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Q 1. In circular measure, the value of the angle {tex} 11 ^ { \circ } 15 ^ { \prime } {/tex} is
{tex} \frac { \pi ^ { c } } { 16 } {/tex}
{tex} \frac { \pi ^ { c } } { 8 } {/tex}
{tex} \frac { \pi ^ { c } } { 4 } {/tex}
{tex} \frac { \pi ^ { c } } { 12 } {/tex}
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Q 2. In a triangle {tex} \mathrm { ABC } , \angle \mathrm { ABC } = 75 ^ { \circ } {/tex} and {tex} \angle \mathrm { ACB } = \frac { \pi ^ { \mathrm { c } } } { 4 } \cdot {/tex} The circular measure of {tex} \angle \mathrm { BAC } {/tex} is
{tex} \frac { 5 \pi } { 12 } {/tex} radian
{tex} \frac { \pi } { 3 } {/tex} radian
{tex} \frac { \pi } { 6 } {/tex} radian
{tex} \frac { \pi } { 2 } {/tex} radian
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Q 3. The circular measure of an angle of an isosceles triangle is {tex} \frac { 5 \pi } { 9 } {/tex} Circular measure of one of the other angles must be
{tex} \frac { 5 \pi } { 18 } {/tex}
{tex} \frac { 5 \pi } { 9 } {/tex}
{tex} \frac { 2 \pi } { 9 } {/tex}
{tex} \frac { 4 \pi } { 9 } {/tex}
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Q 4. The degree measure of 1 radian (taking {tex} \pi = \frac { 22 } { 7 } {/tex} ) is
{tex} 57 ^ { \circ } 61 ^ { ' } 22 ^ { " } {/tex}(approx )
{tex} 57 ^ { \circ } 16 ^ { ' } 22 ^ { "} {/tex} (approx.)
{tex} 57 ^ { \circ } 22 ^ { \prime } 16 ^ { "} {/tex} (approx.)
{tex} 57 ^ { \circ } 32 ^ { \prime } 16 ^ { " } {/tex} (approx.)
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Q 5. If the sum of two angles is {tex} 135 ^ { \circ } {/tex} and their difference is {tex} \frac { \pi } { 12 } , {/tex} then the circular measure of the greater angle is
{tex} \frac { 2 \pi } { 3 } {/tex}
{tex} \frac { 3 \pi } { 5 } {/tex}
{tex} \frac { 5 \pi } { 12 } {/tex}
{tex} \frac { \pi } { 3 } {/tex}
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Q 6. If {tex} 0 \leq \theta \leq \frac { \pi } { 2 } {/tex} and {tex} \sec ^ { 2 } \theta + \tan ^ { 2 } \theta {/tex} {tex} = 7 , {/tex} then {tex} \theta {/tex} is
{tex} \frac { 5 \pi } { 12 } {/tex} radian
{tex} \frac { \pi } { 3 } {/tex} radian
{tex} \frac { \pi } { 5 } {/tex} radian
{tex} \frac { \pi } { 6 } {/tex} radian
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Q 7. If the sum and difference of two angles are {tex} \frac { 22 } { 9 } {/tex} radian and {tex} 36 ^ { \circ } {/tex} respectively, then the value of smaller angle in degree taking the value of {tex} \pi {/tex} as {tex} \frac { 22 } { 7 } {/tex} is:
{tex} 52 ^ { \circ } {/tex}
{tex} 60 ^ { \circ } {/tex}
{tex} 56 ^ { \circ } {/tex}
{tex} 48 ^ { \circ } {/tex}
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Q 8. The circular measure of the included angle formed by the hour hand and minute hand of a clock at 3 p.m. will be
{tex} \frac { \pi } { 4 } {/tex}
{tex} \frac { \pi } { 3 } {/tex}
{tex} \frac { 5 \pi } { 12 } {/tex}
