Algebraic Expressions Test

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Algebraic Expressions Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

The sum of three algebric expressions is $$\displaystyle x^{2}+y^{2}+z^{2}$$. If two of them are $$\displaystyle 4x^{2}-5y^{2}+3z^{2}$$ and $$\displaystyle -3x^{2}+4y^{2}-2z^{2}$$ then the third expression is

A
$$\displaystyle 2x^{2}+2z^{2}$$

B
$$\displaystyle 2y^{2}$$

C
$$\displaystyle 2x^{2}+2y^{2}-z^{2}$$

D
$$\displaystyle 2y^{2}+2z^{2}$$

Solution

Third exp = $$\displaystyle x^{2}+y^{2}+z^{2}-\left \{ \left ( 4x^{2}-5y^{2}+3z^{2} \right )+\left ( -3x^{2}+4y^{2}-2z^{2} \right ) \right \}$$
= $$x^2+y^2+z^2 - ( x^2 - y^2 + z^2) $$
= $$ x^2 + y^2 + z^2 - x^2 + y^2 - z^2$$
= $$2y^2$$
Question 2
1 / -0

If $$\displaystyle P=3x-4y-8z,\:Q=-10y+7x+11z$$ and $$\displaystyle R=19z-6y+4x$$, then $$P - Q + R$$ is equal to

A
$$\displaystyle 13x-20y+16z$$

B
$$0$$

C
$$x + y + z$$

D
$$\displaystyle 2x-4y+3z$$

Solution

Given, $$P=3x-4y-8z, Q=-10y+7x+11z, R=19z-6y+4x$$
We need to find value of $$P - Q + R $$
$$= (3x - 4y - 8z) - (-10y + 7x + 11z) + (19z - 6y + 4x)$$
$$ = 3x - 4y - 8z + 10y - 7x - 11z + 19z - 6y + 4x$$
$$= (3x-7x+4x)+(-4y+10y-6y)+(-8z-11z+19z)$$
$$=0+0+0=0$$
Question 3
1 / -0

$$\displaystyle 5a-\left[ 3b-\left\{ a-3\left( 2a-b \right) \right\} \right] $$ is equal to

A
$$\displaystyle -2b$$

B
$$\displaystyle -a+b$$

C
$$0$$

D
$$\displaystyle -a$$

Solution

Given, $$\displaystyle 5a-\left[ 3b-\left\{ a-3\left( 2a-b \right) \right\} \right] $$
$$\displaystyle =5a-\left[ 3b-\left\{ a-6a+3b \right\} \right] $$
$$\displaystyle =5a-\left[ 3b-\left\{ -5a+3b \right\} \right] $$
$$\displaystyle =5a-\left[ 3b+5a-3b \right] $$
$$\displaystyle =5a-5a=0$$
Hence given expression vanishes.
Question 4
1 / -0

Simplify: $$\displaystyle x^{2}y^{3}-1.5x^{2}y^{3}+1.4x^{2}y^{3}$$

A
$$\displaystyle 0.9x^{2}y^{3}$$

B
$$\displaystyle -0.9x^{2}y^{3}$$

C
$$0.9$$

D
$$-0.9$$

Solution

$$\displaystyle x^{2}y^{3}-1.5x^{2}y^{3}+1.4x^{2}y^{3}$$
=$$\displaystyle x^{2}y^{3}(1-1.5+1.4)$$
$$\displaystyle =0.9x^{2}y^{3}$$
Question 5
1 / -0

$$(5x^{2} + 6x - 3) + (2x^{2} - 7x - 9)$$

A
$$7x^{2} - x - 12$$

B
$$7x^{2} - 2x - 12$$

C
$$7x^{2} - 3x - 12$$

D
None of the above

Solution

$$5x^{2} + 6x - 3$$
$$+\underline { 2x^{2} - 7x - 9}$$

$$7x^{2} - x - 12$$
Question 6
1 / -0

What must be added to $$x^2\,+\, 5x\,-\,6$$ to get $$x^3\, -\,x^2\,+\, 3x\, -\, 2$$?

A
$$x^3\,-\,2x^2\,-\,2x\,-\,4$$

B
$$x^3\,+\,2x^2\,-\,2x\,+\,4$$

C
$$x^3\,-\,2x^2\,-\,2x\,+\,4$$

D
None of these

Solution

Let the polynomial to be added be $$p(x)$$
$$\therefore x^2 + 5x -6 +p(x) = x^3-x^2 +3x-2$$
$$\therefore p(x) = x^3 -x^2-x^2+3x-5x-2+6$$
$$\therefore p(x) = x^3 -2x^2-2x+4$$
Question 7
1 / -0

What is to be added to $$2a^3+4ab^2-5b^3-6a^2b$$ to get $$3a^3-4a^2b+11ab^2+b^3$$?

