| 4451 |
The slope of the tangent to the curve xy = 12 at the point (3, 4) is: |
Mathematics/Applied Mathematics
Derivatives in applications |
Medium |
| 4452 |
The radius of a spherical balloon increases at 2 cm/s. How fast is its volume increasing when the radius is 5… |
Mathematics/Applied Mathematics
Derivatives in applications |
Medium |
| 4453 |
If x = a cos t and y = a sin t, then d²y/dx² equals: |
Mathematics/Applied Mathematics
Derivatives in applications |
Hard |
| 4454 |
Marginal cost is best described as: |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Easy |
| 4455 |
If the total revenue from selling x units is R(x) = 3x² + 36x + 5, the marginal revenue when x = 5 is: |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Easy |
| 4456 |
The total cost of producing x units is C(x) = 0.005x³ − 0.02x² + 30x + 5000. The marginal cost when 3 units a… |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Medium |
| 4457 |
The demand function for a product is p = 50 − 2x. For what output x is the marginal revenue zero? |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Medium |
| 4458 |
The total cost function is C(x) = x² + 4x + 100. At what output is the average cost minimum? |
Mathematics/Applied Mathematics
Marginal cost and marginal revenue |
Hard |
| 4459 |
The function f(x) = x² − 4x + 1 is decreasing on: |
Mathematics/Applied Mathematics
Maxima, minima and monotonicity |
Easy |
| 4460 |
A firm's profit from selling x units is P(x) = −x² + 40x − 300. The maximum profit is: |
Mathematics/Applied Mathematics
Maxima, minima and monotonicity |
Easy |
| 4461 |
The local minimum value of f(x) = 2x³ − 6x + 5 is: |
Mathematics/Applied Mathematics
Maxima, minima and monotonicity |
Medium |
| 4462 |
The absolute maximum value of f(x) = x³ − 12x on the interval [−3, 3] is: |
Mathematics/Applied Mathematics
Maxima, minima and monotonicity |
Medium |
| 4463 |
A farmer has 100 m of fencing to enclose a rectangular field along a straight river; no fence is needed on th… |
Mathematics/Applied Mathematics
Maxima, minima and monotonicity |
Hard |
| 4464 |
The value of ∫(4x³ − 6x) dx is: |
Mathematics/Applied Mathematics
Integration and area |
Easy |
| 4465 |
The value of ∫₀² (2x + 1) dx is: |
Mathematics/Applied Mathematics
Integration and area |
Easy |
| 4466 |
The value of ∫₀¹ eˣ dx is: |
Mathematics/Applied Mathematics
Integration and area |
Medium |
| 4467 |
The area of the region enclosed by the parabola y = 4 − x² and the x-axis is: |
Mathematics/Applied Mathematics
Integration and area |
Medium |
| 4468 |
The area of the region enclosed between the line y = x and the parabola y = x² is: |
Mathematics/Applied Mathematics
Integration and area |
Hard |
| 4469 |
Consumer surplus measures: |
Mathematics/Applied Mathematics
Consumer and producer surplus |
Easy |
| 4470 |
On a price–quantity graph, the consumer surplus at market price p₀ is the area: |
Mathematics/Applied Mathematics
Consumer and producer surplus |
Easy |
| 4471 |
The demand function is p = 20 − 2x and the market quantity is x₀ = 5. The consumer surplus is: |
Mathematics/Applied Mathematics
Consumer and producer surplus |
Medium |
| 4472 |
The supply function is p = 2 + x and the market quantity is x₀ = 4. The producer surplus is: |
Mathematics/Applied Mathematics
Consumer and producer surplus |
Medium |
| 4473 |
The demand function is p = 36 − x² and the supply function is p = 4 + x². The consumer surplus at market equi… |
Mathematics/Applied Mathematics
Consumer and producer surplus |
Hard |
| 4474 |
The order and degree of the differential equation d³y/dx³ + (d²y/dx²)² + y = 0 are: |
Mathematics/Applied Mathematics
Differential equations |
Easy |
| 4475 |
The particular solution of dy/dx = 3x² that satisfies y(1) = 2 is: |
Mathematics/Applied Mathematics
Differential equations |
Easy |
| 4476 |
The general solution of dy/dx = x/y is: |
Mathematics/Applied Mathematics
