NDA 2018 Paper 2 | Height and Distance Question 11 | Mathematics

A spherical balloon of radius r subtends an angle $$\alpha$$ at the eye of an observer, while the angle of elevation of it centre is $$\beta$$. What is the height of the centre of the balloon (neglecting the height of the observer) ?

$${{r\sin \beta } \over {\sin \left( {{\alpha \over 2}} \right)}}$$

$${{r\sin \beta } \over {\sin \left( {{\alpha \over 4}} \right)}}$$

$${{r\sin \left( {{\beta \over 2}} \right)} \over {\sin \alpha }}$$

$${{r\sin \alpha } \over {\sin \left( {{\beta \over 2}} \right)}}$$

NDA 2019 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

A ladder 9m long reaches a point 9m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60$$^\circ$$. What is the height of the flagstaff?

16.7m

10.5m

13.5m

15m

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y. If AB = z, then which one of the following is correct?

h² (cot²y $$-$$ cot²x) = z²

z² (cot²y $$-$$ cot²x) = h²

h² (tan²y $$-$$ tan²x) = z²

z² (tan²y $$-$$ tan²x) = h²

NDA Mathematics 16 April 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next two (02) items that follow :

A flagstaff 20 m long standing on a pillar 10 m high subtends an angle tan^-1(0.5) at a point P on the ground. Let θ be the angle subtended by the pillar at this point P.

If x is the distance of P from the bottom of the pillar, then consider the following statements :

1. x can take two values which are in the ratio 1 : 3

2. x can be equal to the height of the flagstaff

Which of the statements given above is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Questions Asked from Marks 2.5

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