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Maths 1 Marks Question

Statistics · Gujarat Board (GSEB) STD 10 (GSEB - English Medium). 28 questions.

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28 questions · timed · auto-graded

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 $2^m× 5^n$ 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 $LCM \times HCF =$ Product of the two numbers
$LCM \times 9 = 306 \times 657$
$LCM$ $=\frac{306\times 657}{9}= 22338$
Therefore $LCM (306, 657) = 22338$.
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Question 51 Mark
Determine the prime factorisation of the following positive integer:
$20570$
Answer
$20570 = 2 × 5 × 12^4× 17$
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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.
$468 = 2^2× 3^2× 13$
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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.
$945 = 3^3× 5 × 7$
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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.
$420 = 2^2× 3 × 5 × 7$
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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
$45470971 = 7^2× 13^2× 17^2× 19$
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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 $\mathrm{n}=0$, then $2^0 \times 5^0=1 \times 1=1$
If $\mathrm{n}=1$, then $2^1 \times 5^1=2 \times 5=10$
If $\mathrm{n}=2$, 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
$98 = 2 × 7 × 7 = 2^1× 7^2$
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
$58500 = 2^2× 3^2× 5^2× 13$
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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.
$7325 = 5^2× 293$
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Question 191 Mark
Find the mode of the following data:
3, 5, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
Answer
xTally mark(f)
3
4
5
6
7
8
9		III
II
IIII
II
II
I
II		4
2
5
2
2
1
2
We see that 5 occurs in maximum times which is 5
$\therefore$ Mode = 5
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Question 201 Mark
Find the mode of the following data:
15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15
Answer
xTally mark(f)
8
15
18
19
20
24
25
26		I
IIII
I
I
I
II
I
I		1
4
1
1
1
2
1
1
Here we see that 15 occurs in maximum times i.e. 54
$\therefore$ Mode = 15
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Question 211 Mark
What is the algebraic sum of deviations of a frequency distribution about its mean?
Answer
The algebraic sum of deviation of a frequency distribution about its mean is zero.
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Question 221 Mark
Define Mean.
Answer
The mean of a set of observations is equal to their sum divided by the total number of observations. Mean is also called an average.
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Question 231 Mark
Write the empirical relation between mean, mode and median.
Answer
The empirical relation is Mode = 3 Mode = 3 Median - 2 mean
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Question 251 Mark
Write the modal class for the following frequency distribution:
Class 10-15 15-20 20-25 25-30 30-35 35-40
Frequency 30 35 75 40 30 15
Answer
The modal class is 20-25 as it has the maximum frequency of 75 in the given distribution.
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Question 261 Mark
Find the mode of the following data:
3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
Answer
xTally marks(f)
3
4
5
6
7
8
9		IIII
II
IIII
II
II
I
II		5
2
4
2
2
1
2
we see that 3 occurs in maximum times i.e. 5$\therefore$ Mode = 3
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Question 271 Mark
Which measure of central tendency can be determine graphically?
Answer
Median can be determined graphically.
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Question 281 Mark
Which measure of central tendency is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive?
Answer
Median is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive.
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1 Marks Question - Maths STD 10 Questions - Vidyadip