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 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 7 and their LCM is 420, what is the product of the three numbers? (2023)
A.
2940
B.
840
C.
2100
D.
1470
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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 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
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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
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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 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 180 and their HCF is 3, what is the product of the three numbers? (2023)
A.
540
B.
1800
C.
5400
D.
18000
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Solution
The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.
Correct Answer: C — 5400
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Q. If the LCM of two numbers is 120 and their HCF is 10, what is the product of the two numbers? (2023)
A.
1200
B.
1000
C.
2400
D.
600
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Solution
The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 10 = 1200.
Correct Answer: A — 1200
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Q. If the LCM of two numbers is 120 and their HCF is 5, what is the product of the two numbers? (2023)
A.
600
B.
1200
C.
240
D.
300
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Solution
The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 5 = 600.
Correct Answer: A — 600
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Q. If the LCM of two numbers is 180 and their HCF is 15, what is the sum of the two numbers? (2023)
A.
75
B.
90
C.
105
D.
120
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Solution
Let the two numbers be 15a and 15b. Then, LCM = 15ab = 180, so ab = 12. The pairs (3, 4) give the numbers 45 and 60, summing to 105.
Correct Answer: C — 105
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Q. If the LCM of two numbers is 60 and their HCF is 4, what is the product of the two numbers? (2023)
A.
240
B.
120
C.
300
D.
180
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Solution
The product of two numbers is equal to the product of their LCM and HCF. Therefore, 60 * 4 = 240.
Correct Answer: A — 240
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Q. If the LCM of two numbers is 72 and one of the numbers is 24, what is the other number? (2023)
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Solution
Using the relationship between LCM and the numbers: (24 * x) / HCF = 72. The other number is 36.
Correct Answer: B — 36
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
A.
720
B.
180
C.
120
D.
60
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Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Correct Answer: A — 720
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Q. If the lengths of the diagonals of a rhombus are 10 cm and 24 cm, what is the area of the rhombus?
A.
120 cm²
B.
240 cm²
C.
60 cm²
D.
300 cm²
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Solution
The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².
Correct Answer: B — 240 cm²
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Q. If the lengths of the sides of a triangle are in the ratio 3:4:5, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
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Solution
A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, thus it is a right triangle.
Correct Answer: D — Right
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Q. If the linear equation 3x + 4y = 12 is graphed, what is the y-intercept?
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Solution
Setting x = 0 in the equation gives y = 3, so the y-intercept is 3.
Correct Answer: B — 3
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Q. If the linear equation 5x + 2y = 10 is graphed, what is the point where it intersects the x-axis?
A.
(2, 0)
B.
(0, 5)
C.
(5, 0)
D.
(0, 2)
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Solution
To find the x-intercept, set y = 0. Solving gives x = 2, so the intersection point is (2, 0).
Correct Answer: A — (2, 0)
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Q. If the linear equation 5x - 2y = 10 is graphed, what is the point of intersection with the x-axis?
A.
(2, 0)
B.
(0, 5)
C.
(0, -5)
D.
(5, 0)
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Solution
Setting y to 0 in the equation gives x = 2, so the intersection with the x-axis is (2, 0).
Correct Answer: A — (2, 0)
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Q. If the linear equation 5x - 2y = 10 is graphed, what is the y-intercept?
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Solution
Setting x = 0 in the equation gives y = -5, so the y-intercept is -5.
Correct Answer: B — 2
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Q. If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?
A.
20 degrees
B.
30 degrees
C.
40 degrees
D.
60 degrees
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Solution
Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.
Correct Answer: B — 30 degrees
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?
A.
(6, 7)
B.
(8, 9)
C.
(4, 5)
D.
(0, 1)
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Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer: A — (6, 7)
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?
A.
(6, 7)
B.
(8, 9)
C.
(4, 5)
D.
(2, 3)
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Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer: A — (6, 7)
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Q. If the nth term of a harmonic progression is given by 1/(1/n + 1/a), what does 'a' represent?
A.
The first term
B.
The last term
C.
The common difference
D.
The sum of the terms
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Solution
'a' represents the first term of the harmonic progression in the formula for the nth term.
Correct Answer: A — The first term
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Q. If the nth term of a harmonic progression is given by 1/(1/n + 1/m), what does this represent?
A.
The average of n and m
B.
The product of n and m
C.
The sum of n and m
D.
The difference of n and m
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Solution
The nth term of a harmonic progression can be expressed as the harmonic mean of n and m, which is 1/(1/n + 1/m).
Correct Answer: A — The average of n and m
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Q. If the nth term of a sequence is given by a_n = 5n - 3, what is the value of a_7? (2023)
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Solution
Substituting n = 7 into the formula gives a_7 = 5*7 - 3 = 35 - 3 = 32.
Correct Answer: B — 34
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Q. If the nth term of a sequence is given by n^2 + n, what is the 4th term? (2023)
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Solution
The 4th term is 4^2 + 4 = 16 + 4 = 20.
Correct Answer: A — 20
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Q. If the number 1011 in binary is converted to decimal, what is its value?
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Solution
The binary number 1011 converts to decimal as follows: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.
Correct Answer: A — 11
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