Q. The family of curves defined by the equation x^2 + y^2 = r^2 represents:
A.
Ellipses
B.
Hyperbolas
C.
Circles
D.
Parabolas
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Solution
The equation x^2 + y^2 = r^2 represents a circle with radius r.
Correct Answer: C — Circles
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Q. The family of curves defined by the equation y = a(x - h)^2 + k represents which type of function?
A.
Linear
B.
Quadratic
C.
Cubic
D.
Rational
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Solution
The equation y = a(x - h)^2 + k represents a quadratic function in vertex form.
Correct Answer: B — Quadratic
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Q. The family of curves defined by the equation y = a(x - h)^2 + k represents:
A.
Parabolas
B.
Circles
C.
Ellipses
D.
Hyperbolas
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Solution
The equation y = a(x - h)^2 + k represents a family of parabolas with vertex (h, k).
Correct Answer: A — Parabolas
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Q. The family of curves defined by the equation y = ax^2 + bx + c is known as:
A.
Linear functions
B.
Quadratic functions
C.
Polynomial functions
D.
Rational functions
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Solution
The equation y = ax^2 + bx + c represents a quadratic function.
Correct Answer: B — Quadratic functions
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Q. The family of curves defined by the equation y = e^(kx) is classified as:
A.
Linear
B.
Exponential
C.
Logarithmic
D.
Polynomial
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Solution
The equation y = e^(kx) represents a family of exponential curves.
Correct Answer: B — Exponential
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Q. The family of curves defined by the equation y = k/x represents which type of function?
A.
Linear
B.
Quadratic
C.
Rational
D.
Exponential
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Solution
The equation y = k/x represents a rational function.
Correct Answer: C — Rational
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Q. The family of curves defined by the equation y = k/x represents:
A.
Linear functions
B.
Hyperbolas
C.
Parabolas
D.
Circles
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Solution
The equation y = k/x represents a family of hyperbolas.
Correct Answer: B — Hyperbolas
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Q. The family of curves defined by y = kx^3 represents:
A.
Linear curves
B.
Cubic curves
C.
Quadratic curves
D.
Exponential curves
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Solution
The equation y = kx^3 represents a family of cubic curves.
Correct Answer: B — Cubic curves
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Q. The family of curves given by the equation y = a sin(bx + c) is known as:
A.
Linear functions
B.
Trigonometric functions
C.
Exponential functions
D.
Polynomial functions
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Solution
The equation y = a sin(bx + c) represents a family of trigonometric functions.
Correct Answer: B — Trigonometric functions
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Q. The family of curves given by the equation y = kx + b is characterized by:
A.
Different slopes
B.
Different intercepts
C.
Both a and b
D.
None of the above
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Solution
The equation y = kx + b represents a family of straight lines with different slopes (k) and intercepts (b).
Correct Answer: C — Both a and b
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Q. The family of curves given by y = a sin(bx) is characterized by:
A.
Linear behavior
B.
Periodic behavior
C.
Exponential growth
D.
Quadratic growth
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Solution
The equation y = a sin(bx) represents a family of periodic curves.
Correct Answer: B — Periodic behavior
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Q. The family of curves given by y = k(x - a)(x - b) is a representation of:
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Exponential functions
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Solution
The equation y = k(x - a)(x - b) represents a family of quadratic functions.
Correct Answer: B — Quadratic functions
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Q. The family of curves given by y^2 = 4ax represents which type of conic section?
A.
Circle
B.
Ellipse
C.
Parabola
D.
Hyperbola
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Solution
The equation y^2 = 4ax represents a parabola that opens to the right.
Correct Answer: C — Parabola
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Q. The family of curves represented by the equation x^2 + y^2 = r^2 describes which geometric shape?
A.
Ellipse
B.
Circle
C.
Hyperbola
D.
Parabola
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Solution
The equation x^2 + y^2 = r^2 represents a circle with radius r.
Correct Answer: B — Circle
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Q. The family of curves represented by the equation x^2 + y^2 = r^2 is known as:
A.
Ellipses
B.
Hyperbolas
C.
Circles
D.
Parabolas
Show solution
Solution
The equation x^2 + y^2 = r^2 represents a family of circles.
Correct Answer: C — Circles
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Q. The family of curves represented by the equation y = e^(kx) is characterized by:
A.
