NTA Mathematics

Question 1

Which of the following is the derivative of sin(x)?

Accepted Answer

cos(x)

Answer

The derivative of sin(x) with respect to x is cos(x).

Question 2

What is the value of ∫₀¹ x² dx?

Accepted Answer

1/3

Answer

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)?

Accepted Answer

40

Answer

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:

Accepted Answer

2

Answer

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?

Accepted Answer

Ellipse

Answer

An equation of the form x²/a² + y²/b² = 1 with a ≠ b represents an ellipse.

NTA - National Testing Agency Practice Test