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CBSE Questions for Class 7 Maths Algebraic Expressions Quiz 1 - MCQExams.com
CBSE
Class 7 Maths
Algebraic Expressions
Quiz 1
State True or False:
Addition of $$ 5a+3b, \ a-2b, \ 3a+5b $$ is $$9a+6b$$.
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0%
True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (5+1+3)a+(3-2+5)b=9a+6b$$
State True or False:
$$ b^2y-9b^2y+2b^2y-5b^2y $$ is equal to $$-11b^2y $$.
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True
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False
Explanation
$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (1-9+2-5)b^{ 2 }y=-11b^{ 2 }y$$
State True or False:
$$ -7x^2+18x^2+3x^2-5x^2 $$ is equal to $$9x^2 $$
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True
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False
Explanation
$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (-7+18+3-5){ x }^{ 2 }\quad =9{ x }^{ 2 }$$
$$\displaystyle 4x-\left( -2y+5x \right) $$ is equal to
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$$\displaystyle 9x-2y$$
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$$\displaystyle 9x+2y$$
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$$\displaystyle x+2y$$
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$$\displaystyle -x+2y$$
Explanation
Given, $$\displaystyle 4x-\left( -2y+5x \right) $$
$$\displaystyle =4x+2y-5x$$
$$\displaystyle =-x+2y$$
Hence simplified form is $$-x+2y$$
On subtracting 7x+5y-3 from 5y-3x-9 we get
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10x +6
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-10x-6
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10x+10y-12
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-10x-12
Explanation
$$(5y-3x-9)-(7x+5y-3)$$
$$=5y-3x-9-7x-5y+3$$
$$=-10x-6$$
The number of terms is $$\displaystyle 6x^{3}+5x^{2}-2x+3$$
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$$2$$
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$$3$$
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$$4$$
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$$5$$
Explanation
$$6x^2-5x^2-2x+3$$ has terms $$6x^3,5x^2,2x\ and\ 3$$, therefore four terms.
What must be subtracted from $$3x^{2}+4y^{2}-5$$
to get $$2x^{2}-3y^{2}+5$$?
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$$x^{2}+3y^{2}+5$$
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$$x^2 - 4y^2 + 5$$
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$$x^2 + 7y^2 - 10$$
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$$x^2 - 7y^2 - 10$$
Explanation
$$(3x^{2}+4y^{2}-5) - a = (2x^{2}-3y^{2}+5)$$
$$\therefore$$ $$a = 3x^2 + 4 y^2 - 5 - (2x^2 - 3y^2 + 5)$$
$$\therefore$$ $$a = 3x^2 + 4 y^2 - 5 - 2x^2 + 3y^2 - 5$$
$$\therefore$$ $$a = x^2 + 7y^2 - 10$$
State true or false.
After Subtracting
$$(1 + x + 2x^{2} - 3x^{3})$$ from $$(2x^{2} -4x^{3} +4x + 9)$$ we get
$$(-x^{3} + 3x +8)$$.
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True
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False
Explanation
$$-(1 + x + 2x^{2} - 3x^{3})$$ + $$(2x^{2} -4x^{3} +4x + 9)$$
$$=-x^{3} + 3x +8$$
Evaluate : $$ 7x-9y+3-3x-5y+8 $$
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$$4x+4y+11 $$
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$$4x-14y+11 $$
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Cannot be determined
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None of these
Explanation
$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (7-3)x+(-9-5)y+(3+8)=4x-14y+11$$
State True or False:
Addition of
$$ a-3b+3, \ 2a+5-3c, \ 6c-15+6b $$ is $$3a+3b+3c-7$$.