Linear growth
B.
Exponential growth
C.
Quadratic growth
D.
Logarithmic growth
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Solution
The equation y = e^(kx) represents exponential growth for different values of k.
Correct Answer: B — Exponential growth
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Q. The family of curves represented by the equation y = e^(kx) is classified as:
A.
Linear
B.
Polynomial
C.
Exponential
D.
Logarithmic
Show solution
Solution
The equation y = e^(kx) represents an exponential function.
Correct Answer: C — Exponential
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Q. The family of curves represented by the equation y = kx^2, where k is a constant, is known as:
A.
Linear curves
B.
Parabolic curves
C.
Circular curves
D.
Exponential curves
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Solution
The equation y = kx^2 represents a parabola for different values of k.
Correct Answer: B — Parabolic curves
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Q. The family of curves represented by the equation y = kx^n, where n is a constant, is known as:
A.
Polynomial curves
B.
Rational curves
C.
Trigonometric curves
D.
Exponential curves
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Solution
The equation y = kx^n represents a family of polynomial curves.
Correct Answer: A — Polynomial curves
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Q. The family of curves represented by the equation y = mx + c, where m and c are constants, is known as:
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Exponential functions
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Solution
The equation y = mx + c represents a straight line, which is a linear function.
Correct Answer: A — Linear functions
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Q. The family of curves represented by y = a sin(bx + c) is known as:
A.
Linear functions
B.
Trigonometric functions
C.
Polynomial functions
D.
Exponential functions
Show solution
Solution
The equation y = a sin(bx + c) represents a family of trigonometric functions.
Correct Answer: B — Trigonometric functions
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Q. The family of curves represented by y = kx^n, where n is a constant, is known as:
A.
Polynomial curves
B.
Rational curves
C.
Trigonometric curves
D.
Logarithmic curves
Show solution
Solution
The equation y = kx^n represents a family of polynomial curves.
Correct Answer: A — Polynomial curves
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Q. The family of curves represented by y = mx + c can be described as:
A.
Quadratic functions
B.
Linear functions
C.
Cubic functions
D.
Exponential functions
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Solution
The equation y = mx + c describes linear functions for varying m and c.
Correct Answer: B — Linear functions
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Q. The family of curves represented by y^2 = 4ax is known as:
A.
Parabolas
B.
Ellipses
C.
Hyperbolas
D.
Circles
Show solution
Solution
The equation y^2 = 4ax represents a family of parabolas.
Correct Answer: A — Parabolas
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Q. The family of curves y = ax^3 + bx^2 + cx + d is classified as:
A.
Linear
B.
Quadratic
C.
Cubic
D.
Quartic
Show solution
Solution
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic curves.
Correct Answer: C — Cubic
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Q. The family of curves y = kx^3 is known for having:
A.
One turning point
B.
Two turning points
C.
No turning points
D.
Three turning points
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Solution
The cubic function y = kx^3 has one turning point at x = 0.
Correct Answer: A — One turning point
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Q. The family of curves y = kx^n, where n is a constant, represents:
A.
Linear functions
B.
Polynomial functions
C.
Rational functions
D.
Trigonometric functions
Show solution
Solution
The equation y = kx^n represents a family of polynomial functions.
Correct Answer: B — Polynomial functions
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Q. The famous rock edicts were issued by which Mauryan emperor?
A.
Ashoka
B.
Bindusara
C.
Chandragupta
D.
Samudragupta
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Solution
The rock edicts were issued by Emperor Ashoka, promoting Buddhism and moral governance.
Correct Answer: A — Ashoka
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Q. The Faraday's first law of electrolysis states that: (2018)
A.
The mass of substance deposited is directly proportional to the current
B.
The voltage is directly proportional to the current
C.
The energy is conserved
D.
The temperature remains constant
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Solution
Faraday's first law states that the mass of a substance deposited at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.
Correct Answer: A — The mass of substance deposited is directly proportional to the current
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Q. The female reproductive part of a flower is called the: (2022)
A.
Stamen
B.
Pistil
C.
Petal
D.
Sepal
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Solution
The pistil is the female reproductive part of the flower, consisting of the ovary, style, and stigma.
Correct Answer: B — Pistil
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