If \(x = \frac{1}{5}\), the value of cos (cos^-1x+2sin^-1x) is

(a)

\(-\sqrt { \frac { 24 }{ 25 } } \)

(b)

\(\sqrt { \frac { 24 }{ 25 } } \)

(c)

\(\frac{1}{5}\)

(d)

\(-\frac{1}{5}\)

sin (tan^-1x), |x| < 1 is equal to

(a)

\(\frac{x}{\sqrt{1-x^2}}\)

(b)

\(\frac{1}{\sqrt{1-x^2}}\)

(c)

\(\frac{1}{\sqrt{1+x^2}}\)

(d)

\(\frac{x}{\sqrt{1+x^2}}\)

The value of \({ cos }^{ -1 }\left( \cos\cfrac { 5\pi }{ 3 } \right) +sin^{ -1 }\left( \sin\cfrac{5\pi }{ 3 } \right) \) is ______________ 

(a)

\(\cfrac { \pi }{ 2 } \)

(b)

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

(c)

\(\cfrac { 10\pi }{ 3 } \)

(d)

0

The equation of the normal to the circle x² + y² − 2x − 2y + 1 = 0 which is parallel to the line 2x + 4y = 3 is

(a)

x + 2y = 3

(b)

x + 2y + 3 = 0

(c)

2x + 4y + 3 = 0

(d)

x − 2y + 3 = 0

Area of the greatest rectangle inscribed in the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is

(a)

2ab

(b)

ab

(c)

\( \sqrt{ ab}\)

(d)

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

The volume of the parallelepiped with its edges represented by the vectors \(\hat { i } +\hat { j } ,\hat { i } +2\hat { j } ,\hat { i } +\hat { j } +\pi \hat { k } \) is

(a)

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

(b)

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

(c)

\( { \pi }\)

(d)

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

If \(\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] \)= 3 and \(\left| \overset { \rightarrow }{ c } \right| =1\) then \(\left| \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) \right| \) is _____________

(a)

1

(b)

3

(c)

6

(d)

9

If \(\left| \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right| =\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \), then the angle between the vector \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) is _____________

(a)

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

(b)

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

(c)

\(\frac { \pi }{ 6 } \)

(d)

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

The law of linear motion of a particle is given s = \(\frac{1}{3}\) t³-16t, the acceleration at the time when the velocity vanishes is __________

(a)

4

(b)

6

(c)

2

(d)

8

The equation of the tangent to the curve x = t cost, y = t sin t at the origin is __________

(a)

x = 0

(b)

y = 0

(c)

x +y = 0

(d)

x + y = 7