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

If $f(\theta)=\frac{1}{1+\tan \theta}$ and $\alpha+\beta=\frac{5\pi}{4}$, then what is the value of $f(\alpha) f(\beta)$?

A

$\frac{1}{2}$

B

$\frac{1}{2}$

C

$1$

D

$2$

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

If $\tan \alpha$ and $\tan \beta$ are the roots of the equation $x^2-6x+8=0$, then what is the value of $\cos(2 \alpha+2 \beta)$?

A

$\frac{13}{75}$

B

$\frac{13}{85}$

C

$\frac{17}{85}$

D

$\frac{19}{85}$

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

What is the value of $\tan 65^\circ +2 \tan 45^\circ-2 \tan 40^\circ-\tan 25^\circ$?

A

$0$

B

$1$

C

$2$

D

$4$

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

Consider the following statements:

1. In a triangle $ABC$, if $\cot A \cdot \cot B \cdot \cot C>0$, then the triangle is an acute-angled triangle.

2. In a triangle $ABC$, if $\tan A \cdot \tan B \cdot \tan C > 0$, then the triangle is an obtuse-angled triangle.

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

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