## Math Topic - Surds And Indices

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PBI (ab)n = anbn (a/b)n = an/ b PBI INSTITUTE Indices and Surds 1. 2. 3. 1. Laws of Indices i. am xan = am + n ii. a / a = am n (amr = amn iii. iv. v. Surds: - nvß. Let a be rational number and n be a positive integer such that a(l/n) — Laws of Surds: ii. iii. — a (l/n) (n+l)n - EXERCISE If 3125, then the value of 5(a-3) is A. 25 c. 625 =3125 = 55 — 52 = 25. B. D. Solution 5(a-3) 2. Solution 3. If €2 n 125 1625 4 12 , then the value of n is = 64 = (2 n)1/2 = 12. If m and n are whole numbers such that m B. D. n = 121, B. D. then the value of (m - 1 Y +1 10 1000 is c. 121 Solution We know that 112 Putting m = 11 and (m - 1)11+1 =121. n = 2, we get = (11 - 1)2+1
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PBI 4. > 103 = 1000. (17)3.5 = 178 A. 2.29 c. 4.5 Solution Let (17)3 = 178 = 178 = 4.5 - 3.5) 5. The value A. 1000 c. 100000 B. D. B. PBI INSTITUTE 2.75 4.75 10000 106 Solution I O) 150 I O) 146 6. Given that 100•48 A. 1.45 c. 2.9 Solution 2 0.48z = 1.40 7. = / 10146 = 104. = 10000. 100•70 — — Y and xz = y2, then the value of z is close to < = > (10 0.48 (100.70)2 = (10 0.48z = 101•40 140/48 = 35/12 = 2.9(approx.). The value of (256)5/4 is A. 984 c. 1014 B. D. B. D. Solution (256)5/4 8. Solution If = 5/4 _ 45 = 1024. 27 and then x is equal to B. D. = 27 = 33 1.88 3.7 512 1024 2 6
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PBI 3(X+Y) On solving equations 1 and 2, we get 9. PBI INSTITUTE = 243 = 35 If ax =b, c and a, then the value of xyz is C. l/abc Solution al Therefore, 10. Solution 49 49 x = (bYZ) = (aX)Yz xyz= 1 49 _ = (72 x 72 x 72 x 72 7(2+2++2+2) = 78 So, the correct answer is 8. 11. If = 3V32, then x is equal to c. 3/5 Solution 2X = 3V32 12. (0.04)-1.5 A. 25 c. 250 = (32)1/3 = (25)1/3 — 25/3 < = > x=5/3. = (4/100) -1.5 = (1/25)-3/2 = (25)3/2 = 53 = 125. B. D. D. B. D. B. D. 1 abc 7 16 3 5/3 125 625 Solution (0.04)-1.5

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