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Maths 1 Marks Question

Real Numbers · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 39 questions.

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Question 11 Mark
If a and b are relatively prime numbers, then what is their LCM?
Answer
If a and b are relatively prime numbers, then their LCM is ab.
In LCM we choose all prime factor and if two numbers are relatively prime, so their factor is a and b.
So, LCM (a, b) = ab
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Question 21 Mark
Write the condition to be satisfied by q so that a rational number $\frac{\text{p}}{\text{q}}$ has a terminating decimal expansion.
Answer
In the rational number $\frac{\text{p}}{\text{q}},$ the factorization of denominator q must be in form of $2^m \times 5^n$ where m and n are non-negative integers.
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Question 41 Mark
Given that HCF (306. 657) = 9, find LCM (306, 657).
Answer
By the property that LCM × HCF = Product of the two numbers
LCM × 9 = 306 × 657
LCM $=\frac{306\times 657}{9}= 22338$
Therefore LCM (306, 657) = 22338.
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Question 51 Mark
Determine the prime factorisation of the following positive integer:
20570
Answer
$20570 = 2 \times 5 \times 12^4 \times 17$
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Question 61 Mark
If p and q are two prime numbers, then what is their LCM?
Answer
If p and q are two primes, their LCM will be their product.
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Question 71 Mark
Express the following integers as a product of its prime factors:
468
Answer
To Express: Each of the following numbers as a product of their prime factors.
$468 = 2^2 \times 3^2 \times 13$
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Question 81 Mark
Express the following integers as a product of its prime factors:
945
Answer
To Express: Each of the following numbers as a product of their prime factors.
$945 = 3^3 \times 5 \times 7$
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Question 91 Mark
Express the following integers as a product of its prime factors:
420
Answer
To Express: Each of the following numbers as a product of their prime factors.
$420 = 2^2 \times 3 \times 5 \times 7$
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Question 101 Mark
If a and b are relatively prime numbers, then what is their HCF?
Answer
a and b are relatively prime numbers than their HCF is 1 because in HCF we choose common prime factor and if two numbers are relatively prime then their common factor is 1.
HCF (a, b) = 1
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Question 111 Mark
What is the HCF of the smallest composite number and the smallest prime number?
Answer
We know that 2 is the smallest prime number and 4 is the smallest composite number HCF of 2 and 4 = 2
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Question 121 Mark
Determine the prime factorisation of the following positive integer:
45470971
Answer
$45470971 = 7^2 \times 13^2 \times 17^2 \times 19$
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Question 131 Mark
What is the total number of factors of a prime number?
Answer
Total number of factors of a prime number is 2 i.e., 1 and itself.
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Question 141 Mark
For what value of n, $2^n \times 5^n$ ends in 5.
Answer
$2^n \times 5^n$
If $n =0$, then $2^0 \times 5^0=1 \times 1=1$
If $n=1$, then $2^1 \times 5^1=2 \times 5=10$
If $n=2$, then $2^2 \times 5^2=4 \times 25=100$
Thus, no value of $n, 2^n \times 5^n$ and in 5 .
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Question 151 Mark
Write the sum of the exponents of prime factors in the prime factorisation of 98.
Answer
$98 = 2 \times 7 \times 7 = 2^1 \times 7^2$
Sum of exponents = 1 + 2 = 3
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Question 161 Mark
What is an algorithm?
Answer
Algorithm: An algorithm is a series of well defined slips which gives a procedure for solving a type of problem.
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Question 171 Mark
Determine the prime factorisation of the following positive integer:
58500
Answer
$58500 = 2^2 \times 3^2 \times 5^2 \times 13$
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Question 181 Mark
Express the following integers as a product of its prime factors:
7325
Answer
To Express: Each of the following numbers as a product of their prime factors.
$7325 = 5^2 \times 293$
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Question 211 Mark
Two positive integers a and b can be written as $a=x^3 y^2$ and $b=x y^3$, where x, y are prime numbers. Find LCM (a, b).
Answer
$x^3 y^3$
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Question 251 Mark
Has the rational number $\frac{441}{2^2 \times 5^7 \times 7^2}$ a terminating or a nonterminating decimal representation?
Answer
Terminating
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Question 261 Mark
Write whether $\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}$ on simplification gives a rational or an irrational number.
Answer
Rational Number
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Question 271 Mark
The decimal expansion of the rational number $\frac{43}{2^4 \times 5^3}$ will terminate after how many places of decimals?
Answer
4
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Question 321 Mark
If the prime factorization of a natural number n is $2^3 \times 3^2 \times 5^2 \times 7$, write the number of consecutive zeros in n.
Answer
2
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