Modern Maths(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

MODERN MATHS MCQs

Total Questions : 95 | Page 5 of 10 pages

Question 41. 5 Nephrologists decide to hold daily meetings such that (i) At least one Nephrologist attend each day. (ii) A different set of Nephrologists must attend on different days. (iii) On day N for each

1 \leq d < N

, at least one Nephrologist must attend who was present on day d. How many maximum days can meetings be held?

14
16
20
None of these
10

Discuss Question

Answer: Option B. -> 16
:
B
We need to find the largest possible number of subsets of {1, 2, 3, 4, 5} such that no 2 subsets are disjoint. Fix one element from the set to be presented in each subset and we can have

2^{4}

such possibilities.
Because one element is common. So, remaining 4 can be selected

^{4} C_{0}

^{4} C_{1}

^{4} C_{2}

^{4} C_{3}

^{4} C_{4}

2^{4}

= 16 ways. There are total 16 days.

Question 42. 5 people dine together at a round table. They dine together till each of them dines with different neighbours. Determine the number of days they dine together.

Discuss Question

Answer: Option A. -> 12
:
A
5 people can sit together around a round table in

(5 - 1)! = 4!

Ways. But in anticlockwise and clockwise arrangements each of them will have the same neighbour. So, no. of arrangements possible =

\frac{1}{2} (4!) = 12

.
So, they dine together for 12 days.
Hence option (a)

Question 43. Find the value of ‘n’ if

^{n} P_{6} = 12^{n} P_{4}

Discuss Question

Answer: Option A. -> 8
:
A
Soln:

\frac{n!}{(n - 6)!} = \frac{12 \times n!}{(n - 4)!}

(n - 4)! = 12 \times (n - 6)!

(n - 4) (n - 5) = 4 \times 3

n = 8
Hint: go from answer options. Only option(a) satisfies given equation.

Question 44. Determine the number of ways in which 5 prizes can be distributed among 4 students.

Discuss Question

Answer: Option A. -> 45
:
A
This is a type of “Different to Different” question.
5 prizes can be distributed among 4 students in

4^{5}

ways.
Hence option (a)

Question 45. If

^{n} C_{r} = 5

and

^{n} P_{r} = 120

, then determine the value of n, r.

5, 3
4, 2
7, 4
6, 4
5, 4

Discuss Question

Answer: Option E. -> 5, 4
:
E
Soln:

\frac{^{n} P_{r}}{^{n} C_{r}}

\frac{120}{5}

= 2

^{n} C_{r} = \frac{(^{n} P_{r})}{(r!)}

\frac{^{n} P_{r}}{[\frac{^{n} P_{r}}{r!}]}

r! = 24
r = 4
Given

^{n} P_{r}

= 120

^{n} P_{4}

= 120

\frac{n!}{(n - 4)!} = 120

n(n-1)(n-2)(n-3) = 120
n = 5
Hence option (e)

Question 46.

The number of 5 digit telephone numbers having at least one of their digits repeated is? (0 can be the starting digit of the number)

30240
10500
45600
69760
62660

Discuss Question

Answer: Option D. -> 69760
:
D

Total number of 5 digit telephone numbers which can be formed using digits 0,1,2…9 is $10^{5}$
Number of 5 digit numbers having not even a single digit repeated is $^{10} P_{5}$ = 30240

Required number of telephone numbers = $10^{5}$ -30240 = 69760

Question 47.

In how many ways can you select 2 numbers till 50, which will have their product as a multiple of 3?

Discuss Question

Answer: Option B. -> 664
:
B

To get a two factor product out of 50 numbers, we can choose the two numbers in $^{50} C_{2}$ ways, out of

which we need to negate pairs wherein both numbers are not multiples of 3.

Non multiples of 3 till $50 = 50 - \frac{50}{3} = 34$ .

$^{50} C_{2} -^{34} C_{2}$

Question 48.

In how many ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?

736
768
792
840
62660

Discuss Question

Answer: Option D. -> 840
:
D

Since the order of vowels will always remain the same despite these occupying different positions -> if we assume each vowel as X then our question is same as asking "arrange JPTRXXX" => in all $\frac{7!}{3!}$ ways. => Choice (d) is the right answer

Question 49.

To set up a farm, a farmer goes to buy some animals. He selects from cows, sheep, goats, chickens and pigs. In how many ways can he select 15 animals such that he selects atleast 1 cow, 2 sheep, 2 goats and 3 chicken.