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This is one of our many quizzes on Polynomial basics. Click on this to access more such competitive quizzes on Polynomials.

Polynomial basics Quiz 2

mathematics

 What is the value of $''X''$ in \[142X055-246315=1180740\]?

 Take the given numbers in the RHS then solve by addition.

\[\begin{align} &nbsp;&nbsp;& 142X055-246315=1180740 \\ &nbsp;& 246315+1180740=1427055 \\ \end{align}\]

 To create one bottle of fruit juice of one kind we require 200ml of sugar solution and 25ml fruit flavour. Another kind of fruit juice required 100ml of sugar solution and 50ml fruit flavour. What is the maximum number of bottles of juice that can be made from 5liter of sugar solution and 1liter of fruit flavour?

 Form two equations by taking two variables, one for the number of bottles and one for the second kind, then solve the two equations.

\[\begin{align} &nbsp;&nbsp;& \text{According to the question let there be ''}x''\text{ bottles of first and ''}y''\text{ bottles of second kind}. \\ &nbsp;& 200x+100y=5000 \\ &nbsp;& 25x+50y=1000 \\ &nbsp;& \text{Multiplying the second equation with 8 and then subtracting it from the first, } \\ &nbsp;& \text{So, x=20 and }y=10~ \\ &nbsp;& \text{Maximum number of bottles that can be made is }30. \\ \end{align}\]

 Given that, \[1.5\left( a-10 \right)+2.5\left( b-1.8 \right)=-1\], then find the maximum value of \[\left( a-b \right)\], if $''a''\text{ and }''b''$ are positive integers?

 Form one equation by simplifying the given expression then two values will be obtained, find the maximum value from there.

\[\begin{align} &nbsp;&nbsp;& 1.5\left( a-10 \right)+2.5\left( b-1.8 \right)=-1 \\ &nbsp;& \Rightarrow 3\left( a-10 \right)+5\left( b-\left( \dfrac{9}{5} \right) \right)=-23a-30+5b-9 \\ &nbsp;& \Rightarrow -23a+5b=37 \\ &nbsp;& \text{Now only two values }\left( 9,2 \right)\text{ and }\left( 4,5 \right)\text{satisfy the equation therefore maximum value of }\left( a-b \right)=4-5=-1 \\ \end{align}\]

 Three truck drivers, Mr. A, Mr. B and Mr. C stop at a roadside eating joint. Mr. A orders 10 rotis, 4 plates of tadka and a cup of tea. Mr. B orders 7 rotis, 3 plates of tadka and a cup of tea. Mr. A pays Rs. 80 for the meal and Mr. B pays Rs. 60. Meanwhile, Mr. C orders 5 rotis, 5 plates of tadka and 5 cups of tea. How much will Mr. C pay?

 Form two equations by taking three variables, one for the number of rotis, one for tadka and one for the tea, then solve the two equations by addition subtraction rules of polynomials.

\[\begin{align} &nbsp;&nbsp;& \text{Let the cost of 1 roti, 1 tadka and 1 cup of tea be ''}r'',\text{ ''}t''\text{ }and\text{ ''}c''\text{ respectively}\text{.} \\ &nbsp;& 10r+4t+1c=80\ldots (1) \\ &nbsp;& 7r+3t+1c=60\ldots (2) \\ &nbsp;& \text{Subtracting equation (1) from (2), } \\ &nbsp;& 3r+1t=20\ldots (3) \\ &nbsp;& \text{Multiply equation (3) by 2 and subtract equation (2) from it}\text{.} \\ &nbsp;& r+t+c=20 \\ &nbsp;& \therefore \text{Mr}\text{. C pays for }5r+5t+5c=100 \\ \end{align}\]

$''x''$ is a positive integer divisible by 4; as $''x''$ increases from 1824 to 1896, which of the following must decrease? \[\begin{array}{*{35}{l}} &nbsp;&nbsp;&nbsp;I.\text{ }4{{x}^{2}}-4x+4 \\ &nbsp;&nbsp;&nbsp;II.-10-\dfrac{1}{{{x}^{2}}} \\ &nbsp;&nbsp;&nbsp;III.\text{ }\dfrac{4}{{{x}^{2}}} \\ \end{array}\]

 Substitute the value of $''x''$ in the given three expressions and check for the value which is getting reduced.

\[\begin{align} &nbsp;&nbsp;& \text{If }x=1,\text{ then }I=~4{{x}^{2}}~-\text{ }4x+4=4.\text{ } \\ &nbsp;& \text{If }x=2,\text{ then }I=~4{{x}^{2}}~-\text{ }4x+4=12,\text{ } \\ &nbsp;& \text{''}x\text{'' value increased }\left( \text{I} \right)\text{ value also increased}\text{. } \\ &nbsp;& \text{If }x=1,\text{ then }II=-10-\dfrac{1}{{{x}^{2~~}}}=-11 \\ &nbsp;& \text{If }x=1,\text{ then }\!\!~\!\!\text{ }II= -10-\dfrac{1}{{{x}^{2~~}}}=-10.5,\text{ } \\ &nbsp;& ''x\text{'' value increased }\left( \text{II} \right)\text{ value also increased}\text{.} \\ &nbsp;& \text{If }x=1,\text{ then }III=\text{ }\dfrac{4}{{{x}^{2~}}}=4, \\ &nbsp;& \text{If }x=2,\text{ then }III=~\dfrac{4}{{{x}^{2~}}}=1,~\text{ } \\ &nbsp;& ''x\text{'' value increased }\left( \text{III} \right)\text{ value also decreased}. \\ \end{align}\]