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

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.

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 ?

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

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

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

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

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is the value of cosec$\left(−\frac{73 \pi}{3}\right)$ ?

$\frac{2}{\sqrt{3}}$

$−\frac{2}{\sqrt{3}}$

−2

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

What is the value of $\cos \left(\frac{5 \pi}{17}\right)+\cos \left(\frac{7 \pi}{17}\right)+2 \cos \left(\frac{11 \pi}{17}\right) \cos \left(\frac{\pi}{17}\right)$ ?

4 cos$\left(\frac{6 \pi}{17}\right)$ cos$\left(\frac{\pi}{17}\right)$

4 cos$\left(\frac{11 \pi}{17}\right)$ cos$\left(\frac{\pi}{17}\right)$

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