10 Question MCQ (including Assertion)

Question 1 of 10

NCERT Exemplar

If $\sin \theta+\cos \theta=1$, then the value of $\sin 2 \theta$ is equal to

A 1 B $\frac{1}{2}$ C 0 D -1

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Question 2 of 10

NCERT Exemplar

The value of $\cot \left(\frac{\pi}{4}+\theta\right) \cot \left(\frac{\pi}{4}-\theta\right)$ is

A -1 B 0 C 1 D Not defined

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Question 3 of 10

NCERT Exemplar

Number of solutions of the equation $\tan x+\sec x=2 \cos x$ lying in the interval $[0,2 \pi]$ is

A 0 B 1 C 2 D 3

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Question 4 of 10

NCERT Exemplar

If $\sin \theta$ and $\cos \theta$ are the roots of the equation

$$ a x^2-b x+c=0 $$

then $a, b$, and $c$ satisfy the relation

A $a^2+b^2+2 a c=0$ B $\quad a^2-b^2+2 a c=0$ C $a^2+c^2+2 a b=0$ D $\quad a^2-b^2-2 a c=0$

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Question 5 of 10

NCERT Exemplar

The value of $\frac{1-\tan ^2 15^{\circ}}{1+\tan ^2 15^{\circ}}$ is

A 1 B $\sqrt{3}$ C $\frac{\sqrt{3}}{2}$ D 2

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Question 6 of 10

NCERT Exemplar

The value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 179^{\circ}$ is

A $\frac{1}{\sqrt{2}}$ B 0 C 1 D -1

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Question 7 of 10

NCERT Exemplar

If $\tan \theta=\frac{a}{b}$, then $b \cos 2 \theta+a \sin 2 \theta$ is equal to

A $a$ B $b$ C $\frac{a}{b}$ D None

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Question 8 of 10

NCERT Exemplar

$\cos 2 \theta \cos 2 \phi+\sin ^2(\theta-\phi)-\sin ^2(\theta+\phi)$ is equal to

A $\sin 2(\theta+\phi)$ B $\cos 2(\theta+\phi)$ C $\sin 2(\theta-\phi)$ D $\cos 2(\theta-\phi)$

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Question 9 of 10

NCERT Exemplar

The value of $\cos 12^{\circ}+\cos 84^{\circ}+\cos 156^{\circ}+\cos 132^{\circ}$ is

A $\frac{1}{2}$ B 1 C $-\frac{1}{2}$ D $\frac{1}{8}$

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Question 10 of 10

NCERT Exemplar

The value of $\sin \frac{\pi}{18}+\sin \frac{\pi}{9}+\sin \frac{2 \pi}{9}+\sin \frac{5 \pi}{18}$ is given by

A $\quad \sin \frac{7 \pi}{18}+\sin \frac{4 \pi}{9}$ B 1 C $\cos \frac{\pi}{6}+\cos \frac{3 \pi}{7}$ D $\cos \frac{\pi}{9}+\sin \frac{\pi}{9}$

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10 Question MCQ (including Assertion)