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

Exams > Cat > Quantitaitve Aptitude

MODERN MATHS MCQs

Total Questions : 95 | Page 2 of 10 pages

Question 11. Parul and Vijay throw 3 dice in a single throw. It is known that Parul throws a total of 16. Find Vijay’s probability of getting a higher value.

Discuss Question

Answer: Option C. -> 152
:
C
The maximum total possible = 18
There are two options for Vijay
1) A+B+C=17 Possibilities = 6,6,5
Number of combinations =

\frac{3!}{2!}

=3
2) A+B+C=18Possibilities = 6,6,6
Number of combinations = 1
Required Probability=

\frac{4}{216}

\frac{1}{52}

.
Option (c)

Question 12. Determine the no. of terms in the expansion of

(a + b + c + d)^{5}

and

(1 + a + a^{2} + a^{3})^{5}

56, 16
32, 24
165, 32
32, 32
5, 4

Discuss Question

Answer: Option A. -> 56, 16
:
A
No. of terms in expansion of

(a + b + c + d)^{5}

= Number of solution of (a + b + c + d) = 5,

^{8} C_{3}

= 56
No. of terms in expansion of

(1 + a + a^{2} + a^{3})^{5} = (5 \times 3) + 1 = 16

Hence option (a)

Question 13. Find out the number of ways in which 18 flowers can be arranged in a necklace/garland.

18!
17!
16!
12(17!)
9

Discuss Question

Answer: Option D. -> 12(17!)
:
D
This is a case of “Circular Permutation” where you cannot differentiate between clockwise and anticlockwise directions.
No. of arrangements =

\frac{1}{2} (18 - 1)! = \frac{1}{2} (17!)

Hence option (d)

Question 14. The number of natural numbers which lie between

10^{8}

and

10^{9}

which have products of their digits as 6 is___.

Discuss Question

10^{8}

<n<

10^{9}

n is a 9 digit number
Product of 6 is possible in the following cases
Exactly one digit is 6 and the remaining digits are 1
Number of possible numbers= 9
One digit is 2 and the other is 3, remaining are 1 =

^{9} P_{2}

= 72
Total possible numbers = 72+9 = 81

Question 15. The maximum number of rectangles that can be formed from a set of 5 parallel lines intersecting another set of 6 parallel lines is

Discuss Question

Answer: Option B. -> 150
:
B
To form a rectangle we need four intersecting lines.
The first two parallel lines can be selected in

^{5} C_{2}

ways and the other two parallel lines can be selected in

^{6} C_{2}

ways.
Total number of parallelograms which can be formed=

10 \times 15 = 150

Question 16. If all the letters of the word RASAM can be arranged as in a dictionary, what is its rank?

40
35
41
42
None of these

Discuss Question

Answer: Option C. -> 41
:
C
First we fix A as the first letter
No. of words possible with A as the first letter = 4! = 24
No. of words possible with M as the first letter=

\frac{4!}{2!}

= 12
No. of words possible with RAA as the first 3 letters = 2
No. of words possible with RAM as the first 3 letters = 2
Next word will be RASAM
Rank= 41

Question 17. What are the numbers of ways in which 5 similar balls will be put in 4 distinct baskets when the first basket has 0 balls?

Discuss Question

Answer: Option B. -> 21
:
B
0 balls are going to basket A. hence we will consider the distribution only in the remaining 3 baskets
B+C+D = 5
Total =