MEDIUM
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If Kavita bought (3x+7) copies from the bookseller. If the cost of each copy is rupees (2x1), then if x=5, then  x rupees did Kavita give to the bookseller, find the value of x.

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Important Questions on Operations on Algebraic Expressions

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Express the following product as a monomial and verify the result for x=1

3x×4x×(-5x)

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Express the following product as a monomial and verify the result for x=1, y=2.

18x2y4×14x4y2×xy×5

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Write down the product of -8x2y6 and -20xy. Verify the product for x=2.5, y=1.
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Find the product of the following pairs of monomials.

4 and 7p

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Express the following product as a monomial and verify the result for x=1, y=2

-xy3×yx3×(xy)

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The volume of a cube is given by 27a3-54a2+36a-8. If each of its sides is (3 a-2), find the area of one of its faces by dividing the volume by the side, and verify it by finding the square of the side.
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Express the following product as a monomials and verify the result for x=1, y=2.

25a2b×-15b2ac×-12c2

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Express the following product as a monomial and verify the result for x=1, y=2.

-47a2b×-23b2c×(-76c2a)

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Express the following products as a monomial and verify the result for x=1

x23×2x×-4x×(5)

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Obtain the volume of rectangular box with the following length, breadth and height respectively.

5a, 3a2, 7a4

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Express the following products as a monomial and verify the result for x=1

5x4×x23×2x2

EASY

Find the area of rectangle with the following pair of monomials as its length and breadth respectively.

(p, q)

HARD

Complete the table of products:

First monomialSecond monomial 2x -5y 3x2 -4xy 7x2y2 -9x2y2
2x 4x2          
-5y     -15x2y      
3x2            
-4xy            
7x2y2            
-9x2y2            

 

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Express the following product as a monomial and verify the result for x=1

4x2×-3x×45x3

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Express the following products as a monomial and verify the result for x=1, y=2.

49abc3×-275a3b2×(-8b3c)