Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$(2.3 a^{5}b^{2})\times (1.2a^{2}b^{4})$$, when $$a = 1$$ and $$b = 0.5$$ is ________.

A
$$0.011625$$

B
$$0.043125$$

C
$$0.031825$$

D
$$0.041525$$

Solution

Given expression is $$(2.3a^5b^2)\times (1.2a^2b^4)$$ $$ = 2.76 \times a^{7}b^{6} $$
Also given $$a=1, b=0.5$$
Subtituting the values, we get
$$ 2.76 \times 1^{7}\times (0.5)^{6} $$
$$ = 2.76 \times (0.015625) $$
$$=0 .043125$$
Question 2
1 / -0

Simplify: $$(l + m)^2- 4lm$$

A
$$(l -m)^2$$

B
$$4l^2m^2$$

C
$$(l+2m)^2$$

D
$$(l-2m)^2$$

Solution

$$(l+m)^2-4lm$$
$$=l^2+2lm+m^2-4lm$$
$$=l^2-2lm+m^2$$
$$=(l-m)^2$$
Question 3
1 / -0

Obtain the product of: $$2, 4y, 8y^2, 16y^3$$

A
$$1024^6$$

B
$$1000y^6$$

C
$$1024y^5$$

D
$$1024y^6$$

Solution

$$2, 4y, 8y^2, 16y^3$$
$$=2\times 4y\times 8y^2\times 16y^3$$
$$=1024y^6$$
Question 4
1 / -0

Find the errors and correct the given expression.
$$(z + 5)^2 = z^2 + 25$$

A
$$(2z) = z^2 + 10z + 25$$

B
$$(z + 5) = z^2 + 10z + 25$$

C
$$(z + 5)^2 = z^2 + 10z + 25$$

D
$$(z + 10)^2 = z + 10 - 5$$

Solution

LH.S=$$(z+5)^2=z^2+2(z)(5)+5^2 ..................... [(a+b)^2=a^2+2ab+b^2]$$
$$=z^2+10z+25 \neq$$ R.H.S

The correct option is C.
Question 5
1 / -0

Find the product of given expressions:
$$a, 2b, 3c, 6abc$$

A
$$36a^2b^2c^2$$

B
$$6a^2b^2c^2$$

C
$$a^2b^2c^2$$

D
$$2a^36b^2c^2$$

Solution

$$a, 2b, 3c, 6abc$$
$$=a\times 2b\times 3c\times 6abc$$
$$=36a^2b^2c^2$$
Question 6
1 / -0

Multiply
$$(5-2x)$$ and $$ (3 + x)$$

A
$$15-x+{2 x }^{ 2 }$$

B
$$15-x-{ x }^{ 2 }$$

C
$$15-x-{2 x }^{ 2 }$$

D
$$15-x+{ x }^{ 2 }$$

Solution

$$(5 -2x)\times (3 + x)$$
$$=5(3 + x)-2x(3 + x)$$
$$=15+5x-6x-2x^2$$
$$=15-x-2x^2$$
Question 7
1 / -0

Obtain the product of: $$a, a^2, a^3$$

A
$$ a^5$$

B
$$ a^4$$

C
$$ a^6$$

D
$$ 6^a$$

Solution

Given monomials are $$a, a^2, a^3$$
Product of the given monomials $$=a\times a^2\times a^3$$
We know that, $$a^m\times a^n=a^{m+n}$$
$$\therefore \ a\times a^2\times a^3=a^{1+2+3}$$
$$=a^6$$

Hence, the product of the given terms is $$a^6$$.
Question 8
1 / -0

Find the product. $$\left ( \dfrac{2}{3}xy \right ) \times \left ( \dfrac{-9}{10}x^2 y^2 \right )$$

A
$$-\dfrac{1}{5}x^6 y^-3$$

B
$$-\dfrac{2}{7}x^2 y^7$$

C
$$-\dfrac{3}{5}x^3 y^3$$

D
$$-\dfrac{2}{5}y^3 x^3$$

Solution

$$\left ( \frac{2}{3}xy \right ) \times \left ( \frac{-9}{10}x^2 y^2 \right )$$
$$=-\frac{3}{5}x^3 y^3$$
Question 9
1 / -0

The coefficient of $$x$$ in the product $$(x-1)(1-2x)$$ is:

A
$$-3$$

B
$$3$$

C
$$-2$$

D
$$1$$

Solution

We solve the given product $$(x-1)(1-2x)$$ as follows:
$$(x-1)(1-2x)=(x\times 1)+\left[ x\times (-2x) \right] +(-1\times 1)+\left[ (-1)\times (-2x) \right]$$
$$ =x-2x^{ 2 }-1+2x$$
$$=-2x^{ 2 }+3x-1$$
From the above calculations, we observe that the coefficient of $$x^2$$ is $$-2$$ and coefficient of $$x$$ is $$3$$.
Hence, the coefficient of $$x$$ is $$3$$.
Question 10
1 / -0

Find the product of $$\left ( -\dfrac{10}{3}pq^3 \right ) \times \left ( \dfrac{6}{5}p^3 q \right )$$

A
$$ p^4q^4$$

B
$$- 4p^4q^4$$

C
$$ 4p^2q^4$$

D
$$ 4q^4p^5$$

Solution

$$\left ( -\frac{10}{3}pq^3 \right ) \times \left ( \frac{6}{5}p^3 q \right )$$
$$=-2pq^3\times 2p^3q$$
$$=-4p^4q^4$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 22

Result

Algebraic Expressions and Identities Test - 22

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SHARING IS CARING

Question 1

$$0.011625$$

$$0.043125$$

$$0.031825$$

$$0.041525$$

Solution

Question 2

$$(l -m)^2$$

$$4l^2m^2$$

$$(l+2m)^2$$

$$(l-2m)^2$$

Solution

Question 3

$$1024^6$$

$$1000y^6$$

$$1024y^5$$

$$1024y^6$$

Solution

Question 4

$$(2z) = z^2 + 10z + 25$$

$$(z + 5) = z^2 + 10z + 25$$

$$(z + 5)^2 = z^2 + 10z + 25$$

$$(z + 10)^2 = z + 10 - 5$$

Solution

Question 5

$$36a^2b^2c^2$$

$$6a^2b^2c^2$$

$$a^2b^2c^2$$

$$2a^36b^2c^2$$

Solution

Question 6

$$15-x+{2 x }^{ 2 }$$

$$15-x-{ x }^{ 2 }$$

$$15-x-{2 x }^{ 2 }$$

$$15-x+{ x }^{ 2 }$$

Solution

Question 7

$$ a^5$$

$$ a^4$$

$$ a^6$$

$$ 6^a$$

Solution

Question 8

$$-\dfrac{1}{5}x^6 y^-3$$

$$-\dfrac{2}{7}x^2 y^7$$

$$-\dfrac{3}{5}x^3 y^3$$

$$-\dfrac{2}{5}y^3 x^3$$

Solution

Question 9

$$-3$$

$$3$$

$$-2$$

$$1$$

Solution

Question 10

$$ p^4q^4$$

$$- 4p^4q^4$$

$$ 4p^2q^4$$

$$ 4q^4p^5$$

Solution

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