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Quiz 1
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Q.1
The value of cos
2
20° + cos
2
70° is?
$$\sqrt 2 $$
2
$$\frac{1}{{\sqrt 2 }}$$
1
Q.2
If $${\text{0}} < {\text{A}} < {90^ \circ }{\text{,}}$$ then the value of $$\frac{1}{2}\cot {\text{A}}$$ $$\left[ {\frac{{1 + \left( {\operatorname{sec A} - {\text{tan A}}} \right)}}{{\operatorname{cosecA} \left( {\sec {\text{A}} - {\text{tan A}}} \right)}}} \right]$$ = ?
0
2
1
$$\frac{1}{2}$$
Q.3
The value of following is : $$\frac{{\sin \theta .\operatorname{cosec} \theta .\tan \theta .\cot \theta }}{{{{\sin }^2}\theta + {\text{co}}{{\text{s}}^2}\theta }}$$ ?
2
0
tanθ
1
Q.4
If θ is a positive acute angle and 4cos
2
θ - 1 = 0, then the value of tan(θ - 15°) is equal to?
0
1
$$\sqrt 3 $$
$$\frac{1}{{\sqrt 3 }}$$
Q.5
The value of $$\frac{{\sin {{25}^ \circ }.\cos {{65}^ \circ } + \cos {{25}^ \circ }.\sin {{65}^ \circ }}}{{{{\tan }^2}{{70}^ \circ } - {\text{cose}}{{\text{c}}^2}{{20}^ \circ }}}$$ is?
-1
0
1
2
Q.6
If cosθ + secθ = $$\sqrt 3 ,$$ then the value of (cos
3
θ + sec
3
θ) is?
$$\frac{1}{{\sqrt 2 }}$$
1
0
$$\sqrt 2 $$
Q.7
The value of sin
2
2° + sin
2
4° + sin
2
6° + ........ + sin
2
90° is?
23
0
44
22
Q.8
If $$\theta + \phi = \frac{\pi }{2}$$ and $$\sin \theta = \frac{1}{2},$$ then the value of $${\text{sin}}\phi $$ is?
1
$$\frac{1}{{\sqrt 2 }}$$
$$\frac{1}{2}$$
$$\frac{{\sqrt 3 }}{2}$$
Q.9
Find the value of the following 3(sin
4
θ + cos
4
θ) + 2(sin
6
θ + cos
6
θ) + 12sin
2
θ.cos
2
θ = ?
3
2
0
5
Q.10
The numerical value of $$\frac{{{\text{co}}{{\text{s}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{60}^ \circ }}}$$ + $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ }}}{{{{\sin }^2}{{45}^ \circ }}}$$ - $$\frac{{{\text{ta}}{{\text{n}}^2}{{30}^ \circ }}}{{{\text{co}}{{\text{t}}^2}{{45}^ \circ }}}$$ - $$\frac{{{{\sin }^2}{{30}^ \circ }}}{{{\text{co}}{{\text{t}}^2}{{30}^ \circ }}}$$ is?
$$\frac{3}{4}$$
$$\frac{1}{4}$$
$$\frac{1}{2}$$
$${\text{1}}\frac{1}{4}$$
Q.11
If $${\text{A}} \times {\text{tan}}\left( {\theta + {{150}^ \circ }} \right)$$ = $${\text{B}} \times \tan $$ $$\left( {\theta - {{60}^ \circ }} \right){\text{,}}$$ the value of $$\frac{{{\text{A}} - {\text{B}}}}{{{\text{A}} + {\text{B}}}}$$ is?
$$ - \frac{{\sin \theta }}{2}$$
$$\frac{{\sin 2\theta }}{2}$$
$$\frac{{\cos 2\theta }}{2}$$
0
Q.12
If tanθ - cotθ = 0 find the value of sinθ + cosθ ?
0
1
$$\sqrt 2 $$
2
Q.13
If xsin60°.tan30° = sec60°.cot45° , then the value of x is?
2
$${\text{2}}\sqrt 3 $$
4
$${\text{4}}\sqrt 3 $$
Q.14
If $$x\cos \theta - y\sin \theta $$ = $$\sqrt {{x^2} + {y^2}} $$ and $$\frac{{{{\cos }^2}\theta }}{{{a^2}}}$$ + $$\frac{{{{\sin }^2}\theta }}{{{b^2}}}$$ = $$\frac{1}{{{x^2} + {y^2}}}{\text{,}}$$ then the correct relation is?
$$\frac{{{x^2}}}{{{b^2}}} - \frac{{{y^2}}}{{{a^2}}} = 1$$
$$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$$
$$\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1$$
$$\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$$
Q.15
If cos
2
θ - sin
2
θ = $$\frac{1}{3}{\text{,}}$$ where 0 ≤ θ ≤ $$\frac{\pi }{2}{\text{,}}$$ then the value of cos
4
θ - sin
4
θ is?
$$\frac{1}{3}$$
$$\frac{2}{3}$$
$$\frac{1}{9}$$
$$\frac{2}{9}$$
Q.16
The numerical value of 1 + $$\frac{1}{{{\text{co}}{{\text{t}}^2}{{63}^ \circ }}}$$ - $${\text{se}}{{\text{c}}^2}{27^ \circ }$$ + $$\frac{1}{{{{\sin }^2}{{63}^ \circ }}}$$ - $${\text{cose}}{{\text{c}}^2}{27^ \circ }$$ is?
