\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

(a)

\(\sqrt{2}\)

(b)

\(\sqrt{3}\)

(c)

2

(d)

4

cos 2ፀ cos 2ф + sin²(ፀ - ф) - sin²(ፀ + ф) is equal to

(a)

sin2(ፀ+\(\phi \))

(b)

cos2(ፀ+\(\phi \))

(c)

sin2(ፀ-\(\phi \))

(d)

cos2(ፀ-\(\phi \))

\(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) is equal to

(a)

cos 2x

(b)

cos x

(c)

cos 3x

(d)

2 cos x

The angle between the minute and hour hands of a clock at 8.30 is ___________

(a)

80⁰

(b)

75⁰

(c)

60⁰

(d)

105⁰

If tan A = \(\frac { a }{ a+1 } \) and B = \(\frac { 1 }{ 2a+1 } \) then the value of A + B is ___________

(a)

0

(b)

\(\frac { \pi }{ 2 } \)

(c)

\(\frac { \pi }{ 3 } \)

(d)

\(\frac { \pi }{ 4 } \)

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

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)

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

(sec A + tan A-1) (sec A - tan A+1)-2 tan A = _______________

(a)

0

(b)

1

(c)

2

(d)

2 tan A

The value of tan 1° tan 2° tan 3°...tan 89° is ____________ 

(a)

\(\infty\)

(b)

0

(c)

1

(d)

\(\sqrt{3}\)

If cos θ + \(\sqrt{3}\) sin θ = 2 and θ∈[0, 2π] then θ is _______________

(a)

\(\frac{\pi}{3}\)

(b)

\(\frac{5\pi}{3}\)

(c)

\(\frac{2\pi}{3}\)

(d)

\(\frac{4\pi}{3}\)

The numerical value of tan^-11 + tan^-12 + tan^-13 = _______________

(a)

\(\pi\)

(b)

\(\frac{\pi}{2}\)

(c)

0

(d)

\(\frac{\pi}{4}\)

If in a triangle ABC, ∠B = 60°, then _______________

(a)

(a-b)² = c²- ab

(b)

(b-c)² = a²- bc

(c)

(c-a)² = b²- ac

(d)

a² + b² = c²

Area of triangle ABC is _______________

(a)

\(\frac{1}{2}\)ab cos C

(b)

\(\frac{1}{2}\)ab sin C

(c)

\(\frac{1}{2}\)ab cos B

(d)

\(\frac{1}{2}\)bc sin B

\(\underset { x\rightarrow \infty }{ lim } \left( \cfrac { { x }^{ 2 }+5x+3 }{ { x }^{ 2 }+x+3 } \right) ^{ x }\)is

(a)

e⁴

(b)

e²

(c)

e³

(d)

1

If f(x) = x(-1)^{\(\left\lfloor 1\over x \right\rfloor \)}, \(x\le0\), then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to

(a)

-1

(b)

0

(c)

2

(d)

4

\(lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}\) is

(a)

\(\sqrt{2}\)

(b)

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

(c)

1

(d)

2

The function \(f(x)= \begin{cases}\frac{x^{2}-1}{x^{3}+1} & x \neq-1 \\ P & x=-1\end{cases}\)is not defined for x = −1. The value of f(−1) so that the function extended by this value is continuous is

(a)

\({2\over3}\)

(b)

-\({2\over3}\)

(c)

1

(d)

0

Let A and B be two events such that \(P(\overline{A\cup B})={1\over6}, P(A\cap B)={1\over4}\) and \({P(\overline{A})}={1\over4}\). Then the events A and B are

(a)

Equally likely but not independent

(b)

Independent but not equally likely

(c)

Independent and equally likely

(d)

Mutually inclusive and dependent

If X and Y be two events such that P(X/Y) = \({1\over2},P(Y/X)={1\over3}\) and \(P(X\cap Y)={1\over6}\), then P(X\(\cup\)Y) is

(a)

\({1\over3}\)

(b)

\({2\over5}\)

(c)

\({1\over6}\)

(d)

\({2\over3}\)

In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is

(a)

\({2\over 11}\)

(b)

\({3\over 11}\)

(c)

\({5\over 11}\)

(d)

\({7\over 11}\)