Modern Maths Test

Result

Modern Maths Test - 1

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Question 1
1 / -0.25

Find ⁸P₆

A
33425

B
20160

C
18972

D
6625

Solution
Question 2
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Find ⁸C₆

A
33

B
32

C
30

D
28

Solution
Question 3
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Find the number of ways in which the letters of the word BIHAR can be arranged.

A
99

B
129

C
120

D
125

Solution

Since there are 5 letters in the word so the total number of arrangement is ⁵P₅= 5! that is 120.
Question 4
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Find the number of ways in which the letters of the word AMERICA can be rearranged.

A
2519

B
2620

C
1250

D
2500

Solution

In the word AMERICA there are 7 letters and the letter ‘A’ is coming twice.

So the total number of rearrangement

Note: No. of Rearrangements = Total no. of arrangements – 1(initial arrangement)
Question 5
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Find the number of ways in which the letters of the word CALCUTTA can be rearranged.

A
3000

B
5039

C
5029

D
3029

Solution

In the word CALCUTTA, there are 8 letters

Letter C comes twice

Letter A comes twice

Letter T comes twice

So the total number of rearrangements

Note: No. of Rearrangements = Total no. of arrangements – 1 (initial arrangement)
Question 6
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How many 4-letter different words can be formed by using the letters a, b, c and d?

A
296

B
346

C
440

D
256

Solution

Letter a can be placed in all 4 positions.

Similarly, b can be placed in all 4 positions.

Similarly, c can be placed in all 4 positions.

Similarly, d can be placed in all 4 positions.

So the total number of arrangement is 4 × 4 × 4 × 4 = 256
Question 7
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How many numbers can be formed by using the digits 2, 3, 4 and 5?(repetitions of digits is not allowed).

A
50

B
60

C
64

D
68

Solution

The number formed can be one-digit, two-digit, three-digit or four-digit number

Number of one-digit numbers formed = 4

Hence, total numbers formed = 4 + 12 + 24 + 24 = 64
Question 8
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How many numbers greater than 4000 can be formed by using the digits 2, 3, 4 and 5? (repetitions of digits is not allowed).

A
12

B
14

C
20

D
24

Solution

Thousand’s place can be filled by using two digits i.e. 4 or 5

Hundred’s place can be filled in 3 ways.

Ten’s place can’t be filled in 2 ways.

Unit’s place can be filled in 1 way.

So total number of possible numbers = 2 × 3 × 2 × 1 = 12.
Question 9
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How many numbers greater than 4000 can be formed by using the digits 2, 3, 4 and 5?

A
120

B
130

C
138

D
128

Solution

Thousands place can be filled in two ways.

Hundred’s place can be filled with any of the 4 digits.

Ten’s place can be filled with any of the 4 digits.

Unit’s place can be filled with any of the 4 digits.

So the total numbers formed = 2 × 4 × 4 × 4 = 128.
Question 10
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There are 3 roads from A to B, 4 roads from B to C and only 1 road from C to D. How many combinations of roads are there from A to D?

A
12

B
15

C
14

D
18

Solution