- Properties of multiplication amp- Representation- 1-Distributive Property amp- a-a - b - b - a- 2- Commutative Property amp- b-a - -b - c- - -a - b- - c- 3- Associative Property amp- c- a - -b-c- - a - b- a - c- - Pick the option which shows the correct match-1-c- 2-b- 3-a-1-c- 2-a- 3-b-1-a- 2-b- 3-c-1-b- 2-a- 3-c-

The correct option is B 1 c; 2 a; 3 b Distributive Property: a × (b +c)= (a × b) + (a × c) Commutative Property: (a × b) = (b × a) Associative Property: a × ...

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Byju's Answer

Standard VI

Mathematics

Associative Property

[ Prope...

Question

$\begin{matrix} Properties of multiplication & Representation 1. Distributive Property & a . a \times b = b \times a 2. Commutative Property & b . a \times (b \times c) = (a \times b) \times c 3. Associative Property & c . a \times (b + c) = a \times b + a \times c \end{matrix}$

Pick the option which shows the correct match.

$1 - a; 2 - b; 3 - c$

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$1 - b; 2 - a; 3 - c$

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$1 - c; 2 - b; 3 - a$

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$1 - c; 2 - a; 3 - b$

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Solution

The correct option is D
$1 - c; 2 - a; 3 - b$

Distributive Property: $a \times (b + c) = (a \times b) + (a \times c)$

Commutative Property: $(a \times b) = (b \times a)$

Associative Property: $a \times (b \times c) = (a \times b) \times c$

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Similar questions

Q. If a, b, c are in G.P., prove that:

(i) a (b² + c²) = c (a² + b²)

(ii)

a^{2} b^{2} c^{2} (\frac{1}{a^{3}} + \frac{1}{b^{3}} + \frac{1}{c^{3}}) = a^{3} + b^{3} + c^{3}

(iii)

\frac{(a + b + c)^{2}}{a^{2} + b^{2} + c^{2}} = \frac{a + b + c}{a - b + c}

(iv)

\frac{1}{a^{2} - b^{2}} + \frac{1}{b^{2}} = \frac{1}{b^{2} - c^{2}}

(v) (a + 2b + 2c) (a − 2b + 2c) = a² + 4c².

Q. Show that:
(i)

\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1

(ii)

{[\{\frac{x^{a (a - b)}}{x^{a (a + b)}}\} \div \{\frac{x^{b (b - a)}}{x^{b (b + a)}}\}]}^{a + b} = 1

(iii)

{(x^{\frac{1}{a - b}})}^{\frac{1}{a - c}} {(x^{\frac{1}{b - c}})}^{\frac{1}{b - a}} {(x^{\frac{1}{c - a}})}^{\frac{1}{c - b}} = 1

(iv)

{(\frac{x^{a^{2} + b^{2}}}{x^{a b}})}^{a + b} {(\frac{x^{b^{2} + c^{2}}}{x^{b c}})}^{b + c} {(\frac{x^{c^{2} + a^{2}}}{x^{a c}})}^{a + c} = x^{2 (a^{3} + b^{3} + c^{3})}

(v)

{(x^{a - b})}^{a + b} {(x^{b - c})}^{b + c} {(x^{c - a})}^{c + a} = 1

(vi)

{\{{(x^{a - a^{- 1}})}^{\frac{1}{a - 1}}\}}^{\frac{a}{a + 1}} = x

(vii)

{(\frac{a^{x + 1}}{a^{y + 1}})}^{x + y} {(\frac{a^{y + 2}}{a^{z + 2}})}^{y + z} {(\frac{a^{z + 3}}{a^{x + 3}})}^{z + x} = 1

(viii)

{(\frac{3^{a}}{3^{b}})}^{a + b} {(\frac{3^{b}}{3^{c}})}^{b + c} {(\frac{3^{c}}{3^{a}})}^{c + a} = 1

\frac{(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3}}{(a - b)^{3} + (b - c)^{3} + (c - a)^{3}} =

(a) 3(a + b) ( b+ c) (c + a)

(b) 3(a − b) (b − c) (c − a)

(c) (a − b) (b − c) (c − a)

(d) none of these

$\begin{matrix} Properties of multiplication & Representation 1. Distributive Property & a . a \times b = b \times a 2. Commutative Property & b . a \times (b \times c) = (a \times b) \times c 3. Associative Property & c . a \times (b + c) = a \times b + a \times c \end{matrix}$

Pick the option which shows the correct match.

$\begin{matrix} Properties of multiplication of integers & Representation 1) . Distributive Property & a) . a \times b = b \times a 2) . Commutative Property & b) . a \times (b \times c) = (a \times b) \times c 3) . Associative Property & c) . a \times (b + c) = (a \times b) + (a \times c) \end{matrix}$

Pick the option which shows the correct match.

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Properties of multiplicationRepresentation1.Distributive Propertya. a×b=b×a2.Commutative Propertyb. a×(b×c)=(a×b)×c3.Associative Propertyc. a×(b+c)=a×b+a×c Pick the option which shows the correct match.

The correct option is D 1−c;2−a;3−b Distributive Property: a×(b+c)=(a×b)+(a×c) Commutative Property: (a×b)=(b×a) Associative Property: a×(b×c)=(a×b)×c

The correct option is D
$1 - c; 2 - a; 3 - b$

Distributive Property: $a \times (b + c) = (a \times b) + (a \times c)$

Commutative Property: $(a \times b) = (b \times a)$

Associative Property: $a \times (b \times c) = (a \times b) \times c$