Q. If a man can do a piece of work in 15 days, how much work can he do in 3 days?
-
A.
1/5
-
B.
1/4
-
C.
1/3
-
D.
1/2
Solution
In 1 day, he does 1/15 of the work. In 3 days, he does 3/15 = 1/5 of the work.
Correct Answer:
B
— 1/4
Learn More →
Q. If a man can finish a work in 25 days, how long will it take for him to finish 40% of the work?
-
A.
10 days
-
B.
12 days
-
C.
15 days
-
D.
20 days
Solution
40% of the work = 0.4 * 25 days = 10 days.
Correct Answer:
B
— 12 days
Learn More →
Q. If a man can walk 5 km in 1 hour, how long will it take him to walk 20 km?
-
A.
3 hours
-
B.
4 hours
-
C.
5 hours
-
D.
6 hours
Solution
Time = Distance / Speed = 20 km / 5 km/h = 4 hours.
Correct Answer:
B
— 4 hours
Learn More →
Q. If y = (2x + 1)^3, find dy/dx at x = 1.
Solution
dy/dx = 6(2x + 1)^2. At x = 1, dy/dx = 6(2(1) + 1)^2 = 6(3)^2 = 54.
Correct Answer:
A
— 12
Learn More →
Q. If y = (2x + 1)^3, find dy/dx.
-
A.
6(2x + 1)^2
-
B.
3(2x + 1)^2
-
C.
2(2x + 1)^2
-
D.
12(2x + 1)^2
Solution
dy/dx = 6(2x + 1)^2 by the chain rule.
Correct Answer:
A
— 6(2x + 1)^2
Learn More →
Q. If y = (x^2 + 1)^5, find dy/dx at x = 1.
Solution
dy/dx = 5(x^2 + 1)^4(2x). At x = 1, dy/dx = 5(2)^4(2) = 5(16)(2) = 160.
Correct Answer:
B
— 20
Learn More →
Q. If y = (x^2 + 1)^5, find dy/dx.
-
A.
10x(x^2 + 1)^4
-
B.
5(x^2 + 1)^4
-
C.
5x(x^2 + 1)^4
-
D.
20x(x^2 + 1)^3
Solution
dy/dx = 10x(x^2 + 1)^4 by the chain rule.
Correct Answer:
A
— 10x(x^2 + 1)^4
Learn More →
Q. If y = 2^x, find dy/dx at x = 1.
-
A.
0.693
-
B.
1.386
-
C.
2.718
-
D.
3.141
Solution
dy/dx = 2^x * ln(2). At x = 1, dy/dx = 2^1 * ln(2) = 2 * 0.693 = 1.386.
Correct Answer:
A
— 0.693
Learn More →
Q. If y = 3x^2 + 2x, find dy/dx at x = 2.
Solution
First, find dy/dx = 6x + 2. At x = 2, dy/dx = 6(2) + 2 = 12 + 2 = 14.
Correct Answer:
B
— 18
Learn More →
Q. If y = 4x^2 + 3x + 2, find dy/dx at x = -1.
Solution
dy/dx = 8x + 3. At x = -1, dy/dx = 8(-1) + 3 = -8 + 3 = -5.
Correct Answer:
A
— -5
Learn More →
Q. If y = 4x^3 - 2x + 1, find dy/dx at x = -1.
Solution
dy/dx = 12x^2 - 2. At x = -1, dy/dx = 12(-1)^2 - 2 = 12 - 2 = 10.
Correct Answer:
C
— -6
Learn More →
Q. If y = 5x^4 + 3x^2 - x, find dy/dx at x = 1.
Solution
dy/dx = 20x^3 + 6x - 1. At x = 1, dy/dx = 20(1)^3 + 6(1) - 1 = 20 + 6 - 1 = 25.
Correct Answer:
B
— 22
Learn More →
Q. If y = 5x^4 - 3x^3 + 2x - 1, find dy/dx at x = 1.
Solution
dy/dx = 20x^3 - 9x^2 + 2. At x = 1, dy/dx = 20 - 9 + 2 = 13.
Correct Answer:
B
— 16
Learn More →
Q. If y = cos(5x^2), find dy/dx.
-
A.
-10xsin(5x^2)
-
B.
-5xsin(5x^2)
-
C.
