Show that n {P [P (P ( \(\phi\) ))]}=4

2

(a)

Let T = { \({x:\frac { x+5 }{ x-7 } -5=\frac { 4x-40 }{ 13-x }}\) }. Is T a singleton set? Justify your answer.

2

(a)

In \(\triangle \)ABC, if a cos A=b cos B, show that the triangle is either isosceles or right angled.

2

(a)

If cos \(\alpha \) +cos \(\beta\) = 0 = sin \(\alpha \) +sin\(\beta\), then find the value of cos2\(\alpha \)+cos 2\(\beta\)

2

(a)

Find the sum of n terms of the series whose nth term is given by
(2n - 1)^{2 .}

2

(a)

Evaluate \(\lim_ { h\rightarrow 0 } \frac { (a+h)^{ 2 }sin(a+h)-a^{ 2 }sin\quad a }{ h } \)

2

(a)

Evaluate \(\lim_ { x\rightarrow 0 }{ lim } \frac { x\quad tan4x }{ 1-cos4x } \)

2

(a)

If \(\bar { x } \) is mean and \(MD\left( \bar { x } \right) \) is the mean deviation from mean then find the number of observations lying between \(\bar { x } -MD\left( \bar { x } \right) \) and \(\bar { x } +MD\left( \bar { x } \right) \) . Use the data 22,24,30,27,29,31,25,28,41,42.

2

(a)

The number lock of a suitcase has four wheels, each labelled with 10 digits.i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

2

(a)

If  A and B are two events such that P(A) = \(\frac { 1 }{ 4 } \)  P(B) = \(\frac { 1 }{ 2 } \) and \(P(A\cap B)=\frac { 1 }{ 8 } \) .Then , find P ( not A and not B).

2

(a)