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CBSE Questions for Class 7 Maths Algebraic Expressions Quiz 2 - MCQExams.com
CBSE
Class 7 Maths
Algebraic Expressions
Quiz 2
State True or False:
On subtracting
$$ x^3-4x-1 $$ from $$ 3x^3-x^2+6 $$, the answer is $$2x^3-x^2+4x+7 $$.
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True
0%
False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 3{ x }^{ 3 }-x^{ 2 }+6\quad -(\quad { x }^{ 3 }-4x-1)\\ \Longrightarrow (3-1){ x }^{ 3 }+(-1+0){ x }^{ 2 }+(+4)x+(6+1)
=2{ x }^{ 3 }-x^{ 2 }+4x+7$$
State True or False:
Addition of
$$-2ax-6by+4cz, \ 4by-14ax, \ 9cz-4ax-6by$$
is $$-16ax-8by+13cz $$.
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True
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False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad variables\quad directly,\\ -2ax-6by+4cz\quad +\quad 4by-14ax\quad +9cz-4ax-6by\\ =-16ax-8by+13cz\\ $$
State True or False:
On subtracting
$$ a-b-2c $$ from $$ 4a+6b-2c $$, the answer is $$3a+7b $$.
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True
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False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad variables\quad directly\quad \\ a-b-2c\quad -\quad 4a-6b+2c\\ =3a+7b\\ $$
State True or False:
On subtracting
$$ 3a-5b+c+2d$$ from $$ 7a-3b+c-2d $$, the answer is $$ 4a+2b-4d $$.
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True
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False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad variables\quad directly\quad \\ 7a-3b+c-2d\quad -\quad 3a+5b-c-2d\\ =4a+2b-4d\\ $$
State True or False:
Addition of
$$ 13ab-9cd-xy, \ 15cd-7ab, \ 6xy-3cd $$ is $$ 6ab+3cd+5xy$$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (13-7)ab+(-9+15-3)c+(-1+6)=6ab+3cd+5xy$$
State True or False:
On subtracting $$ 4xy^2$$ from $$3xy^2 $$, the answer is $$-xy^2 $$.
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True
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False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad variables\quad directly\quad \\ { 3xy }^{ 2 }-{ 4xy }^{ 2 }\\ ={ (3-4)xy }^{ 2 }\quad =\quad { -xy }^{ 2 }\\ $$
State True or False:
Addition of
$$ x^3-x^2y+5xy^2+y^3, \ -x^3-9xy^2+y^3, \ 3x^2y+9xy^2 $$ is $$ 2x^2y+5xy^2+2y^3 $$.
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True
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False
Explanation
$$\quad We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ \Longrightarrow (1-1){ x }^{ 3 }+(-1+3){ x }^{ 2 }y+(5-9+9)xy^{ 2 }+(1+1)y^{ 3 }=2{ x }^{ 2 }y+5xy^{ 2 }+2{ y }^{ 3 }$$
State True or False:
On subtracting
$$ -2x^2y+3xy^2$$ from $$8x^2y $$, the answer is $$10x^2y-3xy^2$$.
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True
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False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad variables\quad directly\quad \\ { 8x }^{ 2 }y-{ 3xy }^{ 2 }+2x^{ 2 }y\\ ={ (8+2)x^{ 2 }y-3xy }^{ 2 }\quad =\quad { 10x^{ 2 }y-3xy }^{ 2 }\\ $$
State True or False:
Addition of
$$ a^6-4a^4+6a, \ 5a^6+5a^4+6a, \ 12a^6-10a $$ is $$18a^6+a^4+2a$$.
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True
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False
Explanation
$$We\quad can\quad add\quad the\quad coefficient\quad of\quad like\quad powers\quad directly,\\ { a }^{ 6 }-{ 4a }^{ 4 }+6a\quad +\quad { 5a }^{ 6 }+{ 5a }^{ 4 }+6a\quad +\quad { 12a }^{ 6 }-10a\\ =(1+5+12){ a }^{ 6 }+(-4+5){ a }^{ 4 }+(6+6-10)a\\ =18{ a }^{ 6 }+{ a }^{ 4 }+2a\\ $$
State True or False:
On subtracting
the sum of $$ 5y^2+y-3 $$ and $$y^2-3y+7 $$ from $$6y^2+y-2 $$, the answer is $$3y-6$$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad and\quad subtract\quad the\quad coefficients\quad of\quad like\quad variables,\\ 6y^{ 2 }+y-2\quad -\quad( 5y^{ 2 }+y-3\quad+\quad y^{ 2 }-3y+7)\\ \Longrightarrow (6-5-1){ y }^{ 2 }+(1-1+3)y+(-2+3-7)\\ =3y-6$$
How much more than $$2x^2+4xy+2y^2 $$ is $$5x^2+10xy-y^2 $$?
State True or False: T
he answer is $$3x^2+6xy-3y^2 $$.
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True
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False
Explanation
$$We\quad will\quad subtract\quad the\quad 2\quad to\quad find\quad the\quad difference,\\ We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 5x^{ 2 }+10xy-y^{ 2 }\quad -\quad (2x^{ 2 }+4xy+2y^{ 2 })\\ =3x^{ 2 }+6xy-3y^{ 2 }$$
How much less than $$3a^2-6 $$ is $$ 2a^2+1 $$?
