9

Q1. Using identity, evaluate (x - 3)(x + 3).

• 2x² - 9
• x² + 9
• x² - 9
• x² - 3

Solution

(x - 3)(x + 3) = x² - 9     ...........since  (a - b)(a + b) = ( a² - b² )

Q2. The coefficient of xyz if 2x, -3y and 5z are multiplied is:

• -xyz
• xyz
• 30
• -30

Solution

Q3. The expression (0.3x + 0.2y)(0.1x + 0.4y) - (x + y)(0.5x - y) can be simplified as

• 0.03x² - 0.08y² - 0.54xy
• -0.03x² + 0.08y² + 0.54xy
• -0.47x² + 1.08y² + 0.64xy
• 0.47x² + 1.08y² - 0.64xy

Solution

(0.3x + 0.2y)(0.1x + 0.4y) - (x + y)(0.5x - y)= 0.03x² + 0.12xy + 0.02xy + 0.08y² - 0.5x² + xy - 0.5xy + y²= -0.47x² + 1.08y² + 0.64xy

Q4. 92² = 10000 - __ + __ 

• 1600 and −64
• 1600 and 64
• 1600 and 4
• −1600 and −4

Solution

Using

Q5. Multiply (x + 1) and 2x:

• x² + x
• x² + 2x
• 2x² + x
• 2x² + 2x

Solution

2x(x + 1) = 2x² + 2x.

Q6. If the base of a triangle is 4x(x+ 1) and its corresponding height is (x - 3), then the area of the triangle is ____.

• 2x³ + 4x² - 6x
• 2x³ - 4x² + 6x
• 2x³ - 4x² - 6
• 2x³ - 4x² - 6x

Solution

A =  (4x)(x+1)(x-3) = 2x(x² -2x -3) =2x³ - 4x² - 6x

Q7. Add the given expressions: -6x² - 3y + 5, -x² - 2y - 7 and 3x² - y + 5 

• -4x² + 6y + 3
• -4x² + 6y - 3
• -4x² - 6y + 3
• -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 

Q8. Sum of 4x and 3 is:

• 7x
• 4x + 3
• 12x
• Cannot be added

Solution

The sum is 4x + 3.

Q9. Number of variables used in the expression 3x²z + 2yz are:

• 1
• 2
• 3
• 0

Solution

3 variables are used x, y and z.

Q10. Addition of -4x and 6x is:

• -2x
• 2x
• -24x
• 5x

Solution

-4x + 6x = 2x.

Q11. The product of 47 x 53 can be solved using the identity

• (a + b)²
• (a - b)²
• (a² + b²)
• (a² - b²)

Solution

The given expression can be expresses as 47 x 53 = (50 - 3)(50 + 3) = (50)² - (3)²        ........since, ( a - b ) ( a + b ) = (a² - b²) Therefore, the product of 47 x 53 can be solved using the identity (a² - b²)

Q12. The result obtained on subtracting the product of 2x and (x - 3y) from the product of (5x + 3y) and  (2y + 1) is ____.

• 16xy + 6y² - 2x² + 5x + 3y
• 16xy + 6y² - 2x² + 5x - 3y
• 16xy + 6y² - 2x² + 5x + 3
• 16xy + 6y² - 2x² + 5x 

Solution

(5x + 3y)(2y + 1) - 2x(x -3y) =10xy + 5x +6y ² +3y -2x² + 6xy =16xy + 6y² - 2x² + 5x + 3y

Q13. Multiply (w + 1) and 4w:

• w² + w
• w² + 4w
• 4w² + w
• 4w² + 4w

Solution

4w(w + 1) = 4w² + 4w

Q14. The product of the monomials (2q¹²), (-3q²⁹) and (5q¹³) is

• 10q⁴¹
• 10q⁴¹
• -30q⁵⁰
• -30q⁵⁴

Solution

Q15. Subtract -5x² + xy - 5 from 5x² - 2xy + 2. 

• 10x² + 3xy + 7
• 10x² - 3xy + 7
• 10x² + 3xy - 7
• 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 

Q16. Calculate 101². 

• 10001
• 10101
• 10200
• 10201

Solution

Using  

Q17. The coefficient of x in the expression 2xyz + 7xy + 4xz + 4x + 1 is:

• 2
• 4
• 7
• 1

Solution

4 is the coefficient of x.

Q18. Simplify: (p² + q²) - (q² + r²) - (r² + p²)

• 2r² 
• r²
• -r²
• -2r² 

Solution

(p² + q²) - (q² + r²) - (r² + p²) = (p² - p²) + (q² - q²) + (- r² - r²) = -2r² 

Q19. If the sides of a triangle are 4x units, 2x units and 5x units then its perimeter is:

• 11x
• 10x
• 4x
• 9x

Solution

P = 4x + 2x + 5x = 11x units

Q20. The square of the number 499 is ____.

