Q. Deficiency of which nutrient causes chlorosis in plants? (2022)
-
A.
Nitrogen
-
B.
Phosphorus
-
C.
Potassium
-
D.
Calcium
Solution
Nitrogen deficiency leads to chlorosis, which is the yellowing of leaves due to insufficient chlorophyll production.
Correct Answer:
A
— Nitrogen
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Q. Deficiency of which nutrient causes the 'chlorosis' symptom in plants? (2022)
-
A.
Nitrogen
-
B.
Phosphorus
-
C.
Potassium
-
D.
Magnesium
Solution
Nitrogen deficiency leads to chlorosis, which is the yellowing of leaves due to insufficient chlorophyll production.
Correct Answer:
A
— Nitrogen
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Q. Determine the angle between the lines y = 2x + 3 and y = -1/2x + 1.
-
A.
90 degrees
-
B.
60 degrees
-
C.
45 degrees
-
D.
30 degrees
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2)/(1 + m1*m2)| = tan^(-1)(5/4) which is approximately 60 degrees.
Correct Answer:
B
— 60 degrees
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Q. Determine the coefficient of x^4 in the expansion of (2x - 3)^6.
-
A.
540
-
B.
720
-
C.
810
-
D.
960
Solution
The coefficient of x^4 is given by 6C4 * (2)^4 * (-3)^2 = 15 * 16 * 9 = 2160.
Correct Answer:
B
— 720
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Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0). (2023)
-
A.
(2, 2, 0)
-
B.
(2, 3, 0)
-
C.
(3, 2, 0)
-
D.
(0, 0, 0)
Solution
Centroid = ((0+6+0)/3, (0+0+8)/3, (0+0+0)/3) = (2, 2.67, 0).
Correct Answer:
A
— (2, 2, 0)
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Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(0, 4, 0), and C(3, 0, 0). (2021)
-
A.
(1, 1.33, 0)
-
B.
(1, 2, 0)
-
C.
(0, 1.33, 0)
-
D.
(0, 2, 0)
Solution
Centroid = ((0+0+3)/3, (0+4+0)/3, (0+0+0)/3) = (1, 1.33, 0).
Correct Answer:
B
— (1, 2, 0)
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Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2023)
-
A.
(1, 1, 0)
-
B.
(2, 1, 0)
-
C.
(4/3, 1, 0)
-
D.
(0, 1, 0)
Solution
Centroid G = ((0+4+0)/3, (0+0+3)/3, (0+0+0)/3) = (4/3, 1, 0).
Correct Answer:
B
— (2, 1, 0)
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Q. Determine the coordinates of the centroid of the triangle with vertices A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2021)
-
A.
(4, 5, 6)
-
B.
(3, 4, 5)
-
C.
(5, 6, 7)
-
D.
(6, 7, 8)
Solution
Centroid G = ((1+4+7)/3, (2+5+8)/3, (3+6+9)/3) = (4, 5, 6).
Correct Answer:
B
— (3, 4, 5)
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Q. Determine the coordinates of the foot of the perpendicular from the point (1, 2, 3) to the plane x + 2y + 3z = 14. (2023)
-
A.
(2, 3, 4)
-
B.
(1, 2, 4)
-
C.
(2, 1, 3)
-
D.
(3, 2, 1)
Solution
Using the formula for the foot of the perpendicular, we find the coordinates to be (1, 2, 4).
Correct Answer:
B
— (1, 2, 4)
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Q. Determine the critical points of f(x) = 3x^4 - 8x^3 + 6. (2021)
-
A.
(0, 6)
-
B.
(1, 1)
-
C.
(2, 0)
-
D.
(3, -1)
Solution
f'(x) = 12x^3 - 24x^2. Setting f'(x) = 0 gives x = 0, 2. Check f(1) = 1.
Correct Answer:
B
— (1, 1)
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Q. Determine the critical points of f(x) = e^x - 2x. (2021)
Solution
f'(x) = e^x - 2. Setting f'(x) = 0 gives e^x = 2, so x = ln(2).
Correct Answer:
B
— 1
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Q. Determine the distance between the points (2, 3) and (5, 7). (2020)
Solution
Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. Determine the distance from the point (3, 4) to the line 2x + 3y - 12 = 0.
Solution
Using the formula for distance from a point to a line, d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), we find d = |2(3) + 3(4) - 12| / sqrt(2^2 + 3^2) = 3.
Correct Answer:
B
— 3
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Q. Determine the intervals where f(x) = -x^2 + 4x is concave up. (2023)
-
A.
(-∞, 0)
-
B.
(0, 2)
-
C.
(2, ∞)
-
D.
(0, 4)
Solution
f''(x) = -2, which is always negative, indicating concave down everywhere.
Correct Answer:
C
— (2, ∞)
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Q. Determine the intervals where f(x) = x^3 - 3x is increasing. (2021)
-
A.
