1
Which of the following is the derivative of sin(x)?