1
2
-1
0
Q.17
The value of $$\frac{1}{{\sqrt 2 }}{\text{sin}}\frac{\pi }{6}$$ . $${\text{cos}}\frac{\pi }{4}$$ - $$\cot \frac{\pi }{3}$$ . $${\text{sec}}\frac{\pi }{6}$$ + $$\frac{{5\tan \frac{\pi }{4}}}{{12\sin \frac{\pi }{2}}}$$ is equal to?
0
1
2
$$\frac{3}{2}$$
Q.18
If $$\frac{{2{{\tan }^2}{{30}^ \circ }}}{{1 - {{\tan }^2}{{30}^ \circ }}}$$ + $${\sec ^2}{45^ \circ }$$ - $${\sec ^2}{0^ \circ }$$ = $$x\sec {60^ \circ }{\text{,}}$$ then the value of x is?
2
1
0
-1
Q.19
If xsin60°.tan30° - tan
2
45° = cosec60°.cot30° - sec
2
45° then x = ?
2
-2
6
-4
Q.20
If sinθ + cosθ = $$\sqrt 2 $$ sin(90° - θ) then the value of cotθ is?
-$$\sqrt 2 $$ - 1
$$\sqrt 2 $$ + 1
$$\sqrt 2 $$ - 1
-$$\sqrt 2 $$ + 1
Q.21
If $$\frac{{\sin \theta + \cos \theta }}{{\sin \theta - \cos \theta }} = 3{\text{,}}$$ then the value of $${\sin ^4}\theta $$ is?
$$\frac{{16}}{{25}}$$
$$\frac{2}{5}$$
$$\frac{1}{5}$$
$$\frac{3}{5}$$
Q.22
0 < θ < 90°, tanθ + sinθ =m and tanθ - sinθ = n, where m ≠ n, then the value of m
2
- n
2
is?
2(tan
2
θ + sin
2
θ)
4mn
4$$\sqrt {\text{mn}} $$
2(m
2
+ n
2
)
Q.23
If $$x{\sin ^2}{60^ \circ }$$ - $$\frac{3}{2}{\text{sec}}{60^ \circ }$$ . $${\text{ta}}{{\text{n}}^2}{30^ \circ }$$ + $$\frac{4}{5}{\sin ^2}{45^ \circ }$$ . $${\text{ta}}{{\text{n}}^2}{60^ \circ }$$ = 0, then x is?
$$ - \frac{1}{{15}}$$
-4
$$ - \frac{4}{{15}}$$
-2
Q.24
If 0° < A < 90°, then the value of tan
2
A + cot
2
A - sec
2
A cosec
2
A is?
0
1
2
-2
Q.25
The value of $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ } + 4{\text{se}}{{\text{c}}^2}{{30}^ \circ } - {\text{ta}}{{\text{n}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{30}^ \circ } + {\text{co}}{{\text{s}}^2}{{30}^ \circ }}}$$ is?
$$\frac{{64}}{{\sqrt 3 }}$$
$$\frac{{55}}{{12}}$$
$$\frac{{67}}{{12}}$$
$$\frac{{67}}{{10}}$$
Q.26
The value of 152(sin30° + 2cos
2
45° + 3sin30° + 4cos
2
45° + ...... + 17sin30° + 18cos
2
45°) is?
An integer but not perfect square
A rational number but not an integer
A perfect square of an integer
Irrational
Q.27
If α and β are positive acute angles, sin(4α - β) = 1 and cos(2α + β) = $$\frac{1}{2}{\text{,}}$$ then the value of sin(α + 2β) is?
0
1
$$\frac{{\sqrt 3 }}{2}$$
$$\frac{1}{{\sqrt 2 }}$$
Q.28
In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value of B is?
$$\frac{\pi }{6}$$
$$\frac{\pi }{{12}}$$
$$\frac{\pi }{4}$$
$$\frac{\pi }{2}$$
Q.29
If $$x\sin {45^ \circ }$$ = $$y\operatorname{cosec} {30^ \circ },$$ then $$\frac{{{x^4}}}{{{y^4}}}$$ is equal to?
4
3
6
3
2
3
8
3
Q.30
If tan
2
α = 1 + 2tan
2
β (α, β are positive acute angles), then √2cosα - cosβ is equal to?
0
$$\sqrt 2 $$
1
-1
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