A
$$a^3 + 2a^2b+ 7ab^2-6b^3$$

B
$$a^3 -2a^2b-7ab^2+ 6b^3$$

C
$$a^3+2a^2b+7ab^2+6b^3$$

D
$$a^3+2a^2b-7ab^2+6b^3$$

Solution

$$3a^3-4a^2b+11ab^2+b^3$$
$$\underline {-2a^3+6a^2b-4ab^2+5b^3}$$
$$a^3+2a^2b+7ab^2+6b^3$$
Question 8
1 / -0

How many terms are there in the expression $$5x^3+7x^2+8xy$$?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

There are $$3$$ terms in the given expression: $$5x^3, 7x^2, 8xy$$.
Question 9
1 / -0

What must be subtracted from $$x^4\, +\, 2x^2\,-\,3x\, +\, 7$$ to get $$x^3\,+\, x^2\,+\, x\, -\,1$$?

A
$$x^4\, -\,x^3\,+ x^2\, -\, 4x\, +\, 8$$

B
$$x^3\,+\, x^2\, -\, 4x\, +\, 8$$

C
$$x^4\, -\,x^3\, +\, x^2\,+\, 4x\, -\,8$$

D
$$x^4\, -\,x^3\, -\,x^2\,+\, 4x\, -\,8$$

Solution

Let the polynomial to be subtracted be $$p(x)$$

$$\therefore x^4 +2x^2 - 3x +7 -p(x) = x^3 + x^2 + x -1$$

$$\therefore x^4-x^3+2x^2-x^2-3x-x+7+1 = p(x)$$

$$\therefore p(x) = x^4 - x^3 + x^2 - 4x + 8$$
Question 10
1 / -0

What must be added to the sum of $$\displaystyle 2a^{2}-3a+7,-5a^{2}-2a-11$$ and $$\displaystyle 3a^{2}+5a-8$$ to get $$0$$?

A
$$-12$$

B
$$12$$

C
$$\displaystyle a^{2}+a$$

D
$$\displaystyle a-1$$

Solution

Let '$$x$$' be added to these polynomial to get $$0$$.
$$\Rightarrow (2a^2-3a+7)+(-5a^2-2a-11)+(3a^2+5a-8)+x=0$$
$$\Rightarrow (2a^2-5a^2+3a^2)+(-3a-2a+5a)+(7-11-8)+x=0$$
$$\Rightarrow 0+0+(-12)+x=0$$
$$\Rightarrow x=12$$
Option B is correct.

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 15

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Algebraic Expressions Test - 15

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SHARING IS CARING

Question 1

$$\displaystyle 2x^{2}+2z^{2}$$

$$\displaystyle 2y^{2}$$

$$\displaystyle 2x^{2}+2y^{2}-z^{2}$$

$$\displaystyle 2y^{2}+2z^{2}$$

Solution

Question 2

$$\displaystyle 13x-20y+16z$$

$$0$$

$$x + y + z$$

$$\displaystyle 2x-4y+3z$$

Solution

Question 3

$$\displaystyle -2b$$

$$\displaystyle -a+b$$

$$0$$

$$\displaystyle -a$$

Solution

Question 4

$$\displaystyle 0.9x^{2}y^{3}$$

$$\displaystyle -0.9x^{2}y^{3}$$

$$0.9$$

$$-0.9$$

Solution

Question 5

$$7x^{2} - x - 12$$

$$7x^{2} - 2x - 12$$

$$7x^{2} - 3x - 12$$

None of the above

Solution

Question 6

$$x^3\,-\,2x^2\,-\,2x\,-\,4$$

$$x^3\,+\,2x^2\,-\,2x\,+\,4$$

$$x^3\,-\,2x^2\,-\,2x\,+\,4$$

None of these

Solution

Question 7

$$a^3 + 2a^2b+ 7ab^2-6b^3$$

$$a^3 -2a^2b-7ab^2+ 6b^3$$

$$a^3+2a^2b+7ab^2+6b^3$$

$$a^3+2a^2b-7ab^2+6b^3$$

Solution

Question 8

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 9

$$x^4\, -\,x^3\,+ x^2\, -\, 4x\, +\, 8$$

$$x^3\,+\, x^2\, -\, 4x\, +\, 8$$

$$x^4\, -\,x^3\, +\, x^2\,+\, 4x\, -\,8$$

$$x^4\, -\,x^3\, -\,x^2\,+\, 4x\, -\,8$$

Solution

Question 10

$$-12$$

$$12$$

$$\displaystyle a^{2}+a$$

$$\displaystyle a-1$$

Solution

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