-25xsin(5x^2)
-
D.
-2xsin(5x^2)
Solution
dy/dx = -10xsin(5x^2) by the chain rule.
Correct Answer:
A
— -10xsin(5x^2)
Learn More →
Q. If y = e^(3x), find dy/dx at x = 0.
Solution
dy/dx = 3e^(3x). At x = 0, dy/dx = 3e^(0) = 3.
Correct Answer:
A
— 1
Learn More →
Q. If y = e^(3x), find dy/dx.
-
A.
3e^(3x)
-
B.
e^(3x)
-
C.
9e^(3x)
-
D.
6e^(3x)
Solution
dy/dx = 3e^(3x) by the chain rule.
Correct Answer:
A
— 3e^(3x)
Learn More →
Q. If y = ln(5x^2 + 3), find dy/dx at x = 1.
-
A.
5/8
-
B.
3/8
-
C.
1/8
-
D.
1/5
Solution
dy/dx = (10x)/(5x^2 + 3). At x = 1, dy/dx = (10)/(5(1) + 3) = 10/8 = 5/4.
Correct Answer:
A
— 5/8
Learn More →
Q. If y = ln(5x^2 + 3), find dy/dx.
-
A.
10/(5x^2 + 3)
-
B.
5/(5x^2 + 3)
-
C.
2/(5x^2 + 3)
-
D.
15/(5x^2 + 3)
Solution
dy/dx = (10x)/(5x^2 + 3) by the chain rule.
Correct Answer:
A
— 10/(5x^2 + 3)
Learn More →
Q. If y = sin(2x), find dy/dx at x = π/4.
Solution
dy/dx = 2cos(2x). At x = π/4, dy/dx = 2cos(π/2) = 2(0) = 0.
Correct Answer:
D
— √2
Learn More →
Q. If y = sqrt(4x^2 + 1), find dy/dx.
-
A.
(4x)/(sqrt(4x^2 + 1))
-
B.
(2x)/(sqrt(4x^2 + 1))
-
C.
(8x)/(sqrt(4x^2 + 1))
-
D.
(2)/(sqrt(4x^2 + 1))
Solution
Using the chain rule, dy/dx = (4x)/(2sqrt(4x^2 + 1)) = (4x)/(sqrt(4x^2 + 1)).
Correct Answer:
A
— (4x)/(sqrt(4x^2 + 1))
Learn More →
Q. If y = sqrt(x^2 + 1), find dy/dx at x = 0.
Solution
dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 0, dy/dx = (1/2)(1)^(-1/2)(0) = 0.
Correct Answer:
B
— 1
Learn More →
Q. If y = tan(3x), find dy/dx at x = π/6.
Solution
dy/dx = 3sec^2(3x). At x = π/6, dy/dx = 3sec^2(π/2) = 3(∞) = undefined.
Correct Answer:
A
— 3√3
Learn More →
Q. If y = tan(3x), find dy/dx.
-
A.
3sec^2(3x)
-
B.
3tan^2(3x)
-
C.
sec^2(3x)
-
D.
3tan(3x)
Solution
Using the chain rule, dy/dx = 3sec^2(3x).
Correct Answer:
A
— 3sec^2(3x)
Learn More →
Q. If y = x^3 * e^x, find dy/dx at x = 0.
Solution
Using product rule, dy/dx = 3x^2 * e^x + x^3 * e^x. At x = 0, dy/dx = 0 + 0 = 0.
Correct Answer:
A
— 0
Learn More →
Q. If y = √(4x^2 + 1), find dy/dx.
-
A.
4x/(√(4x^2 + 1))
-
B.
2x/(√(4x^2 + 1))
-
C.
2/(√(4x^2 + 1))
-
D.
8x/(√(4x^2 + 1))
Solution
dy/dx = (4x)/(2√(4x^2 + 1)) = 4x/(√(4x^2 + 1)).
Correct Answer:
A
— 4x/(√(4x^2 + 1))
Learn More →
Q. If y = √(x^2 + 1), find dy/dx at x = 1.
Solution
dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 1, dy/dx = (1/2)(2)^(-1/2)(2) = 1/√2.
Correct Answer:
A
— 1/√2
Learn More →
Showing 31 to 56 of 56 (2 Pages)
