RS Aggarwal

Mark (√) against the correct answer in the following: If f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)} then (g o f) = ?
A. {(3, 1), (1, 3), (3, 4)}
B. {(1, 3), (3, 1), (4, 3)}
C. {(3, 4), (4, 3), (1, 3)}
D. {(2, 5), (5, 2), (1, 5)}

Solution: Option(B) is correct. $\begin{array}{l} \mathrm{f}=\{(1,2),(3,5),(4,1)\} \\ \mathrm{g}=\{(2,3),(5,1),(1,3)\} \end{array}$ According to the combination of $\mathrm{f}$ and $\mathrm{g}$,...

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A medicine company has factories at two places, X and Y. From these places, supply is made to each of its three agencies situated at \mathrm{P}, \mathrm{Q} and \mathrm{R}. the monthly requirement of the agencies are respectively 40 packets, 40 packets and 50 packets of medicine, while the production capacity of the factories at X and Y are 60 packets and 70 packets respectively. The transportation costs per packet from the factories to the agencies are given as follows.

How many packets from each factory should be transported to each agency so that the cost of transportation is minimum? Also, find the minimum cost. Solution: Let $x$ packets of medicines be...

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In a culture the bacteria count is 100000 . The number is increased by 10 \% in 2 hours. In how many hours will the count reach 200000 , if the rate of growth of bacteria is proportional to the number present?

Solution: Suppose $y$ be the bacteria count, therefore, we have, the rate of growth of bacteria is proportional to the no. present $\mathrm{So}_{\mathrm{s}} \frac{d y}{d t}=c y$ Where $c$ is a...

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The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after t seconds.

Solution: It is given that: Volume $\mathrm{V}=\frac{4 \pi r^{3}}{\mathrm{a}}$ $\frac{d V}{d t}=\frac{4}{3} \pi 3 r^{2} \frac{d r}{d t}$ $\Rightarrow \frac{d V}{d t}=k$ (constant) $\begin{array}{l}...

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A curve passes through the point (-1,1) and at any point (x, y) of the curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3). Find the equation of the curve.

Solution: $\begin{array}{l} \text { It is given that: } \frac{d y}{d x}=\frac{2(y+3)}{x+4} \\ \Rightarrow \frac{d y}{y+3}=\frac{2 d x}{x+4} \\ \Rightarrow \int \frac{d y}{y+3}=2 \int \frac{d x}{x+4}...

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A curve passes through the point (0,-2) and at any point (x, y) of the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point. Find the equation of the curve.

Solution: It is given that product of slope of tangent and $y$ coordinate equals the $x$-coordinate i.e., $y \frac{d y}{d x}=x$ We have, $y d y=x d x$ $\begin{array}{l} \Rightarrow \int y d y=\int x...

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