6. A fair 6 -sided die is rolled twice. What is the probability of: a getting two consecutive 6 s? b getting a 5 on the first throw and an even nut

3 Calculate \( \frac{3}{10} \) of 36 metres.

7 The two angles of a triangle are in the ratio \( 2: 3 \). If the third angle is \( 20^{\circ} \) less than the sum of the other two angles, find the largest angle of the triangle.

\( \int _ { 0 } ^ { 2 } x ^ { 5 } e ^ { - x ^ { 2 } } d x \)

\( \lim _ { x 2 } \frac { x ^ { 2 } + 1 } { x ^ { 2 } - 1 } = \)

It is given that \( x-1 \) is a factor of \( f(x) \), where \( f(x)=x^{3}-6 x^{2}+a x+b \). (i) Express \( b \) in terms of a. [2] (ii) Show that the remainder when \( f(x) \) is divided by \( x-3 \) is twice the remainder when \( f(x) \) is divided by \( x-2 \). [4]