Differential equations |
Medium |
| 4477 |
The general solution of the linear differential equation dy/dx + 2y = 4 is: |
Mathematics/Applied Mathematics
Differential equations |
Medium |
| 4478 |
A sum of money grows continuously so that dA/dt = 0.05A, with t in years. Approximately how long does it take… |
Mathematics/Applied Mathematics
Differential equations |
Hard |
| 4479 |
For a random variable X with P(X = 0) = 1/4, P(X = 1) = 1/2 and P(X = 2) = 1/4, the value of E(X) is: |
Mathematics/Applied Mathematics
Random variables and expectation |
Easy |
| 4480 |
A random variable has P(X = x) = kx for x = 1, 2, 3, 4. The value of k is: |
Mathematics/Applied Mathematics
Random variables and expectation |
Easy |
| 4481 |
A game pays ₹10 with probability 0.2 and makes the player lose ₹2 with probability 0.8. The expected gain per… |
Mathematics/Applied Mathematics
Random variables and expectation |
Medium |
| 4482 |
Two fair coins are tossed and X is the number of heads. The value of P(X ≥ 1) is: |
Mathematics/Applied Mathematics
Random variables and expectation |
Medium |
| 4483 |
Two cards are drawn without replacement from a well-shuffled pack of 52. If X is the number of aces drawn, E(… |
Mathematics/Applied Mathematics
Random variables and expectation |
Hard |
| 4484 |
If the variance of a random variable is 2.25, its standard deviation is: |
Mathematics/Applied Mathematics
Variance and standard deviation |
Easy |
| 4485 |
For a constant random variable X = 7 (always), the variance of X is: |
Mathematics/Applied Mathematics
Variance and standard deviation |
Easy |
| 4486 |
X takes the values 0, 1, 2 with probabilities 1/4, 1/2, 1/4. The variance of X is: |
Mathematics/Applied Mathematics
Variance and standard deviation |
Medium |
| 4487 |
If Var(X) = 4, then Var(3X + 5) equals: |
Mathematics/Applied Mathematics
Variance and standard deviation |
Medium |
| 4488 |
The variance of the score X obtained on one throw of a fair six-sided die is: |
Mathematics/Applied Mathematics
Variance and standard deviation |
Hard |
| 4489 |
Which of these is NOT a condition for trials to be Bernoulli trials? |
Mathematics/Applied Mathematics
Binomial distribution |
Easy |
| 4490 |
For a binomial distribution with n = 10 and p = 0.4, the variance is: |
Mathematics/Applied Mathematics
Binomial distribution |
Easy |
| 4491 |
A fair coin is tossed 5 times. The probability of getting exactly 3 heads is: |
Mathematics/Applied Mathematics
Binomial distribution |
Medium |
| 4492 |
A binomial distribution has mean 4 and variance 3. The number of trials n is: |
Mathematics/Applied Mathematics
Binomial distribution |
Medium |
| 4493 |
A fair die is thrown 4 times. The probability of getting at least one six is: |
Mathematics/Applied Mathematics
Binomial distribution |
Hard |
| 4494 |
For a Poisson distribution with parameter λ, which statement is true? |
Mathematics/Applied Mathematics
Poisson distribution |
Easy |
| 4495 |
If X follows a Poisson distribution with mean 2, then P(X = 0) equals: |
Mathematics/Applied Mathematics
Poisson distribution |
Easy |
| 4496 |
X follows a Poisson distribution with mean 3. The value of P(X = 2) is: |
Mathematics/Applied Mathematics
Poisson distribution |
Medium |
| 4497 |
A machine produces defective items with probability 0.01. Using the Poisson approximation, the probability th… |
Mathematics/Applied Mathematics
Poisson distribution |
Medium |
| 4498 |
For a Poisson variable X, P(X = 1) = P(X = 2). The standard deviation of X is: |
Mathematics/Applied Mathematics
Poisson distribution |
Hard |
| 4499 |
If X is normal with mean 50 and standard deviation 5, the standard normal value corresponding to X = 60 is: |
Mathematics/Applied Mathematics
Normal distribution |
Easy |
| 4500 |
The mean and standard deviation of the standard normal variate Z are: |
Mathematics/Applied Mathematics
Normal distribution |
Easy |