1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

What is the number of solutions of $(\sin \theta - \cos \theta)^2 = 2$ where $-\pi < \theta < \pi$?

A

Only one

B

Only two

C

Four

D

No solution

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

$ABC$ is a triangle such that angle $C = 60^{\circ}$, then what is $\frac{\cos A + \cos B}{\cos \left(\frac{A - B}{2}\right)}$ equal to?

A

2

B

$\sqrt{2}$

C

1

D

$\frac{1}{\sqrt{2}}$

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

What is $\sqrt{15 + \cot^2 \left( \frac \pi 4 - 2 \cot^{-1} 3 \right)}$ equal to?

A

1

B

7

C

8

D

16

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

What is the value of $\sin10^{\circ} \cdot \sin50^{\circ} + \sin50^{\circ} \cdot \sin250^{\circ} + \sin250^{\circ} \cdot \sin10^{\circ}$ equal to?

A

$-\frac{1}{4}$

B

$-\frac{3}{4}$

C

$3 \sin 10^{\circ} / 4$

D

$3 \cos 10^{\circ} / 4$

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