{tex} \frac { \pi } { 2 } {/tex}
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Q 9. If {tex} \theta {/tex} is an acute angle and {tex} \sin ( \theta + {/tex} {tex} \left. 18 ^ { \circ } \right) = \frac { 1 } { 2 } , {/tex} then the value of {tex} \theta {/tex} in circular measure is :
{tex} \frac { \pi } { 12 } {/tex} radians
{tex} \frac { \pi } { 15 } {/tex} radians
{tex} \frac { 2 \pi } { 5 } {/tex} radians
{tex} \frac { 3 \pi } { 13 } {/tex} radians
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Q 10. What is the measure of central angle of the are whose length is {tex} 11 \mathrm { cm } {/tex} and radius of the circle is {tex} 14 \mathrm { cm } ? {/tex}
{tex} 45 ^ { \circ } {/tex}
{tex} 60 ^ { \circ } {/tex}
{tex} 75 ^ { \circ } {/tex}
{tex} 90 ^ { \circ } {/tex}
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Q 11. The minimum value of {tex} 2 \sin ^ { 2 } \theta {/tex} {tex} + 3 \cos ^ { 2 } \theta {/tex} is
0
3
2
1
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Q 12. The value of {tex} \tan 4 ^ { \circ } . \tan 43 ^ { \circ } . \tan 47 ^ { \circ } . \tan 86 ^ { \circ } \mathrm { is } {/tex}
2
3
1
4
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Q 13. The value of {tex} \tan 1 ^ { \circ } \tan 2 ^ { \circ } \tan 3 ^ { \circ } \ldots \ldots . {/tex} {tex} \tan 89 ^ { \circ } {/tex} is :
1
0
{tex} \sqrt { 3 } {/tex}
{tex} \frac { 1 } { \sqrt { 3 } } {/tex}
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Q 14. The measure of the angles of a triangle are in the ratio {tex}2: 7:11 . {/tex} Measures of angles are
{tex} 16 ^ { \circ } , 56 ^ { \circ } , 88 ^ { \circ } {/tex}
{tex} 18 ^ { \circ } , 63 ^ { \circ } , 99 ^ { \circ } {/tex}
{tex} 20 ^ { \circ } , 70 ^ { \circ } , 90 ^ { \circ } {/tex}
{tex} 25 ^ { \circ } , 175 ^ { \circ } , 105 ^ { \circ } {/tex}
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Q 15. The angles of a triangle are {tex} ( x + 5 ) ^ { \circ } , ( 2 x - 3 ) ^ { \circ } {/tex} and {tex} ( 3 x + 4 ) ^ { \circ } . {/tex} The value of {tex} x {/tex} is
30
31
29
28
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Q 16. The value of {tex} \cot 10 ^ { \circ } . {/tex} cot {tex} 20 ^ { \circ }. {/tex} cot {tex} 60 ^ { \circ } . \cot 70 ^ { \circ } . \cot 80 ^ { \circ } {/tex} is
{tex}1{/tex}
{tex}-1{/tex}
{tex} \sqrt { 3 } {/tex}
{tex} \frac { 1 } { \sqrt { 3 } } {/tex}
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Q 17. The value of {tex} \sin ^ { 2 } 1 ^ { \circ } + \sin ^ { 2 } 5 ^ { \circ } + {/tex} {tex} \sin ^ { 2 } 9 ^ { \circ } + \ldots + \sin ^ { 2 } 89 ^ { \circ } {/tex} is
{tex} 11 \frac { 1 } { 2 } {/tex}
{tex} 11 \sqrt { 2 } {/tex}
11
{tex} \frac { 11 } { \sqrt { 2 } } {/tex}
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Q 18. If {tex} \tan 15 ^ { \circ } = 2 - \sqrt { 3 } , {/tex} the value of {tex} \tan 15 ^ { \circ } \cot 75 ^ { \circ } + \tan 75 ^ { \circ } \cot 15 ^ { \circ } \mathrm { is } {/tex}
14
12
10
8
