Q) Multiple Choice with Explain the solution
1. How many different rearrangement are there of the
letters in the word BUBBLE?
(a) 40 (b) 50 (c) 80 (e) 120
2. A small deck of five cards are numbered 1 to 5. First one card and then a second card are selected at random, with replacement. What is the probability that the sum of the values on the cards is a prime number?
(a) 10/25 (b) 11/25 (c) 12/25 (e) 13/25
3. How many license plates can be made using either one uppercase English letter followed by two digits or three digits followed by one uppercase English letter?
(a) 28600 (b) 100000 (c) 26000 (d) 2600
4. Given the two points [a, f(a)], [b, f(b)], the linear Lagrange polynomial 𝐟𝟏(𝐱) that passes through these two points is given by
(a) 𝒇𝟏(𝒙)=𝒙−𝒃𝒂−𝒃𝒇(𝒂)+𝒙−𝒂𝒂−𝒃𝒇(𝒃) (b) 𝒇𝟏(𝒙)=𝒙𝒃−𝒂𝒇(𝒂)+𝒙𝒃−𝒂𝒇(𝒃)
(c) 𝒇𝟏(𝒙)=𝒇(𝒂)+𝒇(𝒃)−𝒇(𝒂)𝒃−𝒂(𝒃−𝒂) (d) 𝒇𝟏(𝒙)=𝒙−𝒃𝒂−𝒃𝒇(𝒂)+𝒙−𝒂𝒃−𝒂𝒇(𝒃)
5. The Lagrange polynomial that passes through the 3 data points is given by
𝒇𝟐(𝒙)=𝑳𝟎(𝒙)(𝟐𝟒)+𝑳𝟏(𝒙)(𝟑𝟕)+𝑳𝟐(𝒙)(𝟐𝟓), the value of 𝑳𝟏(𝒙) at x=16 is
(a) -0.071430 (b) 0.50000 (c) 0.57143 (d) 4.3333