State True or False: T
he answer is $$a^2-7$$.
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True
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False
Explanation
$$We\quad will\quad subtract\quad the\quad 2\quad to\quad find\quad the\quad difference,\\ We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 3a^{ 2 }-6\quad -\quad (2a^{ 2 }+1)\\ =a^{ 2 }-7$$
State True or False:
If $$ x=6a+8b+9c$$; $$ y=2b-3a-6c $$ and $$ z=c-b+3a $$; then $$ x+y+z $$ is $$6a+9b+4c $$.
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True
0%
False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ x=6a+8b+9c;\quad y=2b-3a-6c;\quad z=c-b+3a\\ x+y+z\quad =6a+9b+4c$$
State True or False:
On subtracting
$$ a^2+ab+b^2 $$ from $$ 4a^2-3ab+2b^2 $$, the answer is $$3a^2-4ab+b^2 $$.
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True
0%
False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 4a^{ 2 }-3ab+2b^{ 2 }\quad -\quad( a^{ 2 }+ab+b^{ 2 })\\ \Longrightarrow (4-1){ a }^{ 2 }+(-3-1)ab+(2-1)b^{ 2 }\\ =3a^{ 2 }-4ab+b^{ 2 }$$
State True or False:
On subtracting
$$-3x^3+4x^2-5x+6 $$ from $$ 3x^3-4x^2+5x-6 $$, the answer is $$6x^3-8x^2+10x-12 $$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 3{ x }^{ 3 }-4x^{ 2 }+5x-6\quad -\quad( { -3x }^{ 3 }+4x-5x+6)\\ \Longrightarrow (3+3){ x }^{ 3 }+(-4-4){ x }^{ 2 }+(5+5)x+(-6-6)\\ =6{ x }^{ 3 }-8x^{ 2 }+10x-12$$
State True or False:
On subtracting
$$ cab-4cad-cbd $$ from $$ 3abc+5bcd-cda $$, the answer is $$ 2abc+3cad+6bcd $$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 3abc+5bcd-cda\quad -\quad( cab-4cad-cbd)\\ \Longrightarrow (3-1)abc+(-1+4)cad+(1+5)bcd\\ =2abc+3cad+6bcd$$
State True or False:
On subtracting
$$ -m^2+m+4 $$ from $$2m^2+m+1 $$, the answer is $$3m^2-m-1$$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ 2m^{ 2 }+m+1\quad -\quad (m^{ 2 }+m+4)\\ \Longrightarrow (2-1){ m }^{ 2 }+(1-1)m+(1-4)\\ =m^{ 2 }-3$$
State True or False:
On subtracting
$$ 6a+3 $$ from $$ a^3-3a^2+4a+1 $$, the answer is $$a^3-3a^2-2a-2 $$.
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True
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False
Explanation
\\ $$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ a^{ 3 }-3a^{ 2 }+4a+1\quad -\quad( 6a+3)\\ \Longrightarrow (1)a^{ 3 }+(-3){ a }^{ 2 }+(4-6)a+(1-3)\\ =a^{ 3 }-3a^{ 2 }-2a-2$$
Add: $$2x+y+z$$ ; $$-x+2y+2z$$ and $$x-y-z$$
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$$2x+2y+2z$$
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$$3x+5y+z$$
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$$3x-3y-z$$
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None of these
Explanation
Sum of $$(2x+y+z),$$ $$(-x+2y+2z)$$ and $$(x-y-z)$$ is:
$$=\displaystyle \left( 2x+y+z \right) +\left( -x+2y+2z \right) +\left( x-y-z \right) $$
$$=(2x-x+x)+(y+2y-y)+(z+2z-z) $$
$$=2x+2y+2z$$
$$=2(x+y+z)$$
The sum of $$\displaystyle 3ab, -8ab$$ and $$5ab$$ is equal to
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$$\displaystyle 10ab$$
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$$\displaystyle 16ab$$
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$$\displaystyle ab$$
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$$0$$
Explanation
We have to find sum of $$3ab, -8ab, 5ab$$
$$\therefore$$ required sum is $$=\displaystyle 3ab+\left( -8ab \right) +5ab$$
$$\displaystyle =8ab-8ab=0$$
Add the given expressions $$5m+0.3n-1.2t; \, \, 0.23m - 2.8t + 4n$$
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$$5.3m + 4.13n-4t$$
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$$5.23m + 4.3n-4t$$
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$$52.33m + 0.43n-4t$$
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$$5.23m + 43n-4t$$
Explanation
$$5m+0.3n-1.2t+ 0.23m-2.8t+4n$$
$$=5m+0.3n-1.2t+0.23m+4n-2.8t$$
$$=5.23m + 4.3n-4t$$
State True or False:
If $$ x=6a+8b+9c$$; $$ y=2b-3a-6c $$ and $$ z=c-b+3a $$; then $$ 2x-y-3z$$ is $$6a+17b+21c $$.
