Q. If the GCD of two numbers is 1, which of the following statements is true?
A.
The numbers are multiples of each other
B.
The numbers are co-prime
C.
The numbers are both even
D.
The numbers are both odd
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Solution
If the GCD of two numbers is 1, it means they have no common factors other than 1, hence they are co-prime.
Correct Answer:
B
— The numbers are co-prime
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Q. If the graph of a function f(x) intersects the x-axis at x = 1 and x = 3, which of the following can be inferred?
A.
f(1) = 0 and f(3) = 0.
B.
The function is linear.
C.
The function has no real roots.
D.
The function is increasing.
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Solution
If the graph intersects the x-axis at x = 1 and x = 3, it means that f(1) = 0 and f(3) = 0, indicating the roots of the function.
Correct Answer:
A
— f(1) = 0 and f(3) = 0.
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Q. If the graph of a function f(x) intersects the x-axis at x = 3, what can be concluded?
A.
f(3) = 0.
B.
f(3) > 0.
C.
f(3) < 0.
D.
f(3) is undefined.
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Solution
The intersection of the graph with the x-axis indicates that the function value at that point is zero.
Correct Answer:
A
— f(3) = 0.
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Q. If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?
A.
f(x) = f(-x) for all x.
B.
f(x) = -f(-x) for all x.
C.
f(x) is always positive.
D.
f(x) has a maximum value.
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Solution
A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.
Correct Answer:
A
— f(x) = f(-x) for all x.
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Q. If the graph of a function is a parabola opening upwards, which of the following can be inferred about the function?
A.
The function has a maximum value.
B.
The function has a minimum value.
C.
The function is linear.
D.
The function is constant.
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Solution
A parabola that opens upwards indicates that the function has a minimum value at its vertex.
Correct Answer:
B
— The function has a minimum value.
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Q. If the graph of a function is symmetric about the y-axis, which of the following types of functions could it represent?
A.
Linear function
B.
Odd function
C.
Even function
D.
Exponential function
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Solution
A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).
Correct Answer:
C
— Even function
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Q. If the graph of a function is symmetric about the y-axis, which of the following types of functions could it be?
A.
Linear function
B.
Odd function
C.
Even function
D.
Exponential function
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Solution
A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).
Correct Answer:
C
— Even function
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Q. If the graph of a function is symmetric about the y-axis, which of the following must be true?
A.
The function is linear.
B.
The function is even.
C.
The function is odd.
D.
The function has no intercepts.
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Solution
A function is even if it is symmetric about the y-axis, meaning f(x) = f(-x) for all x.
Correct Answer:
B
— The function is even.
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Q. If the HCF of 18 and 24 is 6, what is the LCM of these two numbers? (2023)
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Solution
Using the relation HCF * LCM = Product of the numbers, we have 6 * LCM = 18 * 24. Thus, LCM = (18 * 24) / 6 = 72.
Correct Answer:
A
— 72
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Q. If the HCF of 24 and 36 is 12, what is the LCM of these two numbers? (2023)
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Solution
Using the relation HCF * LCM = Product of the numbers, we have LCM = (24 * 36) / 12 = 72.
Correct Answer:
A
— 72
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Q. If the HCF of three numbers is 1, which of the following can be true?
A.
All three numbers are prime
B.
All three numbers are even
C.
All three numbers are odd
D.
Two numbers are even and one is odd
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Solution
If the HCF is 1, it is possible that all three numbers are prime, as they would not share any common factors.
Correct Answer:
A
— All three numbers are prime
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Q. If the HCF of three numbers is 5 and their LCM is 300, what can be said about the numbers?
A.
They are all multiples of 5
B.
They are all prime
C.
They are all even
D.
They are all odd
Show solution
Solution
Since the HCF is 5, all three numbers must be multiples of 5.
Correct Answer:
A
— They are all multiples of 5
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Q. If the HCF of three numbers is 5 and their LCM is 300, what is the product of the three numbers? (2023)
A.
1500
B.
3000
C.
6000
D.
7500
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Solution
The product of the three numbers is equal to HCF * LCM = 5 * 300 = 1500.
Correct Answer:
B
— 3000
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Q. If the HCF of three numbers is 7 and their LCM is 420, what is the maximum possible value of the product of these three numbers? (2023)
A.
2940
B.
840
C.
1260
D.
2100
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Solution
The product of the three numbers is equal to HCF * LCM. Thus, 7 * 420 = 2940.
Correct Answer:
C
— 1260
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Q. If the HCF of three numbers is 7 and their LCM is 420, what is the product of the three numbers? (2023)
A.
2940
B.
840
C.
2100
D.