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0%
True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (1+2)a+(-3+6)b+(-3+6)c+(3+5-15)=3a+3b+3c-7$$
Subtract $$4p^2q - 3pq + 5pq^2 - 8p - 7q - 10$$ from $$18 - 3p + 11q + 5pq - 2pq^2 + 5p^2q$$
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$$pq^2 - 7p^2q + 8pq + 18q + 5p + 28$$
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$$p^2q - 7pq^2 + 8pq + 18p + 5q + 28$$
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$$pq^2 - 7p^2q + 8pq + 18p + 5q + 28$$
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$$p^2q - 7pq^2 + 8pq + 18q + 5p + 28$$
Explanation
Subtract $$4p^2q - 3pq + 5pq^2 - 8p - 7q - 10$$ from $$18-3p+11q+5pq-2pq^{ 2 }+5p^{ 2 }q$$
$$=18-3p+11q+5pq-2pq^{ 2 }+5p^{ 2 }q-(4p^2q - 3pq + 5pq^2 - 8p - 7q - 10)$$
$$=18-3p+11q+5pq-2pq^{ 2 }+5p^{ 2 }q-4p^2q + 3pq - 5pq^2 + 8p + 7q + 10$$
$$=28+5p+18q+8pq-7pq^2+p^2q$$
Simplify: $$-7p-4(-3p + 2 ) $$
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$$-19p + 8$$
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$$5p + 8$$
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$$-19p - 8$$
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$$5p - 8$$
Explanation
Multiplying term by term then adding/subtracting like terms,
$$-7p-4(-3p+2)$$
$$=-7p-4(-3p)-4(2)$$
$$=-7p+12p-8$$
$$=5p-8$$
Simplify :$$(-8pst + 3prq -14) - (7prq - 20 + 2pst) = $$
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$$6-10pst + 10prq$$
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$$6 - 10pst - 4prq$$
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$$-6pst -10prq + 6$$
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$$-10pst-4prq-34$$
Explanation
$$(-8pst + 3prq -14) - (7prq - 20 + 2pst)$$ $$= (-8pst + 3prq -14 - 7prq + 20 - 2pst)$$
$$= (-8pst - 2pst + 3prq - 7prq + 20 - 14)$$
$$= (-10pst - 4prq + 6)$$
Add the following polynomials
$$ 4 + 2y - 3y^{3}, -8 + 4y +7y^{3} $$
$$ and\ 5\ - 6y + 8y^{3} - 6y^{2} $$
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$$12y^{3} - 6y^{2} + 1$$
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$$12y^{3} +6y^{2} + 1$$
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$$12y^{3} - 6y^{2} - 1$$
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$$12y^{3} + 6y^{2} - 1$$
Explanation
Let's add the given polynomials,
$$\therefore\ 4\ + 2y - 3y^{3} -8 + 4y +7y^{3} + 5\ - 6y + 8y^{3} - 6y^{2}\\$$
$$=(7+8-3)y^3+(-6)y^2+(2+4-6)y+(4-8+5)\\$$
$$=12y^{3} - 6y^{2} + 1$$
If $$P = 3x -4y -8z, Q = -10y + 7x + 11z$$ and $$R = 19z - 6y + 4x$$, then $$P-Q + R$$ is equal to
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$$13x -20y + 16z$$
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0
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$$x + y + z$$
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$$2x - by + 3z$$
Explanation
$$P - Q + R$$ $$= 3x - 4y - 8z - (7x - 10y + 11z) + (4x - 6y + 19z)$$
$$P - Q + R$$ $$= 3x - 4y - 8z - 7x + 10y - 11z + 4x - 6y + 19z \\ = (3 - 7 + 4)x + (-4 + 10 - 6)y + (-8 - 11 + 19)z \\ = 0$$
$$(4px^{2}+5q^{2}y -9rz) - (-3q^{2}y + 7px^{2}-rz) = $$
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$$11px^{2} + 9q^{2}y - 10rz$$
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$$-3px^{2} + qy - 8rz$$
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$$-3px^{2} + 8q^{2}y - 8rz$$
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$$-11px^{2}-8q^{2}y-10rz$$
Explanation
$$(4px^{2}+5q^{2}y -9rz) - (-3q^{2}y + 7px^{2}-rz)$$$$=(4px^{2}+5q^{2}y -9rz) + 3q^{2}y - 7px^{2} + rz $$
$$=4px^{2} - 7px^{2} + 5q^{2}y + 3q^{2}y - 9rz + rz $$
$$= (-3)px^{2} + 8q^{2}y - 8rz $$
Simplify :$$(-3pq^{2}+ 4pq) - (7pq - 9pq^{2}).$$
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$$6pq^{2} + 3pq$$
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$$6pq^{2} - 3pq$$
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$$-12pq^{2} + 3pq$$
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$$-12pq^{2}-3pq$$
Explanation
$$(-3pq^{2}+ 4pq) - (7pq - 9pq^{2})$$ $$=(-3pq^{2}+ 4pq - 7pq + 9pq^{2})$$
$$=(6pq^{2} - 3pq)$$
Subtract $$4x+y+2$$ from the sum of $$3x-2y+7$$ and $$5x-3y-8$$.
