1
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $p=\frac{1}{3}-\frac{\tan 3 x}{\tan x}$ and q = 1 - 3 tan2 x, 0 < x < π, $ x \neq \frac{\pi}{2}$.

What is pq equal to ?
A
1
B
2
C
$\frac{8}{3}$
D
$-\frac{8}{3}$
2
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $p=\frac{1}{3}-\frac{\tan 3 x}{\tan x}$ and q = 1 - 3 tan2 x, 0 < x < π, $ x \neq \frac{\pi}{2}$.

For how many values of x does $\frac{1}{p}$ become zero?
A
No value
B
Only one value
C
Only two values
D
Only three values
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$

What is a value of sin 3x + sin 3y?
A
-1
B
0
C
1
D
3
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$

What is a value of cos3 x + cos3 y?
A
$ \frac{3 \sqrt{3}}{8}$
B
$ \frac{3 \sqrt{6}}{8} $
C
$ \frac{3 \sqrt{6}}{4}$
D
1
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