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True
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False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ x=6a+8b+9c;\quad y=2b3a6c;\quad z=cb+3a\\ 2x-y-3z\quad =2(6a+8b+9c)\quad -\quad (2b-3a-6c)\quad -3(c-b+3a)\\ =6a+17b+21c$$
State True or False:
If $$ x=6a+8b+9c$$; $$ y=2b-3a-6c $$ and $$ z=c-b+3a $$; then $$ x-y+z$$ is $$12a+5b+16c$$.
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0%
True
0%
False
Explanation
$$We\quad can\quad directly\quad add\quad the\quad coefficients\quad of\quad like\quad variables,\\ x=6a+8b+9c;\quad y=2b-3a-6c;\quad z=c-b+3a\\ x-y+z\quad =12a+5b+16c$$
State True or False:
If $$ x=6a+8b+9c$$; $$ y=2b-3a-6c $$ and $$ z=c-b+3a $$; then $$ 3y-2z-5x $$ is $$-45a-32b-65c $$.
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True
0%
False
Explanation
$$x=6a+8b+9c;$$ $$y=2b-3a-6c$$ $$\&$$ $$z=c-b+3a$$
The value of $$3y-2z-5x$$ will be,
substitute $$x$$ $$\&$$ $$y$$ $$\&$$ $$z$$ in the expression,
$$=3\left( { 2b-3a-6c } \right) -2\left( { c-b+3a } \right) -5\left( { 6a+8b+9c} \right) $$
$$=6b-9a-18c-2c+2b-6a-30a-40b-45c$$
$$=45a-32b-65c$$
Hence, the answer is true.
If we take away $$\displaystyle -8abc$$ from $$\displaystyle -7abc$$, then the result is equal to
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$$\displaystyle abc$$
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$$\displaystyle 15abc$$
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$$\displaystyle -abc$$
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$$\displaystyle -15abc$$
Explanation
We have to just subtract $$-8abc$$ from $$-7abc$$
$$=\displaystyle \left( -7abc \right) -\left( -8abc \right) $$
$$\displaystyle =-7abc+8abc$$
$$= abc$$
What is the sum of $$\displaystyle \left( 4a+5b \right) ,\left( -6a+2b \right) ,\left( 7a-6b \right) $$?
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$$\displaystyle -5a+b$$
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$$\displaystyle 5a+b$$
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$$\displaystyle 5a-b$$
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$$\displaystyle -5a-b$$
Explanation
We have to find sum of $$(4a+5b), (-6a+2b), (7a-6b)$$
$$\therefore$$ required sum $$=\displaystyle \left( 4a+5b \right) +\left( -6a+2b \right) +\left( 7a-6b \right) $$
$$\displaystyle =\left( 4a-6a+7a \right) +\left( 5b+2b-6b \right) $$
$$=\displaystyle 5a+b$$
What should be added to $$6x^2-3xy+4y^2$$ to get $$2y^2+xy-4x^2$$?
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$$-x^2-y^2+4y$$
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$$-10x^2-y^2+4xy$$
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$$x^2-2y^2+4x$$
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$$-10x^2-2y^2+4xy$$
Explanation
Let the required expression be $$P$$
$$P=(2y^{ 2 }+xy-4x^{ 2 })-(6x^{ 2 }-3xy+4y^{ 2 })$$
$$=-4x^{ 2 }+2y^{ 2 }+xy-6x^{ 2 }+3xy-4y^{ 2 }$$
$$=-10x^2-2y^2+4xy$$
Subtract $$6x+8y+4$$ from the sum of $$4x-2y+3$$ and $$2y-x+3$$?
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$$-x-8y-2$$
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$$-3x-8y+2$$
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$$-3x-y+1$$
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$$-x-8y+2$$
Explanation
Consider, $$(4x-2y+3)+(2y-x+3)$$
$$=4x-2y+3+2y-x+3$$
$$=3x+6$$
Subtracting $$6x+8y+4$$ from $$3x+6$$ we get,
$$(3x+6)-(6x+8y+4)$$
$$=3x+6-6x-8y+4$$
$$=-3x-8y+2$$
By how much is $$\displaystyle a^{4}+4a^{2}b^{2}+b^{4}$$ more than $$\displaystyle a^{4}-8a^{2}b^{2}+b^{4}$$ ?
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$$\displaystyle 12a^{2}b^{2}$$
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$$\displaystyle -12a^{2}b^{2}$$
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$$\displaystyle 2a^{4}+2b^{4}$$
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None
Explanation
$$\displaystyle a^{4}+4a^{2}b^{2}+b^{4}$$
$$\displaystyle a^{4}-8a^{2}b^{2}+b^{4}$$
$$-$$ $$ + $$ $$-$$
$$\displaystyle \overline{\underline{12a^{2}b^{2}}}$$
$$\displaystyle \left( p+q \right) -\left( p-q \right) $$ is equal to
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$$\displaystyle 2p+2q$$
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$$\displaystyle 2p$$
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$$\displaystyle 2q$$
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$$0$$
Explanation
Given,
$$\displaystyle \left( p+q \right) -\left( p-q \right) =p+q-p+q$$
$$=2q$$
Hence simplified form of the given expression is $$2q$$
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