If \(x={1\over 2+\sqrt{3}}\) then the value of x³ - x² - 11x + 3 is 

(a)

0

(b)

1

(c)

2

(d)

4

If sin α + cos α = b, then sin 2α is equal to

(a)

b²- 1, if b ≤\(\sqrt { 2 } \)

(b)

b²- 1, if b >\(\sqrt { 2 } \)

(c)

b²-1, if b ≥ 1

(d)

b²- 1, if b ≥\(\sqrt { 2 } \)

If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

(a)

45

(b)

40

(c)

10!

(d)

2¹⁰

The number of positive integral solution of \(x\times y\times z=30\) is  _________

(a)

3

(b)

1

(c)

9

(d)

27

Which one of the following statements in false?

(a)

A point \((\alpha,\beta)\) will lie on origin side of the line ax+by+c=0 if a\(\alpha\)+b\(\beta\)+c and c have the same sign

(b)

A point \((\alpha,\beta)\)  will lie on non-origin side of the line ax+by+c=0 if a\(\alpha\)+b\(\beta\) +c and c have opposite sign

(c)

If \(\alpha=\frac{\pi}{2},p=0\) , then the equation xcos\(\alpha\)+ysin\(\alpha\)=p represents x-axis

(d)

If \(\alpha =0,p=0\), then the equation xcos\(\alpha\)+ysin\(\alpha\)=presents x-axis

The distance between the parallel lines 3x - 4y + 9 = 0 and 6x - 8y -15 = 0 is ______________

(a)

\(\frac{-33}{10}\)

(b)

\(\frac{10}{33}\)

(c)

\(\frac{33}{10}\)

(d)

\(\frac{33}{20}\)

A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between \(\overrightarrow{OP}\)and the z-axis is

(a)

45°

(b)

60°

(c)

90°

(d)

30°

If the direction cosines of a line are k, k and k, then

(a)

k>0

(b)

0

(c)

k=1

(d)

\(k=\frac { 1 }{ \sqrt { 3 } } or-\frac { 1 }{ \sqrt { 3 } } \)

\(\int \frac{d x}{e^x-1}\) is

(a)

\(log|e^x|-log|e^x-1|+c\)

(b)

\(log|e^x|+log|e^x-1|+c\)

(c)

\(log|e^x-1|-log|e^x|+c\)

(d)

\(log|e^x+1|-log|e^x|+c\)

\(\int { \frac { { e }^{ x } }{ \left( 1+{ e }^{ x } \right) ^{ 2 } } } \) dx =_______+c

(a)

\(\frac { 1 }{ 1+{ e }^{ x } } \)

(b)

-\(\frac { 1 }{ 1+{ e }^{ x } } \)

(c)

1 + e^x

(d)

\(\frac { \left( 1+{ e }^{ x } \right) ^{ 3 } }{ 3 } \)