| 1. | LAWS OF INDICES : |
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| (i) am * an = am + n | |
| (ii) am / an = am - n | |
| (iii) (am)n = amn | |
| (iv) (ab)n = anbn | |
| (v) (a/b)n = an/ bn | |
| (vi) a0 = 1 | |
| 2. | SURDS : Let a be rational number and n be a positive integer such that a(1/n) = n√a |
| 3 | LAWS OF SURDS : |
| (i) n√a = a (1/n) | |
| (ii) n√ab = n√a x n√b | |
| (iii) n√a/b = n√a / n√b | |
| (iv) (n√a)n = a |
| 1. | What is the quotient when (x-1 - 1) is divided by (x - 1)? |
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| Sol. x-1 - 1 / x-1 - (1/x)-1 / x-1 = (1-x)/x
=(1-x)/x * 1/(x-1) = -1/x. Hence, the required quotient is - 1/x |
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| 2. | If 2x-1 + 2x+1 = 1280, then find the value of x |
| Sol. 2x-1 + 2x+1 = 1280 ⇔ 2x-1(1+2x) = 1280 ⇔ 2x-1 = 1280/5 = 256 = 28 ⇔ x-1 = 8 ⇔ x = 9. Hence, x = 9. |
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| 3. | If [1/5]3y = 0.008, then find the value of (0.25)y |
| Sol. [1/5]3y = 0.008 = 8/1000 = 1/125 = [1/5]3 ⇔ 3y = 3 ⇔ y = 1. ∴ (0.25)y = (0.25)1 = 0.25. Hence, the required distance is 6 km. |
| 16. | If 3x - 3x-1 = 18, then the value of xx is |
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| 17. | If 3x-y = 27 and 3x+y = 243, then x is equal to |
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| 18. | If ax = b, by = c and cz = a, then the value of xyz is |
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