Q. How many ways can 5 different letters be selected from the alphabet?
-
A.
26
-
B.
3003
-
C.
156
-
D.
120
Solution
The number of ways to choose 5 letters from 26 is C(26, 5) = 65780.
Correct Answer: B — 3003
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Q. How many ways can 5 different prizes be awarded to 3 students?
-
A.
60
-
B.
100
-
C.
150
-
D.
200
Solution
The number of ways to award 5 different prizes to 3 students is 3^5 = 243.
Correct Answer: C — 150
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Q. How many ways can 6 different books be arranged on a shelf if 2 specific books must be together?
-
A.
120
-
B.
720
-
C.
240
-
D.
480
Solution
Treat the 2 specific books as one unit. Then we have 5 units to arrange: 5! * 2! = 240.
Correct Answer: C — 240
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Q. How many ways can 6 people be arranged in a circle?
-
A.
720
-
B.
120
-
C.
60
-
D.
30
Solution
The number of arrangements in a circle is (n-1)! = (6-1)! = 5! = 120.
Correct Answer: A — 720
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Q. How many ways can 6 people be divided into 2 groups of 3?
Solution
The number of ways to divide 6 people into 2 groups of 3 is (6! / (3!3!)) / 2 = 20.
Correct Answer: A — 20
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Q. How many ways can a committee of 3 be formed from 5 people?
Solution
The number of ways to choose 3 from 5 is C(5,3) = 10.
Correct Answer: A — 10
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Q. How many ways can you arrange the letters of the word 'BANANA'?
Solution
The word 'BANANA' has 6 letters with 'A' repeating 3 times and 'N' repeating 2 times. The arrangements are 6!/(3!2!) = 60.
Correct Answer: B — 30
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Q. How many ways can you choose 3 fruits from a basket of 5 different fruits?
Solution
The number of ways to choose 3 fruits from 5 is given by 5C3 = 10.
Correct Answer: A — 10
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Q. How many ways can you form a committee of 3 from a group of 10 people?
-
A.
120
-
B.
90
-
C.
80
-
D.
100
Solution
The number of ways to form a committee of 3 from 10 is given by 10C3 = 120.
Correct Answer: A — 120
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Q. How many ways can you select 2 fruits from 5 different fruits?
Solution
The number of ways to choose 2 from 5 is given by 5C2 = 10.
Correct Answer: A — 10
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Q. How many ways can you select 2 students from a group of 8?
Solution
The number of ways to select 2 students from 8 is given by 8C2 = 28.
Correct Answer: A — 28
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Q. Identify the family of curves represented by the equation x^2 + y^2 = r^2.
-
A.
Straight lines
-
B.
Ellipses
-
C.
Circles
-
D.
Hyperbolas
Solution
The equation x^2 + y^2 = r^2 represents a family of circles with varying radii 'r'.
Correct Answer: C — Circles
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Q. Identify the family of curves represented by the equation y = a(x - h)^2 + k.
-
A.
Parabolas
-
B.
Circles
-
C.
Ellipses
-
D.
Hyperbolas
Solution
The equation y = a(x - h)^2 + k represents a family of parabolas that open upwards or downwards.
Correct Answer: A — Parabolas
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Q. Identify the family of curves represented by the equation y = ax^2 + bx + c.
-
A.
Linear functions
-
B.
Quadratic functions
-
C.
Cubic functions
-
D.
Exponential functions
Solution
The equation y = ax^2 + bx + c represents a family of quadratic functions with varying coefficients (a, b, c).
Correct Answer: B — Quadratic functions
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Q. Identify the family of curves represented by the equation y = a^x.
-
A.
Exponential functions
-
B.
Logarithmic functions
-
C.
Polynomial functions
-
D.
Trigonometric functions
Solution
The equation y = a^x represents a family of exponential functions where a is a positive constant.
Correct Answer: A — Exponential functions
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Q. Identify the family of curves represented by the equation y = c/x, where c is a constant.
-
A.
Linear functions
-
B.
Hyperbolas
-
C.
Parabolas
-
D.
Circles
Solution
The equation y = c/x represents a family of hyperbolas with varying asymptotes.
Correct Answer: B — Hyperbolas
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Q. Identify the family of curves represented by the equation y = e^(kx), where k is a constant.
-
A.
Linear functions
-
B.
Exponential functions
-
C.
Logarithmic functions
-
D.
Polynomial functions
Solution
The equation y = e^(kx) represents a family of exponential functions with varying growth rates determined by k.
Correct Answer: B — Exponential functions
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Q. Identify the family of curves represented by the equation y = e^(kx).
-
A.
Linear functions
-
B.
Exponential functions
-
C.
Logarithmic functions
-
D.
Polynomial functions
Solution
The equation y = e^(kx) represents a family of exponential functions with varying growth rates determined by 'k'.
Correct Answer: B — Exponential functions
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Q. Identify the family of curves represented by the equation y = mx^3 + c.
-
A.
Cubic functions
-
B.
Quadratic functions
-
C.
Linear functions
-
D.
Exponential functions
Solution
The equation y = mx^3 + c represents a family of cubic functions with varying coefficients m and c.
Correct Answer: A — Cubic functions
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Q. Identify the family of curves represented by the equation y = sin(kx) for varying k.
-
A.
Sine waves
-
B.
Cosine waves
-
C.
Straight lines
-
D.
Parabolas
Solution
The equation y = sin(kx) represents a family of sine waves with varying frequencies determined by k.
Correct Answer: A — Sine waves
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Q. Identify the family of curves represented by the equation y^2 = 4ax.
-
A.
Parabolas
-
B.
Hyperbolas
-
C.
Ellipses
-
D.
Straight lines
Solution
The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of 'a'.
Correct Answer: A — Parabolas
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Q. If 2x + 3y = 12 and x + 2y = 10, what is the value of x?
Solution
From the second equation, x = 10 - 2y. Substituting into the first gives 2(10 - 2y) + 3y = 12, solving gives y = 2, x = 6.
Correct Answer: C — 4
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Q. If 5x - 7 < 3, what is the range of x?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 1
-
D.
x > 1
Solution
5x - 7 < 3 => 5x < 10 => x < 2
Correct Answer: A — x < 2
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Q. If 5x - 7 < 3, what is the value of x?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 1
-
D.
x > 1
Solution
5x - 7 < 3 => 5x < 10 => x < 2
Correct Answer: A — x < 2
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Q. If 5x - 7 < 3x + 1, what is the range of x?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 2
-
D.
x > 2
Solution
5x - 7 < 3x + 1 => 2x < 8 => x < 4.
Correct Answer: A — x < 4
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Q. If 6x + 4 > 10, what is the value of x?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6x + 4 > 10 => 6x > 6 => x > 1.
Correct Answer: B — x > 1
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Q. If 7 - 2x > 3, what is the value of x?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7 - 2x > 3 => -2x > -4 => x < 2.
Correct Answer: B — x > 2
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Q. If 7 - 2x ≥ 1, what is the range of x?
-
A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x < 3
-
D.
x > 3
Solution
7 - 2x ≥ 1 => -2x ≥ -6 => x ≤ 3
Correct Answer: B — x ≥ 3
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Q. If 7 - 2x ≥ 3, what is the value of x?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
7 - 2x ≥ 3 => -2x ≥ -4 => x ≤ 2.
Correct Answer: B — x ≥ 2
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Q. If 7 - 3x ≤ 1, what is the value of x?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
7 - 3x ≤ 1 => -3x ≤ -6 => x ≥ 2.
Correct Answer: B — x ≥ 2
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