CAT4MBA

Q1. Find the number of non-negative integral solutions to the system equations a1 + a2 + a3 + a4 + a5 = 20 and a1 + a2 + a3 = 5.
a. 228
b. 336
c. 448   
d. 528

Q2. I have 7 friends. I call 3 friends at a time to my house. How many distinct group of friends can be called at my house?
a. 7! x 3!
b. 7! x 3
c. C (7, 3)
d. P (7, 3)

Q3. A train runs between P and H. Seven people enter the train somewhere between P and H. It is given that nine stops are there in between P and H. In how many ways can the tickets be purchased if no restriction is there with respect to the number of tickets at any station?
a. C (45, 7)
b. C (63, 7)
a. C (56, 7)
a. C (52, 7)

Q4. How many weights can be measuerd with the following weight 5kg, 1kg, 50 gms, 25gms, 10 gm and 1 gm ?
a. Infinte
b. 2^6
c. 2^6 - 1
d. None of the above

Q5. In how many ways an examiner can assign 50 marks to 10 questions giving not less than 3 marks to any question is :
a. C(29, 9)
b. C(47, 3)
c. C(52, 2)
d. C(40, 10)

Q6. Four boxes of 4 different colors are to be wrapped up in 4 sheets of similar colors. Find the probability that every box is wrapped in the sheet of its own color?
a. 1/18
b. 1/24
c. 1/54
d. 1/216

Q7. A committee of 3 experts is to be chosen from a group of 7 people of which 3 are CAs, 3 are MBAs, and 1 is a CA and an MBA. The committee must have atleast 1 with only a CA and 1 with only an MBA. In how many ways can the committee be selected?
a. 31
b. 35
c. 34
d. 33