If sin \(\theta\) + cos \(\theta\) = 1 then sin⁶ \(\theta\) + cos⁶ \(\theta\) is _______________

(a)

1

(b)

0

(c)

-1

(d)

2

If the arcs of same lengths in two circles sustend central angles 30° and 40° find the ratio of their radii _______________

(a)

3 : 4

(b)

4 : 3

(c)

7 : 12

(d)

none of these

If sin(45 ° + 10°) - sin(45° -10°) = \(\sqrt{2}\)sin x then x is ___________ 

(a)

0^o

(b)

5°

(c)

10°

(d)

15°

The quadratic equation whose roots are tan 75° and cot 75° is _______________

(a)

x²+4x+ 1 = 0

(b)

4x²-x+ 1 = 0

(c)

4x²+ 4x - 1 = 0

(d)

x² - 4x + 1 = 0

sin² \((22{1\over 2}^o)\) is ____________ 

(a)

\({\sqrt{2-\sqrt{2}}}\over2\)

(b)

\({2\sqrt{2}-1\over 4\sqrt{2}}\)

(c)

\({\sqrt{2-\sqrt{2}\over 2}}\)

(d)

none of these

The value of sin\({\pi\over 48}cos {\pi \over 48} cos {\pi \over 24}cos {\pi \over 12}cos{\pi \over 6}cos {\pi \over 3}\) is _____________ 

(a)

\(\sqrt{3}\over32\)

(b)

\(\sqrt{3}\over64\)

(c)

_{\({3}\over32\)}

(d)

_{\({3}\over64\)}

In a \(\triangle\) ABC, C = 90° then the value of sin A + sin B - 2\(\sqrt{2} cos{A\over2}cos {B\over 2}is\) _______________

(a)

-1

(b)

1

(c)

0

(d)

\({1\over 2}\)

The general solution of cosec_\(\theta\) = -2 is _______________

(a)

\(2n\pi +(-1)^n({\pi\over 6})\)

(b)

\(n\pi +(-1)^n({-\pi\over 6})\)

(c)

\(2n\pi \pm({\pi\over 6})\)

(d)

\(-{\pi\over 6}+n\pi\)

In a \(\triangle\)ABC, \(\hat{A}\) = 60°, \(\hat{C}\) = 30°, b = 2\(\sqrt{3}\) ,c = 2 then a is _______________

(a)

0

(b)

1

(c)

4

(d)

2

In \(\triangle\)ABC, \(\hat{C}\) = 90° then a cos A + b cos B is _______________

(a)

2R sin B

(b)

2 sin B

(c)

0

(d)

2a sin B