1470
Show solution
Solution
The product of the three numbers = HCF * LCM = 7 * 420 = 2940.
Correct Answer:
A
— 2940
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Q. If the HCF of two numbers is 1, what can be inferred about the two numbers? (2023)
A.
They are both prime.
B.
They are coprime.
C.
They are multiples of each other.
D.
They are both even.
Show solution
Solution
If the HCF is 1, it means the two numbers are coprime, meaning they have no common factors other than 1.
Correct Answer:
B
— They are coprime.
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Q. If the HCF of two numbers is 1, what can be said about the two numbers? (2023)
A.
They are prime
B.
They are coprime
C.
They are even
D.
They are odd
Show solution
Solution
If the HCF is 1, the two numbers are coprime, meaning they have no common factors other than 1.
Correct Answer:
B
— They are coprime
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Q. If the HCF of two numbers is 12 and their LCM is 120, what is the product of the two numbers?
A.
144
B.
1200
C.
240
D.
100
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Solution
The product of two numbers is equal to the product of their HCF and LCM. Therefore, the product = 12 * 120 = 1440.
Correct Answer:
B
— 1200
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Q. If the HCF of two numbers is 12 and their LCM is 144, what is the product of the two numbers? (2023)
A.
1728
B.
864
C.
144
D.
288
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Solution
The product of two numbers is equal to the product of their HCF and LCM. Therefore, 12 * 144 = 1728.
Correct Answer:
A
— 1728
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Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers? (2023)
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Solution
Let the two numbers be 5x and 5y. Then, HCF(5x, 5y) = 5 and LCM(5x, 5y) = 100. This gives xy = 20. The pairs (x, y) that satisfy this are (4, 5) or (5, 4), leading to the sum 5(4 + 5) = 45.
Correct Answer:
A
— 30
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Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers if one of them is 25?
A.
50
B.
75
C.
100
D.
125
Show solution
Solution
Let the other number be x. Then, HCF(25, x) = 5 and LCM(25, x) = 100. Therefore, 25 * x = 5 * 100, which gives x = 20. The sum is 25 + 20 = 45.
Correct Answer:
A
— 50
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Q. If the HCF of two numbers is 5 and their product is 100, what could be the two numbers? (2023)
A.
5 and 20
B.
10 and 10
C.
15 and 5
D.
25 and 4
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Solution
If HCF is 5, the two numbers can be expressed as 5a and 5b. Thus, 5a * 5b = 100 implies ab = 4. The pair (1, 4) gives us 5 and 20.
Correct Answer:
A
— 5 and 20
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Q. If the HCF of two numbers is 5 and their product is 100, what is their LCM?
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Solution
Using the relationship between HCF, LCM, and product: HCF * LCM = Product. Thus, LCM = 100 / 5 = 20.
Correct Answer:
B
— 25
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Q. If the HCF of two numbers is 5 and their product is 1000, what is their LCM? (2023)
A.
200
B.
100
C.
250
D.
150
Show solution
Solution
Using the relation HCF * LCM = Product of the numbers, we have LCM = 1000 / 5 = 200.
Correct Answer:
A
— 200
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Q. If the HCF of two numbers is 8 and their LCM is 48, what could be one of the possible pairs of numbers? (2023)
A.
16 and 24
B.
8 and 32
C.
4 and 12
D.
20 and 16
Show solution
Solution
The numbers can be 16 and 24, as their HCF is 8 and LCM is 48.
Correct Answer:
A
— 16 and 24
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Q. If the HCF of two numbers is 8 and their product is 288, what is their LCM? (2023)
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Solution
Using the relationship between HCF, LCM, and the product of two numbers: LCM = Product / HCF = 288 / 8 = 36.
Correct Answer:
A
— 36
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Q. If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
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Solution
Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.
Correct Answer:
B
— It doubles
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Q. If the hexadecimal number A3 is converted to decimal, what is its value? (2023)
A.
163
B.
1630
C.
103
D.
83
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Solution
A3 in hexadecimal is calculated as 10*16^1 + 3*16^0 = 160 + 3 = 163.
Correct Answer:
A
— 163
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Q. If the LCM of three numbers is 120 and their HCF is 2, what is the maximum possible product of the three numbers? (2023)
A.
240
B.
480
C.
600
D.
720
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Solution
The maximum product occurs when the numbers are 2, 10, and 6, giving a product of 120.
Correct Answer:
C
— 600
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Q. If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)
A.
540
B.
1800
C.
5400
D.
18000
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Solution
The maximum product of the three numbers can be calculated as (LCM * HCF^2) = 180 * 3^2 = 5400.
Correct Answer:
C
— 5400
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