Solve The Following Question.1MARKS - Maths STD 8 Questions - Vidyadip

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Solve The Following Question.1MARKS

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19 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark

Solve Cryptarithms.
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{A}\ \ \ \text{B} \ \ \ \ 7\ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \underline{+\ \ \ \ 6\ \ \ \ \text{A}\ \ \ \ \text{B}\ }\\\ \ \ \ \ {\ \ \ \ \ \ \ \ \ \ \ \ 9\ \ \ \ 8\ \ \ \ \ \text{A}}$

Answer

If $\text{A}+\text{B}=8,\text{A}+\text{B}\geq9$ is possible only if A = b = 9 But from 7 + B = A, A = B = 9 is impossible. Surely, $\text{A}+\text{B}=8, \text{A}+\text{B}\leq9$
So, A + 7 = 9, Surely A = 27 + B = A, 7 + B = 2, B = 5
So, A = 2, B = 5

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Question 21 Mark

Find the remainder, without performing actual division, when 798 is divided by 11.

Answer

Let n = 798 = a multiple of 11 + [7 + 8 - 9] 798 = a multiple of 11 + 6
$\therefore$ Remainder = 6

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Question 31 Mark

Which of the following statements are true?
If a number divides three numbers exactly, it must divide their sum exactly.

Answer

True.

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Question 41 Mark

Without performing actual addition and division, write the quotient when the sum of 69 and 96. is divided by:
15

Answer

Two numbers are 69 and 96 whose digits are revesed Here a = 6 = 9
If it is divisible by a + b i.e., 6 + 9 = 15, then quotient = 11

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Question 51 Mark

Solve Cryptarithms.
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ \ \ 2 \ \ \ \ \text{A}\ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \underline{+\ \ \ \ 6\ \ \ \ \text{A}\ \ \ \ \text{B}\ \ }\\\ \ \ \ \ {\ \ \ \ \ \ \ \ \ \ \ \ \ \text{A}\ \ \ \ 0\ \ \ \ \ 9}$

Answer

A + B = 9 as the sum of two digits can never be 192 + A = 0, A must be 8A + 9, 8 + B = 9, B = 1
So, A = 8, B = 1

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Question 61 Mark

Without performing actual addition and division, write the quotient when the sum of 69 and 96. is divided by:
11

Answer

Two numbers are 69 and 96 whose digits are revesed Here a = 6 = 9
Sum if 69 + 96 is divisible by 11, then quotient = a + 6 = 6 + 9 = 15

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Question 71 Mark

Which of the following statements are true?
A number is divisible by 18, if it is divisible by both 3 and 6.

Answer

False.Solution:
It must be divisible by 9 and 2 both.

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Question 81 Mark

Without performing acute computations, find the quotient when 94 - 49 is divisible by:
5

Answer

Two numbers are 94 and 49. Whose digits are reversed.When it is divided by a - b i.e., 9 - 4 = 5, then quotient will be = 9

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Question 91 Mark

Which of the following statements are true?
If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

Answer

False.Solution:
It is not necessarily.

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Question 101 Mark

Which of the following statements are true?
If a number is divisible by 8, it must be divisible by 4.

Answer

True.

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Question 111 Mark

Solve Cryptarithms.
$\ \ \ \ \ \ \ \ \ \ \text{A}\ \ \ \ 1\\ \ \ \ \ \underline{+\ \ \ 1\ \ \ \ \text{B}\ }\\\ \ \ \ \ {\ \ \ \ \ \text{B}\ \ \ \ 0\ }$

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Question 121 Mark

Which of the following statements are true?
If a number is divisible by 3, it must be divisible by 9.

Answer

False.
Solution:
It is not necessarily that divide by 9.

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Question 131 Mark

Which of the following statements are true?
If a number is divisible by both 9 and 10, it must be divisible by 90.

Answer

True.

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Question 141 Mark

Without performing acute computations, find the quotient when 94 - 49 is divisible by:
9

Answer

Two numbers are 94 and 49. Whose digits are reversed.
If 94 - 49 is divided by 9, then the quotient = a - b = 9 - 4 = 5

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Question 151 Mark

Which of the following statements are true?
The sum of two consecutive odd numbers is always divisible by 4.

Answer

True.

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Question 161 Mark

Which of the following statements are true?
If a number is divisible by 4, it must be divisible by 8.

Answer

False.Solution:
It is not necessarily that it must divide by 8.

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Question 171 Mark

Which of the following statements are true?
If a number is divisible by 9, it must be divisible by 3.

Answer

True.

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Question 181 Mark

Which of the following statements are true?
If two numbers are co-prime, at least one of them must be a prime number.

Answer

False.Solution:
It is not necessarily.

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Question 191 Mark

Solve Cryptarithms.
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\ \ \ \ \text{A} \ \ \ \ \text{B}\ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \underline{+\ \ \ \ \text{A}\ \ \ \ \text{B}\ \ \ \ \ 1\ \ }\\\ \ \ \ \ {\ \ \ \ \ \ \ \ \ \ \ \ \ \text{B}\ \ \ \ 0\ \ \ \ \ 1}$

Answer

B + 1 = 8, B = 7A + 1, A + 7 = 1, A = 4
So, A = 4, b = 7

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