19 Evaluate 4P3 O 24 Solution19 We know that nPk nnk Theref

Solution

19. We know that    _nP_k   = n!/(n-k)!. Therefore, ₄P₃ = 4!/(4-3)! = 4! = 4*3*2*1 = 24. The 1^st option is the correct answer.

20. We assume that the given sequence is an arithmetic series. Let a be its 1^st term and let b be the common difference. Then, the 2^nd term is a+b = -34..(1) and thew 4^th term is a +3b = 7..(2). Now, on subtracting the 1^st equation from the 2^nd equation, we get a+3b-a-b = 77-(-34) or, 2b = 111 so that b = 111/2 = 55.5. Then, the missing term is -34+55.5 = 21.5. The 3^rd option is the correct answer.

Note:

It is very difficult to identify a sequence from 2 terms only, unless it is an arithmetic series or a geometric series.