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• If a is the arithmetic mean and g is the geometric mean of two numbers, then ...(a) a ≤ g (b) a ≥ g (c) a = g (d) a > g
• If (1 + x) n = C0 + C1x + C2x2 + .... + Cnxn, then C0 + 3 . C1 + 5 . C2 + .... + (2n + 1) . Cn equals(a) 22n–1 (b) (n + 1) 2n (c) n . 2n+1 (d) (n – 1) 2n–1
• If a and b denote the sum of the coefficients in the expansions of (1-3x+10x2)n and (1 + x2)n respectively, then write the relation between a and b.
• Write the number of terms in the expansion of (1-3x+3x2-x3)8.
• 47C4  + \(\sum_{r=1}^{5}\) \(^{52-r}C_3\)  is equal to (a) 47C6 (b) 52C5 (c) 52C4 (d) None of these