1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
$$ \text { What is } \frac{\sqrt{3} \cos 10^{\circ}-\sin 10^{\circ}}{\sin 25^{\circ} \cos 25^{\circ}} \text { equal to ? } $$
A

1

B

$\sqrt{3}$

C

2

D

4

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

What is $\sin 9^\circ - \cos 9^\circ$ equal to?

A

$\frac{\sqrt{5} - \sqrt{5}}{2}$

B

$\frac{\sqrt{5} - \sqrt{3}}{2}$

C

$\frac{\sqrt{5} - \sqrt{5}}{2}$

D

$\frac{\sqrt{5} - \sqrt{5}}{4}$

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

If in a triangle $ABC$, $\sin^3A + \sin^3B + \sin^3C = 3\sin A \sin B \sin C$, then what is the value of the determinant $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$, where $a$, $b$, $c$ are sides of the triangle?

A

$a + b + c$

B

$ab + bc + ca$

C

$(a + b)(b + c)(c + a)$

D

0

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

If $\cos^{-1} x = \sin^{-1} x$, then which one of the following is correct?

A

$x = 1$

B

$x = \frac{1}{2}$

C

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

D

$x = \frac{1}{\sqrt{3}}$

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