Algebraic Expressions and Identities Test

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Algebraic Expressions and Identities Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

If $$49x^2-b=\left (7x+\dfrac {1}{2}\right )\left (7x-\dfrac {1}{2}\right )$$, then the value of $$b$$ is :

A
$$0$$

B
$$\dfrac {1}{\sqrt 2}$$

C
$$\dfrac {1}{4}$$

D
$$\dfrac {1}{2}$$

Solution

$$(7x+\frac12)(7x-\frac {1}{2})=49x^2-b$$
$$\Rightarrow 49x^2-\frac14=49x^2-b$$ ($$\because (a-b)(a+b)=a^2-b^2$$)
$$\Rightarrow b=\frac14$$
Option C is correct.
Question 2
1 / -0

Obtain the volume of rectangular boxes with the given length, breadth and height respectively.
$$2p, 4q, 8r$$

A
$$64pqr$$

B
$$16pqr$$

C
$$32pqr$$

D
$$8pr + r$$

Solution

Given : $$l,b,h$$ of the rectangular box respectively are: $$2p, 4q, 8r$$

Volume$$=l\times b\times h$$

$$=(2\times 4\times 8)pqr$$

$$=64pqr$$
Question 3
1 / -0

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

A
$$1045y^5$$

B
$$1024y^6$$

C
$$1634y^3$$

D
$$102y^5$$

Solution

Product of $$2,4y,8y^2,16y^3$$
$$=(2)\times (4y)\times (8y^2)\times (16y^3)$$
$$=2\times 4 \times 8\times 16 \times y^{(1+2+3)}$$ $$[\because a^m \times a^n =a^{m+n} ]$$
$$=1024y^6$$
Question 4
1 / -0

Find the product $$(p^2 -q^2)(2p + q)$$

A
$$2p^2-q^2+p(p-2q)$$

B
$$2p^3+q^3+pq(p+q)$$

C
$$2p^3-q^3+pq(p-2q)$$

D
$$p^2-q^2+pq(p-q)$$

Solution

$$(p^2 -q^2)(2p + q)$$
$$=p^2(2p + q)-q^2(2p + q)$$
$$=2p^3+p^2q-2pq^2-q^3$$
Question 5
1 / -0

Obtain the product of $$a, 2b, 3c, 6abc$$

A
$$36a^2b^2c^3$$

B
$$36a^3b^2c^2$$

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

D
$$36a^2b^3c^2$$

Solution

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

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

A
$$a^5$$

B
$$-a^6$$

C
$$a^3$$

D
$$-a^5$$

Solution

$$a,a^2,a^3$$
$$=(a)\times (-a^2)\times (a^3)$$
$$=-a^6$$
Question 7
1 / -0

Carry out the multiplication of the expressions of a given pair.
$$ab,a -b$$

A
$$ab-b$$

B
$$a^2b+ab$$

C
$$ab-ab^2$$

D
$$a^2b-ab^2$$

Solution

Given: $$ab,a -b$$

$$=ab\times (a-b)$$

$$=ab\times a-ab\times b$$

$$=a^2b-ab^2$$
Question 8
1 / -0

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
$$xy, 2x^2y, 2xy^2$$

A
$$16x^3y^4$$

B
$$4x^2y^3$$

C
$$4x^4y^4$$

D
$$4x^2y^2$$

Solution

Given: $$xy, 2x^2y, 2xy^2$$

Volume$$=l\times b\times h$$

$$=(xy\times 2x^2y\times 2xy^2)$$

  $$=4x^4y^4$$
Question 9
1 / -0

Find the product $$(x + 7y)(7x -y)$$

A
$$7x^2-7y^2+48xy$$

B
$$6x^2-7y^2+48xy$$

C
$$7x^2-7y^2+49xy$$

D
$$6x^2-7y^2+49xy$$

Solution

$$ (x + 7y)(7x -y)$$
$$=x(7x -y)+7y(7x -y)$$
$$=7x^2-xy+49xy-7y^2$$
$$=7x^2-7y^2+48xy$$
Question 10
1 / -0

Carry out the multiplication of the given expressions.
$$a + b, 7a^2b^2$$

A
$$a^3b^2 - 7a^2b^3$$

B
$$a^3b^2 + 7a^2b^3$$

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

D
$$7a^3b^2 + 7a^2b^3$$

Solution

Given: $$a + b, 7a^2b^2$$

Product$$=(a+b)\times 7a^2b^2$$

$$=(a\times 7a^2b^2) + (b\times 7a^2b^2)$$

$$=7a^3b^2+7a^2b^3$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions and Identities Test - 20

Result

Algebraic Expressions and Identities Test - 20

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Rank

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SHARING IS CARING

Question 1

$$0$$

$$\dfrac {1}{\sqrt 2}$$

$$\dfrac {1}{4}$$

$$\dfrac {1}{2}$$

Solution

Question 2

$$64pqr$$

$$16pqr$$

$$32pqr$$

$$8pr + r$$

Solution

Question 3

$$1045y^5$$

$$1024y^6$$

$$1634y^3$$

$$102y^5$$

Solution

Question 4

$$2p^2-q^2+p(p-2q)$$

$$2p^3+q^3+pq(p+q)$$

$$2p^3-q^3+pq(p-2q)$$

$$p^2-q^2+pq(p-q)$$

Solution

Question 5

$$36a^2b^2c^3$$

$$36a^3b^2c^2$$

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

$$36a^2b^3c^2$$

Solution

Question 6

$$a^5$$

$$-a^6$$

$$a^3$$

$$-a^5$$

Solution

Question 7

$$ab-b$$

$$a^2b+ab$$

$$ab-ab^2$$

$$a^2b-ab^2$$

Solution

Question 8

$$16x^3y^4$$

$$4x^2y^3$$

$$4x^4y^4$$

$$4x^2y^2$$

Solution

Question 9

$$7x^2-7y^2+48xy$$

$$6x^2-7y^2+48xy$$

$$7x^2-7y^2+49xy$$

$$6x^2-7y^2+49xy$$

Solution

Question 10

$$a^3b^2 - 7a^2b^3$$

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

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

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

Solution

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