Number System Test

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Number System Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

If n is any integer, which of the following statements is true?

A
3n + 1 is odd.

B
n (n + 1) is divisible by 2.

C
n (n + 4) is even.

D
n (n + 2) is divisible by 3.

Solution

If n is any odd number, it adds to 1 and becomes even, so it is divisible by 2.

And if n is even, (n + 1) is odd but when multiplied by n (even), it becomes even and then it is divisible by 2.

So, if n is either even or odd, it is divisible by 2.
Question 2
1 / -0

Find the number of pairs of natural numbers with LCM equal to 56.

A
2

B
5

C
10

D
11

Solution

There are ten pairs (1, 56) (2, 56) (4, 56) (7, 56) (8, 56) (14, 56) (28, 56) (7, 8) (8, 28) and (8, 14) with LCM equal to 56.
Question 3
1 / -0

There are 5 consecutive natural numbers with L.C.M. 60. The product of the first two numbers is equal to the 5^th number. What is the sum of the numbers?

A
10

B
20

C
30

D
40

Solution

Let n be 1^st natural number.
So, consecutive natural numbers are
n, n + 1, n + 2, n + 3, n + 4

According to question,
n(n + 1) = n + 4

⇒ n² + n = n + 4
n² = 4

⇒ n = ± 2
– 2 cannot be taken as n is natural number. So, n = 2

Numbers be 2, 3, 4, 5, 6

Hence, sum of numbers = 2 + 3 + 4 + 5 + 6 = 20
Question 4
1 / -0

The numbers a and b have prime factors as 2 and 3 and their ratio b/a is 36. Which of the following statements is true?

A
The LCM is a.

B
The HCF is a.

C
The HCF is 36.

D
The HCF is b.

Solution

The two numbers with prime factors 2 and 3, and ratio 36 are 6 and 216.The HCF of 6 and 216 is 6.
Question 5
1 / -0

In a division, the remainder was 71. With the same divisor, but twice the dividend, the remainder is 43. Which of the following numbers is the divisor?

A
86

B
93

C
94

D
99

Solution

Let the dividend be x and the remainder be 71, so that x + 71 is divisible by the divisor.
When it is done, it comes twice, i.e. 2x + 142, which is also divisible.

According to the question, it leaves the remainder 43.
So, 2x + 142 – 43 = 2x + 99

So, the divisor is 99.
Question 6
1 / -0

If n is a natural number, n⁴+ n²+ 1 is

A
always even

B
always odd

C
even when n is even

D
odd when n is odd

Solution

n⁴ + n² is always even.
We know, even + odd = odd
As 1 is odd
So, n⁴ + n² + 1 = odd
Question 7
1 / -0

Two out of six papers for an examination are of physics. What are the number of ways in which the papers can be arranged so that two physics papers are not together?

A
348

B
480

C
740

D
800

Solution

Arrangement of total number of papers = 6! or 720
Number of ways when two physics papers are set together = 5! × 2 = 240

So, required number of ways = 720 - 240 = 480

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Re-Attempt Weekly Quiz Competition

Number System Test - 1

Result

Number System Test - 1

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SHARING IS CARING

Question 1

3n + 1 is odd.

n (n + 1) is divisible by 2.

n (n + 4) is even.

n (n + 2) is divisible by 3.

Solution

Question 2

2

5

10

11

Solution

Question 3

10

20

30

40

Solution

Question 4

The LCM is a.

The HCF is a.

The HCF is 36.

The HCF is b.

Solution

Question 5

86

93

94

99

Solution

Question 6

always even

always odd

even when n is even

odd when n is odd

Solution

Question 7

348

480

740

800

Solution

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My Perfomance

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Rank

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