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

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 cos A + cos B + cos C equal to ?

$\frac{41}{25}$

$\frac{37}{25}$

$\frac{33}{25}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at distance y from the foot of the tower (x > y). The angles of elevation of the top of the tower from P and Q are 15° and 75° respectively.

At what height is the top of the tower above the ground level ?

$\frac{\text{x−y}}{2\sqrt{3}}$

$\frac{\text{x−y}}{4\sqrt{3}}$

$\frac{\text{x−y}}{4}$

$\frac{\text{x−y}}{2}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

If θ is the inclination of the tower to the horizontal, then what is cot θ equal to ?

2 + $\frac{\sqrt{3}(\text{x−y})}{\text{x+y}}$

2 − $\frac{\sqrt{3}(\text{x−y})}{\text{x+y}}$

2 + $\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}$

2 − $\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is the length of the tower ?

$\frac{\text{x−y}}{2 \sqrt{3}} \sqrt{1+\left\{2+\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$

$\frac{\text{x−y}}{2 \sqrt{3}} \sqrt{1+\left\{2−\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$

$\frac{\text{x−y}}{4 \sqrt{3}} \sqrt{1+\left\{2+\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$

$\frac{\text{x−y}}{4 \sqrt{3}} \sqrt{1+\left\{2−\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$

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