NDA Mathematics 4 September 2022 | NDA Year Wise Previous Years Questions

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NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

Let A = $\left(\begin{array}{ccc}0 & \sin^2 \theta & \cos^2 \theta \\ \cos^2 \theta & 0 & \sin^2 \theta \\ \sin^2 \theta & \cos^2 \theta & 0\end{array}\right)$ and A = P + Q where P is symmetric matrix and Q is skew-symmetric matrix.

What is Q equal to ?

$\left(\begin{array}{ccc}0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0\end{array}\right)$

$\left(\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right)$

cos 2θ$\left(\begin{array}{ccc}0 & −1 & 1 \\ 1 & 0 & −1 \\ −1 & 1 & 0\end{array}\right)$

cos 2θ$\left(\begin{array}{ccc}0 & −1/2 & 1/2 \\ 1/2 & 0 & −1/2 \\ −1/2 & 1/2 & 0\end{array}\right)$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is the minimum value of determinant of A ?

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{3}{4}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

ABC is a triangular plot with AB = 16 m, BC = 10 m and CA = 10 m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45° at the vertex B.

What is the height of the lamp post ?

6 m

7 m

8 m

9 m

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

ABC is a triangular plot with AB = 16 m, BC = 10 m and CA = 10 m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45° at the vertex B.

What is $\frac{\text{AB}}{\sin \text{C}}$ equal to ?

17 m

$\frac{50}{3}$ m

$\frac{40}{3}$ m

16 m

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