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$$4xy+6y-3$$
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$$6x-y+2$$
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$$x-2y-3$$
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$$4x-6y-3$$
Explanation
Sum of $$3x-2y+7$$ and $$5x-3y-8$$
$$=3x-2y+7+5x-3y-8$$
$$=8x-5y-1$$
Thus, $$8x-5y-1-(4x+y+2)$$
$$=8x-5y-1-4x-y-2$$
$$=4x-6y-3$$
State whether the following statement is true or false.
After Subtracting
$$-x^{4} + 4x^{3} y - 8x^{2} y^{2} + 2 xy^{3} - 4y^{4}$$ from $$ -5x^{3}y + x^{2}y^{2} - 6y^{4}$$ we get,
$$ x^{4} - 9x^{3}y + 9x^{2} y^{2} - 2xy^{3} -2y^{4}$$
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True
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False
Explanation
$$-(-x^{4} + 4x^{3} y - 8x^{2} y^{2} + 2 xy^{3} - 4y^{4})$$ + $$ (-5x^{3}y + x^{2}y^{2} - 6y^{4})$$
$$= x^{4} - 9x^{3}y + 9x^{2} y^{2} - 2xy^{3} -2y^{4}$$
Which polynomial should be subtracted from $$y^3+2y^2+5y-1$$ to get $$2y^2+12$$?
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$$y^3+5y-13$$
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$$y^3+y-1$$
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$$5y-3$$
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$$y^3-y-14$$
Explanation
The bigger polynomial is $$ y^3+2y^2+5y-1 $$
Let one polynomial be $$p$$.
Therefore,
$$ y^3+2y^2+5y-1 -p=2y^2+12$$
$$=>y^3+2y^2+5y-1-2y^2-12=p$$
$$=y^3+5y-13$$
Therefore,
The polynomial to be subtracted is $$y^3+5y-13$$
Add the following expressions
$$2a+b+7$$ and $$4a+2b+3$$.
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$$6a+2b+5$$
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$$3b-6a+5$$
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$$6ab+3b-10$$
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$$6a+3b+10$$
Explanation
Adding
$$(2a+b+7)$$ and $$(4a+2b+3)$$
,
$$2a+b+7$$
+$$4a+2b+3$$
___
$$6a+3b+10$$
What must be subtracted from $$ x^{4} + 4x^{2} -3x + 7$$ to get $$3x^{3} - x^{2} + 2x + 1$$?
Answer:
$$x^{4}-3x^{3}+5x^{2} - 5x +6$$
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0%
True
0%
False
Explanation
Let $$p(x)$$ be the polynomial which must be subtracted from $$x^4+4x^2-3x+7$$ to get $$3x^3-x^2+2x+1$$.
So,
$$x^4+4x^2-3x+7$$
$$-p(x)$$=
$$ {3x^3-x^2+2x+1}$$.