(-∞, -1)
-
B.
(-1, 1)
-
C.
(1, ∞)
-
D.
(-∞, 1)
Solution
f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = -1, 1. f'(x) > 0 for x > 1.
Correct Answer:
C
— (1, ∞)
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Q. Determine the intervals where f(x) = x^4 - 4x^3 has increasing behavior. (2023)
-
A.
(-∞, 0)
-
B.
(0, 2)
-
C.
(2, ∞)
-
D.
(0, 4)
Solution
f'(x) = 4x^3 - 12x^2 = 4x^2(x - 3). f'(x) > 0 for x in (0, 3).
Correct Answer:
B
— (0, 2)
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Q. Determine the intervals where f(x) = x^4 - 4x^3 has local minima. (2020)
-
A.
(0, 2)
-
B.
(1, 3)
-
C.
(2, 4)
-
D.
(0, 1)
Solution
f'(x) = 4x^3 - 12x^2. Setting f'(x) = 0 gives x = 0, 3. Testing intervals shows local minima at (0, 2).
Correct Answer:
A
— (0, 2)
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Q. Determine the limit: lim (x -> 0) (tan(5x)/x) (2022)
-
A.
0
-
B.
1
-
C.
5
-
D.
Undefined
Solution
Using the standard limit lim (x -> 0) (tan(kx)/x) = k, we have k = 5. Thus, lim (x -> 0) (tan(5x)/x) = 5.
Correct Answer:
C
— 5
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Q. Determine the limit: lim (x -> 1) (x^3 - 1)/(x - 1) (2020)
Solution
Factoring gives (x - 1)(x^2 + x + 1)/(x - 1). For x ≠ 1, this simplifies to x^2 + x + 1. Evaluating at x = 1 gives 3.
Correct Answer:
C
— 3
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Q. Determine the limit: lim (x -> 1) (x^4 - 1)/(x - 1) (2021)
-
A.
0
-
B.
1
-
C.
4
-
D.
Undefined
Solution
Factoring gives (x - 1)(x^3 + x^2 + x + 1)/(x - 1). For x ≠ 1, this simplifies to x^3 + x^2 + x + 1. Evaluating at x = 1 gives 4.
Correct Answer:
D
— Undefined
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Q. Determine the local maxima of f(x) = -x^3 + 3x^2 + 1. (2021)
-
A.
(0, 1)
-
B.
(1, 3)
-
C.
(2, 5)
-
D.
(3, 4)
Solution
f'(x) = -3x^2 + 6x. Setting f'(x) = 0 gives x = 0 or x = 2. f(2) = 5 is a local maximum.
Correct Answer:
B
— (1, 3)
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Q. Determine the local maxima of f(x) = x^4 - 8x^2 + 16. (2021)
-
A.
(0, 16)
-
B.
(2, 12)
-
C.
(4, 0)
-
D.
(1, 9)
Solution
Find f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. f(2) = 12 is a local maximum.
Correct Answer:
B
— (2, 12)
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Q. Determine the local minima of f(x) = x^3 - 3x + 2. (2021)
Solution
f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = 1. f(1) = 0.
Correct Answer:
B
— 0
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Q. Determine the local minima of f(x) = x^4 - 4x^2. (2021)
Solution
f'(x) = 4x^3 - 8x. Setting f'(x) = 0 gives x = 0, ±2. f(0) = 0.
Correct Answer:
B
— 0
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Q. Determine the maximum area of a triangle with a base of 10 units and height as a function of x. (2020)
Solution
Area = 1/2 * base * height = 5h. Max area occurs when h is maximized, thus Area = 50 when h = 10.
Correct Answer:
B
— 50
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Q. Determine the maximum height of the function f(x) = -x^2 + 6x + 5. (2020) 2020
Solution
The vertex occurs at x = 3. f(3) = -3^2 + 6*3 + 5 = 8.
Correct Answer:
A
— 8
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Q. Determine the maximum height of the projectile given by h(t) = -16t^2 + 64t + 80. (2023)
Solution
The maximum height occurs at t = -b/(2a) = -64/(2*-16) = 2. h(2) = -16(2^2) + 64(2) + 80 = 80.
Correct Answer:
A
— 80
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Q. Determine the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 80. (2020)
Solution
The maximum height occurs at t = -b/(2a) = 64/(2*16) = 2. h(2) = -16(2^2) + 64(2) + 80 = 80.
Correct Answer:
A
— 80
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Q. Determine the maximum value of f(x) = -x^2 + 6x - 8. (2022)
Solution
The maximum occurs at x = 3. f(3) = -3^2 + 6(3) - 8 = 6.
Correct Answer:
C
— 6
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Q. Determine the minimum value of f(x) = x^2 - 4x + 5. (2021)
Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 5 = 1.
Correct Answer:
A
— 1
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