1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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

Let sin β be the GM of sin α and cos α; tan γ be the AM of sin α and cos α.

What is cos 2β equal to ?
A
$(\cos \alpha-\sin \alpha)^2$
B
$(\cos \alpha+\sin \alpha)^2$
C
$(\cos \alpha-\sin \alpha)^3$
D
$\frac{(\cos \alpha-\sin \alpha)^2}{2}$
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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

Let sin β be the GM of sin α and cos α; tan γ be the AM of sin α and cos α.

What is the value of sec2γ?
A
$\frac{3-\sin 2 \alpha}{5+2 \sin 2 \alpha}$
B
$\frac{5+\sin 2 \alpha}{3-\sin 2 \alpha}$
C
$\frac{3-2 \sin 2 \alpha}{4+\sin 2 \alpha}$
D
$\frac{3-\sin 2 \alpha}{4+3 \sin 2 \alpha}$
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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? 

A
1 only 
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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. 

What is a possible value of tan θ ? 
A
$\frac{3}{4}$
B
$\frac{2}{3}$
C
$\frac{1}{3}$
D
$\frac{1}{4}$
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