So,
$$p(x)=x^4+4x^2-3x+7-(3x^3-x^2+2x+1)$$.
$$\Rightarrow p(x)=x^4-3x^3+5x^2-5x+6$$
So, given answer is $$True$$
Which polynomial should be added to $$2x^4-3x^2+5x+8$$ to get $$2x^2-5x+4$$?
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$$x^3+5x^2-x$$
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$$2x^5+x^2-10x-9$$
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$$-2x^4+5x^2-1$$
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$$-2x^4+5x^2-10x-4$$
Explanation
The sum of two polynomials=$$2x^2-5x+4$$
Let one polynomial be $$p$$.
Therefore,
$$2x^4-3x^2+5x+8 +p=2x^2-5x+4$$
$$=>p=2x^2-5x+4-2x^4+3x^2-5x-8$$
$$=>p=-2x^4+5x^2-10x-4$$
The polynomial to be added is $$-2x^4+5x^2-10x-4$$
Simplify :
$$(3x^2-2x+1)+(x^2+5x-3)+(4x^2+8)$$
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$$8x^2+3x+6$$
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$$x^2+x$$
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$$x^2+x_6$$
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$$8x^2+x+9$$
Explanation
$$(3x^2-2x+1)+(x^2+5x-3)+(4x^2+8)$$
$$=3x^2-2x+1+x^2+5x-3+4x^2+8$$
$$=8x^2+3x+6$$
Subtract the second polynomial from the first :
$$x^4+x^2+x-1\, ; \, x^4-x^3-x^2+1$$
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$$2x^2+x-2$$
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$$x^3+2x^2+x-2$$
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$$x^3+2x^2+x-2$$
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$$x+2x^2-2$$
Explanation
$$\begin{aligned}{}\left( {{x^4} + {x^2} + x - 1} \right) - \left( {{x^4} - {x^3} - {x^2} + 1} \right) &= {x^4} + {x^2} + x - 1 - {x^4} + {x^3} + {x^2} - 1\\ &= {x^4} - {x^4} + {x^3} + {x^2} + {x^2} + x - 1 - 1\\ &= {x^3} + 2{x^2} + x - 2\end{aligned}$$
Hence, option $$B$$ is correct.
State True or False:
Addition of $$ 8x-3y+7z, \ -4x+5y-4z, \ -x-y-2z $$ is $$3x + y+z $$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (8-4-1)x+(-3+5-1)y+(7-4-2)z=3x+y+z$$
Hence the given statement is true.
State True or False:
$$ abx-15abx-10abx+32abx $$ is equal to $$8abx $$.
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0%
True
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False
Explanation
$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (1-15-10+32)abx=8abx$$
State True or False:
$$ 3x^2+5xy-4y^2+x^2-8xy-5y^2 $$ is equal to $$4x^2-3xy-9y^2 $$.
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0%
True
0%
False
Explanation
$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (1+3){ x }^{ 2 }+(5-8)xy+(-4-5)y^{ 2 }=4{ x }^{ 2 }-3xy-9{ y }^{ 2 }$$
State True or False:
Addition of
$$ 3b- 7c+10, \ 5c-2b-15, \ 15+12c+b $$ is $$2b+10c+10 $$.
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0%
True
0%
False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (3-2+1)b+(-7+5+12)c+(10-15+15)=2b+10c+10$$
State True or False:
Total savings of a boy who saves Rs.$$(4x-6y) $$, Rs.$$(6x+2y)$$, Rs.$$(4y-x)$$ and Rs.$$(y-2x)$$ for four consecutive weeks is Rs.$$(7x+y)$$.
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0%
True
0%
False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad variables\quad directly\quad to\quad get\quad the\quad savings,\\ Rs.\quad 4x-6y\quad +\quad 6x+2y\quad +\quad 4y-x\quad +\quad y-2x\\ =Rs.7x+y\\ $$
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