In a ∆ABC, if ∠A = 45^o, ∠B = 60^o and ∠C = 75^o, then the ratio of sides is ______.

1

(a)

2 : \(\sqrt { 6 } :(\sqrt { 3 } +1)\)

(b)

\(\sqrt { 2 } :6:(\sqrt { 3 } +1)\)

(c)

\(2:\sqrt { 6 } :(\sqrt { 3 } -1)\)

(d)

None

In a ΔABC if a = 5, b = 6 and c = 5, then ∠B is ______.

1

(a)

cos^-1 \(\left( \frac { 7 }{ 24 } \right) \)

(b)

cos^-1\(\left( \frac { 7 }{ 25 } \right) \)

(c)

cos^-1 \(\left( \frac { 7 }{30 } \right) \)

(d)

None

In a ΔABC, if the sides are 7cm, 4\(\sqrt { 3 } \) cm and .\(\sqrt { 13 } \) cm, then the smallest angle is ______.

1

(a)

45^o

(b)

60^o

(c)

30^o

(d)

90^o

If x = r sin\(\alpha\) cos \(\beta\), y = r sin\(\alpha\) sin \(\beta\)and z = r cos\(\alpha\), then X² + y² + Z² is independent of ______.

1

(a)

\(\alpha , \beta\)

(b)

\(\gamma , \alpha\)

(c)

\(\gamma , \beta\)

(d)

none of these

sin⁶\(\theta\) + cos⁶\(\theta\) + 3 sin²\(\theta\) cos²\(\theta\) is equal to ______.

1

(a)

0

(b)

1

(c)

4

(d)

2

If tan\(\theta\) + cot \(\theta\) = 5 then tan³ \(\theta\) + cot³ \(\theta\) is equal to ______.

1

(a)

135

(b)

140

(c)

110

(d)

90

If tan \(\theta\) + sec \(\theta\) = e^x then cos\(\theta\) is equal to ______.

1

(a)

\({e^x+e^{-x}\over 2}\)

(b)

\({e^x-e^{-x}\over 2}\)

(c)

\({e^x-e^{-x}\over e^x+e^x}\)

(d)

\({2\over e^x+e^{-x}}\)

If tan \(\theta={\alpha\over \alpha+1}\) and tan \(\phi ={1\over 2\alpha+1}\) , then (A+ B) is equal to ______.

1

(a)

0

(b)

\(\pi\over4\)

(c)

\(\pi\over6\)

(d)

\(\pi\over2\)

In a\(\triangle\) ABC, if tan A +tanB+ tan C = o then cot A cot B cot C is equal to______.

1

(a)

6

(b)

3

(c)

\(1\over6\)

(d)

\(1\over3\)

If sin \(\theta\) + sin \(\phi\)= \(\alpha\) and cos\(\theta\) - cos\(\phi\)= b then tan\({\theta -\phi\over 2}\) is equal to ______.

1

(a)

\(\sqrt{a^2+b^2}\)

(b)

\(-{a\over b}\)

(c)

\(-{b\over a}\)

(d)

\(1\over \sqrt{a^2-b^2}\)

If A, B, C are in A.P. then \({sinA-sinC\over cosC-cosA}\) is equal to ______.

1

(a)

sin B

(b)

cot B

(c)

sin 2B

(d)

cot 2B

If 4 sin²\(\theta=1\) then the values of \(\theta\) are ______.

1

(a)

\(2n\pi\pm{\pi\over3},n\in Z\)

(b)

\(n\pi\pm{\pi\over3},n\in Z\)

(c)

\(n\pi\pm{\pi\over6},n\in Z\)

(d)

\(2n\pi\pm{\pi\over6},n\in Z\)

The solution of the equation cos² \(\theta\) -+sin\(\theta\)+ 1=0lies in the interval ______.

1

(a)

\(({\pi\over 4},{3\pi\over4})\)

(b)

\((-{\pi\over 4},{3\pi\over4})\)

(c)

\(({3\pi\over 4},{5\pi\over4})\)

(d)

\(({5\pi\over 4},{7\pi\over4})\)

Find the general solutions of\(\sqrt{3}\) sin x-cos x =2 ______.

1

(a)

X = n\(\pi +{\pi\over 6}+(-1)^n{\pi\over2}\)

(b)

X = n\(\pi -{\pi\over 6}+(-1)^n{\pi\over2}\)

(c)

X = n\(\pi +{\pi\over 6}+(-1)^{n+1}{\pi\over2}\)

(d)

None