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1. State whether the following statements are True or False and also give the reason in support of your answer.

a) Collection of rich persons in India forms a set.

b) Following rule is a function from \(A\) to \(B\).

c) \(\frac{d}{d x}(9-7 x)^5=45(9-7 x)^4\)

d) In exclusive method, upper limit of a class is included in the same class.

e) The order of the matrix \(\left[\begin{array}{lll}2 & 5 & 6 \\ 4 & 3 & 1\end{array}\right]\) is \(3 \times 2\).

2. If four cards are chosen from a pack of 52 playing cards then find the number of ways that all four cards are:
a) of same suit
b) red
c) face cards
d) king
e) of different suit

3. Arrange the numbers 49, 36, 42, 19, 22, 27, 14, 13, 24, 48, 23, 28, 17, 42, 39, 45, 22, 24, 17, \(41,18,42,38,43,11,27,36,13,40,30,24,10,18,47,18,19,23,12,27\) in stretched stemand-leaf display that has single-digit starting parts and leaves, but has stem width of 5. 

4. If the universal set is \(\mathrm{U}=\{1,2,3,4,5,6,7,8\}\) and \(\mathrm{A}=\{2,3,6,7\}, \mathrm{B}=\{4,6,8\}, \mathrm{C}=\{6,7,8\}\) are the subsets of \(U\), then verify
a) De-Morgan’s laws
b) left distributive law

5. Evaluate the following:
a) \(\quad \int x^{2} e^{2 x} d x\)
b) \(\frac{d y}{d x}\), where \(y=(4 x+5)^{4}(9 x+4)^{5}\)

6. a) Prove that \(\left|\begin{array}{lll}\text { a } & \text { b } & c \\ b & c & a \\ c & a & b\end{array}\right|=(a+b+c)\left(a b+b c+c a-a^{2}-b^{2}-c^{2}\right)\)

b) What do you mean by primary data and secondary data? Also give an example in each case.

7. Draw a box plot with whisker, \(+\) ve sign and outliers for the following data:

\(42,37,28,23,32,25,26,39,38,41,22,38,21,31,26,36,42,52,50,47,24,53,28\)

8. a) Find the values of \(\mathbf{a}\) and \(\mathbf{b}\), if the function \(\mathbf{f}\) given below is continuous at \(x=2\)

\[
f(x)= \begin{cases}a+b, & x<2 \\ a+b x+4, & x=2 \\ 5, & x>2\end{cases}
\]

b) Draw a histogram for the following data:

Also draw frequency polygon in the same graph.