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Q1. If 505 × 495 = (a + b) (a - b), then the respective values of a and b are

• 1) 500 and −5
• 2) −500 and 5
• 3) −500 and −5
• 4) 500 and 5

Solution

505 × 495 = (500 + 5) (500 - 5) = (a + b)(a - b) Hence, a = 500 and b = 5. 

Q2. Simplify: a² - b² + (a - b)² 

• 1) 2a² + 2ab
• 2) 2a² - b²
• 3) 2a² + 4ab
• 4) a² - ab

Solution

a² - b² + (a - b)² = a² - b² + a² - 2ab + b² = 2a² - 2ab  

Q3. Simplify:  

• 1) −2xy
• 2) 2xy
• 3) 2y
• 4) 2x

Solution

Using Hence, the answer is 2xy. 

Q4. Which identity is used in the following expression? 

• 1)
• 2)
• 3)
• 4)

Solution

 is used in the given expression.

Q5. If the length of a square plot is 47 cm, then find the area of a square plot. 

• 1) 2209
• 2) 2491
• 3) 2791
• 4) 2809

Solution

Exp: side = 47 cm Area of a square = (side)² = 47² Using  

Q6. Add the given expressions: -6x² - 3y + 5, -x² - 2y - 7 and 3x² - y + 5 

• 1) -4x² - 6y + 3
• 2) -4x² - 6y - 3
• 3) -4x² + 6y + 3
• 4) -4x² + 6y - 3

Solution

-6x² - 3y + 5 + (-x² - 2y - 7) + 3x² - y + 5 = (-6x² - x² + 3x²) + (-3y - 2y - y) + (5 - 7 + 5) = -4x² - 6y + 3 

Q7. 92² = 10000 - __ + __ 

• 1) 1600 and 64
• 2) −1600 and −4
• 3) 1600 and −64
• 4) 1600 and 4

Solution

Using

Q8. Expand . 

• 1)
• 2)
• 3)
• 4)

Solution

Using a² - b² = (a + b)(a - b)

Q9. Subtract x² - 8xy + 4 from -5x² - 3xy - 6. 

• 1) -6x² + 5xy + 10
• 2) -6x² + 5xy - 10
• 3) -6x² - 5xy - 10
• 4) -6x² - 5xy + 10

Solution

-5x² - 3xy - 6 - (x² - 8xy + 4) = -5x² - 3xy - 6 - x² + 8xy - 4 = -5x²- x² - 3xy + 8xy - 6 - 4 = -6x² + 5xy -10 

Q10. Simplify the given expression: 3{8x - 5 - (2x - 8)} 

• 1) 12x - 6
• 2) -12x - 6
• 3) -12x + 6
• 4) 12x + 6

Solution

3{8x - 5 - (2x - 8)}= 3{8x - 5 - 2x + 8}= 3{8x - 2x - 5 + 8}= 2{6x + 3}= 12x + 6 

Q11. If the perimeter of a rectangle is 6x - 8 and the length of the rectangle is x - 3, then find the breadth of the rectangle. 

• 1) 2x - 1
• 2) 1 - 2x
• 3) 4x - 2
• 4) 4x + 2

Solution

Perimeter of a rectangle = 2(length + breadth) 6x - 8 = 2(x - 3 + B) 6x - 8 = 2x - 6 + 2B2B = 6x - 8 - 2x + 6 2B = 4x - 2 B = 2x - 1 

Q12. Simplify the given expression: 2{9x + 5 - (4x - 3)} 

• 1) 10x - 16
• 2) -10x + 16
• 3) -10x - 32
• 4) 10x + 16

Solution

2{9x + 5 - (4x - 3)} = 2{9x + 5 - 4x + 3} = 2{5x + 8} = 10x + 16 

Q13. Simplify using identity:

Solution

Q14. Simplify:

Solution

Q15. 99² =? 

• 1) 9802
• 2) 9899
• 3) 9999
• 4) 9801

Solution

Using  

Q16. Find the value of expression (x + y)² - (x - y)², if .

Solution

Given: (x + y)² - (x - y)² Putting , we get

Q17. If the cost price of a pen is Rs. (x - 1) and the cost price of a pencil is Rs. (2x + 1), then find the total price of 2 pens and 4 pencils. 

