NDA Mathematics 1st September 2024 | NDA Year Wise Previous Years Questions

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

Let (8 + 3√7) ²⁰ = U + V and (8 - 3√7) ²⁰ = W, where U is an integer and 0 < V < 1.

What is the value of (U + V)W?

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

The roots of the quadratic equation

a²(b² - c²)x² + b²(c² - a²)x + c²(a² - b²) = 0 are equal (a² ≠ b² ≠ c²).

Which one of the following statements is correct?

a², b², c² are in AP.

a2, b2, c2 are in GP.

a2, b2, c2 are in HP.

a2, b2, c2 are neither in AP nor in GP nor in HP.

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

The roots of the quadratic equation

a²(b² - c²)x² + b²(c² - a²)x + c²(a² - b²) = 0 are equal (a² ≠ b² ≠ c²).

Which one of the following is a root of the equation?

$\rm \frac{b^2(c^2-a^2)}{a^2(c^2-b^2)}$

$\rm \frac{b^2(c^2-a^2)}{a^2(b^2-c^2)}$

$\rm \frac{b^2(c^2-a^2)}{2a^2(c^2-b^2)}$

$\rm \frac{b^2(c^2-a^2)}{2a^2(b^2-c^2)}$

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

Direction : Consider the following for the items that follow :

Let $\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}$

What is A(adj A) equal to?

$\rm \begin{bmatrix}5&0&0\\\ 0&5&0\\\ 0&0&5\end{bmatrix}$

$\rm \begin{bmatrix}2&0&0\\\ 0&2&0\\\ 0&0&2\end{bmatrix}$

$\rm \begin{bmatrix}1/2&0&0\\\ 0&1/2&0\\\ 0&0&1/2\end{bmatrix}$

$\rm \begin{bmatrix}1&0&0\\\ 0&1&0\\\ 0&0&1\end{bmatrix}$