NDA / CDS / AFCAT - MCQ Practice Questions

The sum of first n natural numbers is 105. Find n.

Find the derivative of x³ + 2x² - 5x + 3 with respect to x.

If log₂(x) + log₂(x-1) = 3, find the value of x.

Find the value of sin 15°.

Find the coefficient of x² in the expansion of (2x - 3)⁴.

If the roots of equation x² + px + q = 0 are in ratio 2:3, find the relationship between p and q.

If a triangle has sides 6, 8, and 10, find its area using Heron's formula.

Solve: |2x - 5| = 7

If cos 2θ = $\frac{1}{2}$, find θ (where 0 < θ < 180°).

What is the domain of f(x) = √(x² - 4)?

Find the value of tan 75°.

A train 100 m long is moving at 60 km/h. How long does it take to cross a platform 200 m long?

If a:b = 3:4 and b:c = 5:6, find a:b:c.

Solve: 2x² - 7x + 3 = 0

If log₁₀(x) = 2, find x.

If cot θ = $\frac{12}{5}$, find sin θ (where θ is acute).

If A = {1,2,3} and B = {2,3,4}, find (A ∪ B) ∩ A.

A quadratic equation has roots 2 and -3. Find the equation.

If 3^x × 3^(x+1) = 243, find x.

A man covers 120 km in 3 hours. What is his speed in m/s?