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Ans.2 (a) (3X + 11 + 9Z) + (6X - 5 - Z)
= 3X + 11 + 9Z + 6X - 5 - Z
= 3X + 6X + 9Z - Z + 11 - 5
= 9X + 8Z + 6
(b) (3ab - 5a² + 3b²) - (6a² - 7ab + 4b²)
= 3ab - 5a² + 3b² - 6a² + 7ab - 4b²
= -5a² - 6a² + 3b² - 4b² + 3ab + 7ab
= -11a² - b² + 10ab
(c) Given, the value of x = 0
ATQ, 2x² + x - a = 5
» 2(0)² + (0) - a = 5
» -a = 5
» a = -5
(d) 2⁰ + 3⁰ + 4⁰
= 1 + 1 + 1 [a⁰ = 1]
= 3
(e) Expanded form of 25,69,874 is 20,00,000 + 5,00,000 + 60,000 + 9,000 + 800 + 70 + 4.
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Ans.3 (a) Let the unknown number be “n”.
So, ATQ, (x² + xy + y²) + (n) = 2x² + 3xy
» n = (2x² + 3xy) - (x² + xy + y²)
» n = 2x² + 3xy - x² - xy - y²
» n = x² - y² + 2xy
∴ x² - y² + 2xy should be added to x² + xy + y² to obtain 2x² + 3xy.
(b) Let the unknown number be “n”.
ATQ, 3x² - 6y² + 4xy + 15 - n = - x² - y² + 2xy + 12
» - n = - x² - y² + 2xy + 12 - 3x² + 6y² - 4xy - 15
» - n = - 4x² + 5y² - 2xy - 3
» n = 4x² - 5y² + 2xy + 3
∴ 4x² - 5y² + 2xy + 3 should be taken away from 3x² - 6y² + 4xy + 15 to obtain - x² - y² + 2xy + 12.
(c) {(4x - 2y + 15) + (-y - 21)} - (7x - y - 9)
= {4x - 2y + 15 - y - 21} - 7x + y + 9
= 4x - 3y - 6 - 7x + y + 9
= -3x - 2y + 3
(d) (i) ((5²)⁴ × 10⁷) ÷ 5⁹
= (5⁸ × (5 × 2)⁷) ÷ 5⁹
= (5⁸ × 5⁷ × 2⁷) ÷ 5⁹
= (5¹⁵ × 2⁷) ÷ 5⁹
= 5⁶ × 2⁷
(e) (i) 22.4 × 10⁷ ; 1.4 × 10¹⁰
» 2.24 × 10⁸ ; 1.4 × 10¹⁰
» 2.24 × 10⁸ < 1.4 × 10¹⁰ [Extra 2 Zeroes]
(ii) 729 × 64
= 9³ × 4³
= (3²)³ × (2²)³
= 3⁶ × 2⁶
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Ans.4 (a) aᵐ × aⁿ = aᵐ⁺ⁿ
(b) aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(c) (aᵐ)ⁿ = aᵐⁿ
(d) aᵐ × bᵐ = (ab)ᵐ
(e) a⁰ = 1
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Regards,
CreativeAB
• The Genius •