The function f:R➝R be defined by f(x) = sinx + cosx is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function

If \({ log }_{ \sqrt { x } }\) 0.25 = 4, then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

\(\sqrt [ 4 ]{ 11 } \) is equal to ___________

(a)

\(\sqrt [ 8 ]{ 11^{ 2 } } \)

(b)

\(\sqrt [ 8 ]{ 11^{ 4 } } \)

(c)

\(\sqrt [ 8 ]{ 11^{ 8 } } \)

(d)

\(\sqrt [ 8 ]{ 11^{ 6 } } \)

If tan α and tan β are the roots of x² + ax + b = 0; then \(\frac { sin(\alpha +\beta ) }{ sin\alpha sin\beta } \) is equal to

(a)

\(\frac { b }{ a } \)

(b)

\(\frac { a }{ b } \)

(c)

\(-\frac { a }{ b } \)

(d)

\(-\frac { b}{ a } \)

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)

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

\(\frac{1}{360}\) of a complete rotation clockwise is _______________

(a)

-1°

(b)

-360°

(c)

-90°

(d)

1°

The product of r consecutive positive integers is divisible by _________

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

If \(\frac { 1 }{ 7! } +\frac { 1 }{ 8! } =\frac { A }{ 9! } ,\) then the value of A is _________

(a)

7²

(b)

8²

(c)

9

(d)

9²

Find the odd one out of the following

(a)

\(\hat { i } +2\hat { j } +3\hat { k } \)

(b)

\(2\hat { i } +4\hat { j } +6\hat { k } \)

(c)

\(7\hat { i } +14\hat { j } +21\hat { k } \)

(d)

\(\hat { i } +3\hat { j } +2\hat { k } \)

If two events A and B are such that \(P(\overline{A})={3\over10}\) and \(P(A \cap \overline{B})={1\over2},\) then \(P(A\cap B)\) is

(a)

\({1\over2}\)

(b)

\({1\over3}\)

(c)

\({1\over4}\)

(d)

\({1\over5}\)