• 249000
• 249001
• 349001
• 246001

Solution

(499)² =(500 - 1)² = 250000 - 1000 + 1   .........................(a - b)² = a² - 2ab + b²  = 249001

Q21. Expand: (a - 1)²

• a² - 2a + 2
• a² - 2a + 1
• a² + 2a + 1
• a² - a + 1

Solution

(a - 1)² = a² - 2a + 1

Q22. Number of terms in the expression "x⁴ + 2x² + 4x - 1" is:

• 3
• 4
• 2
• 1

Solution

Number of terms is 4.

Q23. Which of the following is an example of binomial?

• 3x
• -x + 1
• 2x² + x + 1
• x⁴ + x - 1

Solution

-x + 1 is a binomial.

Q24. Find (200 + 2) (200 - 2) 

• 39204
• 39208
• 39200
• 39996

Solution

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

Q25. The product of the expressions (m + 6n) and (-2m + n + 1) is

• -2m² + 6n² - 11mn + m + 6n
• -2m² + 6n² - 12mn + m + 6n
• -2m² + 6n² - 11mn + 2m + 6n
• -2m² + 6n² - 12mn + 2m + 6n

Solution

Q26. Subtracting -7x²y from -9x²y gives:

• 2x²y
• -16x²y
• -2x²y
• 16x²y

Solution

-9x²y - (-7x²y) = -9x²y + 7x²y = -2x²y

Q27. Simplify the given expression: 3{8x - 5 - (2x - 8)} 

• -12x + 6
• 12x - 6
• 12x + 6
• -12x - 6

Solution

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

Q28. Subtract the product of (5a + 3) and (2a - 1) from 4a (a + 1).

• -6a² + 3a + 3
• 6a² + 3a + 3
• 10a² + 3a + 3
• 10a² - 3a + 3

Solution

Q29. The square of the expression (5a² + 11c) is ____.

• 25a⁴ +11a²c + 121c²
• 5a⁴ +110a²c + 121c²
• 25a⁴ +110a²c + 11c²
• 25a⁴ +110a²c + 121c²

Solution

(5a² + 11c)² = (5a)² + 2(5a²)(11c) + (11c)² = 25a⁴ +110a²c + 121c²

Q30. The value of expression 2x² - 1 at x = 2 is:

• 4
• 5
• 6
• 7

Solution

At x = 2, 2(2)² - 1 = 8 - 1 = 7.

Q31. Add the given expressions: 6x² - 5y + 3, 2x² - y - 1 and 7x² - 2y + 1 

• 15x² - 8y + 3
• 15x² + 8y + 3
• 15x² + 8y - 3
• 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 

Q32. The product 108 x 109 can be written as 10000 + ____ x 100 + 72.

• 17
• 15
• 18
• 19

Solution

108 x 109 = (100 + 8)(100 + 9) =(100)² + (100 x 9) + (100 x 8) + 72 =10000 + 100 x (9 + 8) + 72 = 10000 + 100 x 17 + 72

Q33. If 505 × 495 = (a + b) (a - b), then the respective values of a and b are

• 500 and −5
• −500 and 5
• 500 and 5
• −500 and −5

Solution

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

Q34. Add the following terms: 5x, -7x, 8x

• x
• 5x
• 4x
• 6x

Solution

Sum = 5x - 7x + 8x = -2x + 8x = 6x.

Q35. Simplify the following: (3x + 2) + (2y - 1)

• 3x + 2y + 1
• 3x + 2y
• 3x + y + 1
• x + 2y + 1

Solution

(3x + 2) + (2y - 1) = 3x + 2y + 2 - 1 = 3x + 2y + 1.

Q36. Which of the following polynomials is a binomial?

• 3ac - 2ab - ac +  ab + abc
• 2a² + 5ab - 7ab² - 6a²
• 4st - 9s² - 5s² + 7st - 8st
• 13t² - 9t²

Solution

4st - 9s² - 5s² + 7st - 8st = (4st + 7st - 8st) + (-9s² - 5s²)                                       =  3st - 14s² Thus, the polyniomial in the option (c) contains two terms and hence it is a binomial.

Q37. Subtract x² - 8xy + 4 from -5x² - 3xy - 6. 

• -6x² + 5xy + 10
• -6x² + 5xy - 10
• -6x² - 5xy - 10
• -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 

Q38. Subtract 4x from 4y:

• 4(x - y)
• 4(y - x)
• (y - x)
• 4(y + x)

Solution

4y - 4x = 4(y - x).

Q39. Find the area of a rectangle if its length is 36 cm and breadth is 44 cm.

• 1548
• 1616
• 1584
• 1600

Solution

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

Q40. Find the value of 1.01 × 0.99. 

• 999.9
• 99.99
• 9.999
• 0.9999