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
Solution
The equation y = k(x - a)(x - b) represents a family of quadratic functions.
Correct Answer: B — Quadratic functions
Learn More →
Q. The family of curves given by y^2 = 4ax represents which type of conic section?
-
A.
Circle
-
B.
Ellipse
-
C.
Parabola
-
D.
Hyperbola
Solution
The equation y^2 = 4ax represents a parabola that opens to the right.
Correct Answer: C — Parabola
Learn More →
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
Solution
The equation x^2 + y^2 = r^2 represents a circle with radius r.
Correct Answer: B — Circle
Learn More →
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
Solution
The equation x^2 + y^2 = r^2 represents a family of circles.
Correct Answer: C — Circles
Learn More →
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
Solution
The equation y = e^(kx) represents exponential growth for different values of k.
Correct Answer: B — Exponential growth
Learn More →
Q. The family of curves represented by the equation y = e^(kx) is classified as:
-
A.
Linear
-
B.
Polynomial
-
C.
Exponential
-
D.
Logarithmic
Solution
The equation y = e^(kx) represents an exponential function.
Correct Answer: C — Exponential
Learn More →
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
Solution
The equation y = kx^2 represents a parabola for different values of k.
Correct Answer: B — Parabolic curves
Learn More →
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
Solution
The equation y = kx^n represents a family of polynomial curves.
Correct Answer: A — Polynomial curves
Learn More →
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
Solution
The equation y = mx + c represents a straight line, which is a linear function.
Correct Answer: A — Linear functions
Learn More →
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
Solution
The equation y = a sin(bx + c) represents a family of trigonometric functions.
Correct Answer: B — Trigonometric functions
Learn More →
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
Solution
The equation y = kx^n represents a family of polynomial curves.
Correct Answer: A — Polynomial curves
Learn More →
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
Solution
The equation y = mx + c describes linear functions for varying m and c.
Correct Answer: B — Linear functions
Learn More →
Q. The family of curves represented by y^2 = 4ax is known as:
-
A.
Parabolas
-
B.
Ellipses
-
C.
Hyperbolas
-
D.
Circles
Solution
The equation y^2 = 4ax represents a family of parabolas.
Correct Answer: A — Parabolas
Learn More →
Q. The family of curves y = ax^3 + bx^2 + cx + d is classified as:
-
A.
Linear
-
B.
Quadratic
-
C.
Cubic
-
D.
Quartic
Solution
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic curves.
Correct Answer: C — Cubic
Learn More →
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
Solution
The cubic function y = kx^3 has one turning point at x = 0.
Correct Answer: A — One turning point
Learn More →
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
Solution
The equation y = kx^n represents a family of polynomial functions.
Correct Answer: B — Polynomial functions
Learn More →
Q. The foci of the ellipse x^2/16 + y^2/9 = 1 are located at?
-
A.
(±4, 0)
-
B.
(0, ±3)
-
C.
(±3, 0)
-
D.
(0, ±4)
Solution
For the ellipse x^2/16 + y^2/9 = 1, the foci are located at (±4, 0) where c = √(16 - 9) = 4.
Correct Answer: A — (±4, 0)
Learn More →
Q. The foci of the ellipse x^2/25 + y^2/16 = 1 are located at which points?
-
A.
(±3, 0)
-
B.
(±4, 0)
-
C.
(±5, 0)
-
D.
(±6, 0)
Solution
For the ellipse, c = √(a^2 - b^2) = √(25 - 16) = √9 = 3. The foci are at (±3, 0).
Correct Answer: B — (±4, 0)
Learn More →
Q. The Freundlich adsorption isotherm is applicable to which type of adsorption?
-
A.
Physisorption only
-
B.
Chemisorption only
-
C.
Both physisorption and chemisorption
-
D.
None of the above
Solution
The Freundlich isotherm can describe both physisorption and chemisorption processes.
Correct Answer: C — Both physisorption and chemisorption
Learn More →
Q. The function f(x) = e^x is differentiable at all points?
-
A.
True
-
B.
False
-
C.
Only at x = 0
-
D.
Only at x = 1
Solution
f(x) = e^x is differentiable everywhere as it is an exponential function.
Correct Answer: A — True
Learn More →
Q. The function f(x) = ln(x) + x has a minimum at:
-
A.
x = 1
-
B.
x = 0
-
C.
x = e
-
D.
x = 2
Solution
Finding f'(x) = 1/x + 1. Setting f'(x) = 0 gives x = 1 as the minimum point.
Correct Answer: A — x = 1
Learn More →
Q. The function f(x) = ln(x) is differentiable at x = 1?
-
A.
Yes
-
B.
No
-
C.
Only for x > 1
-
D.
Only for x < 1
Solution
f'(x) = 1/x; f'(1) = 1/1 = 1, hence it is differentiable at x = 1.
Correct Answer: A — Yes
Learn More →
Q. The function f(x) = sqrt(x) is differentiable at x = 0?
-
A.
Yes
-
B.
No
-
C.
Only from the right
-
D.
Only from the left
Solution
f(x) = sqrt(x) is not differentiable at x = 0 because the left-hand derivative does not exist.
Correct Answer: B — No
Learn More →
Q. The function f(x) = x^2 + 2x + 1 is differentiable everywhere?
-
A.
True
-
B.
False
-
C.
Only at x = 0
-
D.
Only for x > 0
Solution
f(x) is a polynomial function, which is differentiable everywhere.
Correct Answer: A — True
Learn More →
Q. The function f(x) = x^2 - 2x + 1 is differentiable at all points?
-
A.
True
-
B.
False
-
C.
Only at x = 0
-
D.
Only for x > 0
Solution
f(x) is a polynomial function, which is differentiable everywhere.
Correct Answer: A — True
Learn More →
Q. The function f(x) = x^2 - 2x + 1 is differentiable at x = 2?
-
A.
Yes
-
B.
No
-
C.
Only left
-
D.
Only right
Solution
f(x) is a polynomial function, hence it is differentiable everywhere including at x = 2.
Correct Answer: A — Yes
Learn More →
Q. The function f(x) = x^2 - 4 is:
-
A.
Always increasing
-
B.
Always decreasing
-
C.
Neither increasing nor decreasing
-
D.
Both increasing and decreasing
Solution
The function has a minimum at x = 0, hence it is neither always increasing nor decreasing.
Correct Answer: C — Neither increasing nor decreasing
Learn More →
Q. The function f(x) = x^2 - 4x + 4 can be expressed in which form?
-
A.
(x - 2)^2
-
B.
(x + 2)^2
-
C.
(x - 4)^2
-
D.
(x + 4)^2
Solution
f(x) = (x - 2)^2 is the completed square form.
Correct Answer: A — (x - 2)^2
Learn More →
Q. The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?
-
A.
Yes
-
B.
No
-
C.
Only left
-
D.
Only right
Solution
f(x) is a polynomial function, hence differentiable everywhere including at x = 2.
Correct Answer: A — Yes
Learn More →
Q. The function f(x) = x^2 - 4x + 4 is differentiable everywhere?
-
A.
True
-
B.
False
-
C.
Only at x = 0
-
D.
Only at x = 2
Solution
f(x) is a polynomial function, hence it is differentiable everywhere.
Correct Answer: A — True
Learn More →
Showing 5611 to 5640 of 10700 (357 Pages)
