If the supply function for a commodity is p = 4 + x and 12 units of goods are sold, then the producer's surplus is given by:
- A70
- ✓72
- C12
- D48
Answer: B.
View full solution →Question types
Integrals and it's Applications question types
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MCQ
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4 Q→Sample Questions
Integrals and it's Applications questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the demand function for a commodity is $p=35-2 x-x^2$ Then the consumer's surplus at equilibrium price $p_0=20$ is given by:
- A20
- ✓27
- C25
- D35
Answer: B.
View full solution →The area of the region bounded by parabola $y^2=x$and the straight line 2y = x is:
- A$\frac{4}{3}$ sq. units
- B1 sq. units
- C$\frac{2}{3}$ sq. units
- D$\frac{1}{3}$ sq. units
The area of the region bounded by the curve $x^2=4 y$ and the straight-line $x=4 y-2$ is:
- A$\frac{3}{8}$ sq. units
- B$\frac{5}{8}$ sq. units
- C$\frac{7}{8}$ sq. units
- ✓$\frac{9}{8}$ sq. units
Answer: D.
View full solution →Find the value of $\int_1^4|x-5| d x$.
- A2
- ✓$\frac{15}{2}$
- C$\frac{2}{15}$
- D15
Answer: B.
View full solution →Read the following text and answer the following questions on the basis of the same
Mohan is the student of class XII of Sunshine School. In the mathematics class, teacher defines the method for evaluation of definite integral, she said, To evaluate the definite integral $\underset{\pi}{\equiv} f(x) d x$ a continuous function f(x) defined on [a, b], we may use the following algorithm.
Step 1: Find the indefinite integral $\stackrel{b}{\equiv} f(x) d x$
Let this be P(x) There is no need to keep the constant of integration.
Step 2: Evaluate $\phi(b)$ and $\phi(a)$.
Step 3: Calculate $\phi(b)-\phi(a)$.
The number obtained in step 3 is the value of definite integral $\int_a^b f(x) d x$
Q.1. Evaluate: $\int_0^1 \frac{1}{\sqrt{1+x}+\sqrt{x}} d x$
Q.2. If $\int_1^a\left(3 x^2+2 x+1\right) d x=1$, find real values of $a$.
View full solution →Mohan is the student of class XII of Sunshine School. In the mathematics class, teacher defines the method for evaluation of definite integral, she said, To evaluate the definite integral $\underset{\pi}{\equiv} f(x) d x$ a continuous function f(x) defined on [a, b], we may use the following algorithm.
Step 1: Find the indefinite integral $\stackrel{b}{\equiv} f(x) d x$
Let this be P(x) There is no need to keep the constant of integration.
Step 2: Evaluate $\phi(b)$ and $\phi(a)$.
Step 3: Calculate $\phi(b)-\phi(a)$.
The number obtained in step 3 is the value of definite integral $\int_a^b f(x) d x$
Q.1. Evaluate: $\int_0^1 \frac{1}{\sqrt{1+x}+\sqrt{x}} d x$
Q.2. If $\int_1^a\left(3 x^2+2 x+1\right) d x=1$, find real values of $a$.
Find the area of region bounded by the curve x = 2y + 3 Y-axis and the lines y = 1 and y = - 1
Find the area of the region bounded by the graph of $f(x)=x^5$ and the $X$-axishetween $x=-1$ and $x=1$.
View full solution →What is the area bounded by the curve y = log x, X-axis and the ordinates x = 1, x = 2 ?
If the demand curve is given by $D(x)=50-0.06 x^2$. Find the surplus or profit of the consumers if the level of sale amounts to twenty units.
View full solution →Find the area of the region bounded by $x^2=4 y$ y = 2 x = 4 and the Y-axis in the first quadrant.
View full solution →Find the area of the region bounded by $y^2=9 x$ x = 2 x = 4 and the X-axis in the first quadrant.
View full solution →Find the area of the region bounded by the curve $y^2=x$ and the lines x = 1 x = 4 and the X-axis.
View full solution →Evaluate: $\int_a^b \frac{\log x}{x} d x$
View full solution →The demand and supply function of an article are $D(q)=1000-0.4 q^2$ and $S(q)=42 q$. Find the consumer's surplus and producer's surplus at equilibrium price.
View full solution →The demand and supply function of a commodity are $P_d=18-2 x-x^2$ and $P_s=2 x-3$. Find the consumer's surplus and producer's surplus at equilibrium price .
View full solution →Suppose the demand for the certain product is given by $p=-0.01 x^2-0.1 x+6$, where $p$ is the unit price given in rupees and x is the quantity demanded per month given in the units of 1000. The unit market price for the product is ₹ 4 per unit
(a) Find the quantity demanded at the given price.
(b) Find the consumer's surplus if the market price for the product is ₹ 4 per unit.
View full solution →(a) Find the quantity demanded at the given price.
(b) Find the consumer's surplus if the market price for the product is ₹ 4 per unit.
Evaluate: $\int_{-1}^2\left|x^3-3 x^2+2 x\right| d x$
View full solution →$\int_1^4\{|x-1|+|x-2|+|x-4|\} d x$
View full solution →
Read the following text and answer the following questions on the basis of the same:
The demand function for a popular make of 12- speed bicycle is given by $p= D (x)=-0.001 x^2$= 250, where p is the unit price in Rupees and x is the quantity demanded in units of a thousands. The supply function for the same product is given by p $= S (x)=0.0006 x^2+0.02 x+100$,where p is the unit price in Rupees and x is the quantity supplied in units of a thousands.
Q.1. If at equilibrium, curves of demand function and supply function intersect at (x, y), then what does the point of intersection represents?