• 1) Rs. 10x - 1
• 2) Rs. 10x
• 3) Rs. 10x + 3
• 4) Rs. 10x + 2

Solution

Total price of 2 pens and 4 pencils= 2(x - 1) + 4(2x + 1)= 2x - 2 + 8x + 4= 10x + 2 

Q18. Find the product of (x - 9) and (x - 3). 

• 1) x² - 12x + 27
• 2) x² - 11x + 27
• 3) x² - 6x - 27
• 4) x² + 6x + 27

Solution

Price of (x - 3) pens = (x - 9) (x - 3) = x(x - 3) - 9(x - 3) = x² - 3x - 9x + 27 = x² - 12x + 27 

Q19. 99 × 101 =? 

• 1) 9909
• 2) 9990
• 3) 9099
• 4) 9999

Solution

Using  

Q20. Find (200 + 2) (200 - 2) 

• 1) 39204
• 2) 39208
• 3) 39996
• 4) 39200

Solution

Comparing with a² - b² = (a + b) (a - b) a = 200 and b = 2(200 + 2)(200 - 2) = 200² - 2² = 40000 - 4  = 39996

Q21. Subtract -5x² + xy - 5 from 5x² - 2xy + 2. 

• 1) 10x² + 3xy + 7
• 2) 10x² - 3xy + 7
• 3) 10x² - 3xy - 7
• 4) 10x² + 3xy - 7

Solution

5x² - 2xy + 2 - (-5x² + xy - 5) = 5x² - 2xy + 2 + 5x² - xy + 5 = 5x² + 5x² - 2xy - xy + 2 + 5 = 10x² - 3xy +7 

Q22. Calculate 101². 

• 1) 10200
• 2) 10201
• 3) 10001
• 4) 10101

Solution

Using  

Q23. Add the given expressions: 6x² - 5y + 3, 2x² - y - 1 and 7x² - 2y + 1 

• 1) 15x² + 8y + 3
• 2) 15x² - 8y + 3
• 3) 15x² + 8y - 3
• 4) 15x² - 8y - 3

Solution

6x² - 5y + 3 + 2x² - y - 1 + 7x² - 2y + 1 = (6x² + 2x² + 7x²) + (-5y - y - 2y) + (3 - 1 + 1) = 15x² - 8y + 3 

Q24. Find the area of a rectangle if its length is 36 cm and breadth is 44 cm.

• 1) 1584
• 2) 1616
• 3) 1548
• 4) 1600

Solution

Area of a rectangle = length × breadth= 36 × 44 36 × 44 = (40 - 4) (40 + 4)= 40² - 4² … = 1600 - 16= 1584

Q25. Expand  

• 1)
• 2)
• 3)
• 4)

Solution

Using  

Q26. Find the area of a rectangle if its length is (y + 7) and its breadth is (x - 3). 

• 1) 7x + 3y - yx - 21
• 2) 7x - 3y + yx + 21
• 3) 7x + 3y + yx - 21
• 4) 7x - 3y + yx - 21

Solution

Area of rectangle = length × breath 

Q27. Simplify: .

Solution

Consider:

Q28. Square of 398 is

• 1) 159996
• 2) 161604
• 3) 158404
• 4) 160004

Solution

Using  

Q29. Simplify:

Solution

Q30. Find the value of 1.01 × 0.99. 

• 1) 99.99
• 2) 0.9999
• 3) 9.999
• 4) 999.9

Solution

1.01 = (1 + 0.01) and 0.99 = (1 - 0.01)1.01 × 0.99 = (1 + 0.01)(1 - 0.01)Using a² - b² = (a + b)(a - b) 1.01 × 0.99 = (1 + 0.01)(1 - 0.01) = 1² - 0.01² = 0.9999 

Q31. Define monomial, binomial and trinomial and give two examples of each.

Solution

Monomial: An algebraic expression consisting only one term is called a monomial. Examples: x²y, -5xy² Binomial: An algebraic expression consisting two terms is called a binomial. Examples: y - 7x², -6 + x² Trinomial: An algebraic expression consisting three terms is called a trinomial. Examples: 1 + x + x², -1 + z² - z²x², 3x + 2y - z

Q32. If , find .

Solution

Q33. Find the product: .

Solution

Q34. Simplify the following:

Solution

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