(A) x = equilibrium quantity, y = equilibrium price
(B) x = equilibrium price, y = equilibrium quantity
(C) x = equilibrium demand, equilibrium price
(D) x = equilibrium supply, y = equilibrium demand
Q.2. Find point of intersection.
(A) (300, 160)
(B) (160,300)
(C) (300,300)
(D) (160, 160)
Q.3. Formula for Consumer's Surplus is:
(A) $C S=\int_0^{Q_e} D(x) d x+Q_e \cdot P_e$
(B) CS $=\int_0^{Q_e} D(x) d x-Q_e \cdot P_e$
(C) $C S=-\int_0^{Q_e} D(x) d x-Q_e \cdot P_e$
(D) $CS =-\int_0^{Q_e} D(x) d x+Q_e \cdot P_e$
Q.4. Formula for Producer's Surplus is:
(A) $P S=Q_e \cdot P_e-\int_0^{Q_e} D(x) d x$
(B) $P S=Q_e \cdot P_e-\int_0^{Q_e} S(x) d x$
(C) $P S=Q_c \cdot P_e+\int_0^{Q_e} S(x) d x$
(D) $P S=-Q_e \cdot P_e+\int_0^{Q_e} D(x) d x$
View full solution →The demand function for a popular make of 12- speed bicycle is given by $p= D (x)=-0.001 x^2$= 250, where p is the unit price in Rupees and x is the quantity demanded in units of a thousands. The supply function for the same product is given by p $= S (x)=0.0006 x^2+0.02 x+100$,where p is the unit price in Rupees and x is the quantity supplied in units of a thousands.
Q.1. If at equilibrium, curves of demand function and supply function intersect at (x, y), then what does the point of intersection represents?
(A) x = equilibrium quantity, y = equilibrium price
(B) x = equilibrium price, y = equilibrium quantity
(C) x = equilibrium demand, equilibrium price
(D) x = equilibrium supply, y = equilibrium demand
Q.2. Find point of intersection.
(A) (300, 160)
(B) (160,300)
(C) (300,300)
(D) (160, 160)
Q.3. Formula for Consumer's Surplus is:
(A) $C S=\int_0^{Q_e} D(x) d x+Q_e \cdot P_e$
(B) CS $=\int_0^{Q_e} D(x) d x-Q_e \cdot P_e$
(C) $C S=-\int_0^{Q_e} D(x) d x-Q_e \cdot P_e$
(D) $CS =-\int_0^{Q_e} D(x) d x+Q_e \cdot P_e$
Q.4. Formula for Producer's Surplus is:
(A) $P S=Q_e \cdot P_e-\int_0^{Q_e} D(x) d x$
(B) $P S=Q_e \cdot P_e-\int_0^{Q_e} S(x) d x$
(C) $P S=Q_c \cdot P_e+\int_0^{Q_e} S(x) d x$
(D) $P S=-Q_e \cdot P_e+\int_0^{Q_e} D(x) d x$
Read the following text and answer the following questions on the basis of the same:
The second new species named Puntius euspilurus is an edible freshwater fish found in the Mananthavady river in Wayanad. The epithet euspilurus is a Greek word referring to the distinct black spot on the caudal fin. The slender bodied fish prefers fast flowing, shallow and clear waters and occurs only in unpolluted areas. It appears in great numbers in paddy fields during the onset of the Southwest monsoon.
Suppose that the supply schedule of this Fish is given in the table below which follows a linear relationship between price and quantity supplied.
Suppose that this Fish can be sold only in the Kerala. The Kerala demand schedule for this Fish is as follows and there is a linear relationship between price and quantity demanded.
Q.1. Which of the following represents the Price (p) - supply (x) relationship?
(A) $p=65-\frac{x}{20}$
(B) $p=65+\frac{x}{20}$
(C) $p=-15+\frac{x}{20}$
(D) $p=15-\frac{x}{20}$
Q.2. The equation of demand curve can be given by:
(A) $p=30-\frac{x}{40}$
(B) $p=30+\frac{x}{40}$
(C) $p=20-\frac{x}{40}$
(D) $p=20+\frac{x}{40}$
Q.3. The value of x at equilibrium is:
(A) 1400/3
(B) 600
(C) 15
(D) 200/3
Q.4. The equilibrium price is:
(A) 400
(B) 20
(C) 600
(D) 15
View full solution →The second new species named Puntius euspilurus is an edible freshwater fish found in the Mananthavady river in Wayanad. The epithet euspilurus is a Greek word referring to the distinct black spot on the caudal fin. The slender bodied fish prefers fast flowing, shallow and clear waters and occurs only in unpolluted areas. It appears in great numbers in paddy fields during the onset of the Southwest monsoon.
Suppose that the supply schedule of this Fish is given in the table below which follows a linear relationship between price and quantity supplied.
| Price P per kg (in) | Quantity (X) of Fish supplied (in kg) |
| 25 | 800 |
| 20 | 700 |
| 15 | 600 |
| 10 | 500 |
| 5 | 400 |
| Price P per kg (in) | Quantity (X) of Fish supplied (in kg) |
| 25 | 200 |
| 20 | 400 |
| 15 | 600 |
| 10 | 800 |
| 5 | 1000 |
(A) $p=65-\frac{x}{20}$
(B) $p=65+\frac{x}{20}$
(C) $p=-15+\frac{x}{20}$
(D) $p=15-\frac{x}{20}$
Q.2. The equation of demand curve can be given by:
(A) $p=30-\frac{x}{40}$
(B) $p=30+\frac{x}{40}$
(C) $p=20-\frac{x}{40}$
(D) $p=20+\frac{x}{40}$
Q.3. The value of x at equilibrium is:
(A) 1400/3
(B) 600
(C) 15
(D) 200/3
Q.4. The equilibrium price is:
(A) 400
(B) 20
(C) 600
(D) 15
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