Surds and Indices

SURDS AND INDICES 1. The value of  125  is: 13 (1) 2 (2) 4 (3) 5 (4) 8 -4 5 2. The value of   is:  243  (1) (3) 81 16 4 9 (2) (4) 81 256 9 4 (5) None of these 3. If I6 × 8n+2 = 2m, then m is equal to : (1) n + 8 (2) 2n + 8 (3) 3n + 2 (4) 3n + 10 (5) None of these (3) 2 (4) (5) None of these 1 8 x -3 , then n the value of x is: (1) 3 (2) 2 (3) 0 (4) -2 (5) None of these a 9. If   b x 1 b    a x 3 (1) 1 (3) 7 2 , then n the value of x is: (2) 1 2 (4) 3 10. If 2X × 81/5 = 21/5, then x is equal to: 4. The value of 3 512 = 2 x , then x is equal to: (1) 5 (2) 4 3 5 (4) 3 (3) (2) 1.5 8. If 22x-1 = (5) None of these  1024  (1) 1 (5) None of these (1) 1 5 (2)  1 5 (3) 2 5 (4)  2 5 (5) None of these 5. The value of x satisfying 4 + 2 x = 4 is: 11. If 2X - 2X-1 = 4 , then The value of x3 is: (1) 125 (2) 144 (1) 27 (2) 4 (3) 120 (4) (3) 1 (4) 256 (5) None of these (5) None of these 6. If 5X+3 = (25)3x-4, then the value of x is: (1) 5 11 (3) 11 3 (2) 11 5 (4) 13 5 (5) None of these 7. If 34x-2 = 729, then the value of x is: 12. The value of x for which 2X+4 - 2X-1 = 3, is: (1) 0 (2) -2 (3) 2 (4) 1 (5) None of these 13. The value of x for which 42x -22x = 12 holds, is: (1) 2 (2) 3 (3) 1 (4) -1 30 (5) None of these (l) 14. If 9X - 10.3x + 9 = 0 then x is equal to: (1) 2 or 0 (2) 1 or 3 (3) 1 or 9 (4) 1 or -2 (5) None of these 15. The value of 3 x12  2 x 6 is: (1) x7 (2) x6 (3) x (4) x 8 10 (5) None of these 16. If 2X-1 + 2X+1 = 320, then value of x is: (1) 6 (2) 8 (3) 5 (4) 7 (1) 0 (b) 2 (3) 3 (4) 4 (3) 3(12+ n) × 9 (2n -7) is: 35n 1 3 (2) 1 9 (4) 3 9 13 2 3 (3)  (4) 2 22. If a = (1 - m), b = (m - n) and c = (n - 1), then the expression (xa)n.(xb)1 .(xc)m in the simplified form is: (1) 0 (2) x (3) x - 1 (4) 1  3   9 5 2  3a  3 3 , then  equals: (1) 2 (2) 3 (3) 4 (4) 5 (1) x = y = 0 (2) x = y = 1 (3) x > y (4) x < y 25. If ax-2 (a2x+2 + a1-x) = a-3 (a9 +a2), then the value of x is: (1) 0 (5) None of these 3 2 (2) 2 3 (4) 9n  32  3 n / 2   27 33m (23 ) (3) 1 (4) a negative integer  3 2 (5) None of these 20. If (2) 0 (3) a positive integer -1 2 (1) -1 (2) a fraction  3   3   1  is equal to:  3  .  +  -   2   2  3 (1) 21. The expression xa(b-c).xb(c-a).xc(a-b) simplifies to: (5) None of these (0.6) 0 - (0.1) -1 -1 (5) None of these 24. If ax-3.ay+2 = a2.ax and ax.ay = a4, then: (5) None of these 19. (4) m - n + 2 = 0 (5) None of these (5) None of these (1) (3) m – n + l = 0 23. If 9n ×35 × (27)3 = 27 , then n equals: 3× (81) 4 18. The value of (2) m – n – l = 0 (5) None of these (5) None of these 17. If m–n-2=0 1  , then: 27 26. If ax = by = cz and b2 = ac, then y equals? (1) xz x+z (2) xz 2(x - z) (3) xz 2(z - x) (4) 2xz (x + z) 1 2 (5) None of these  xa  27. The value of  b  x  (a  b)  xb   c  x  (b  c)  xc   a  x  (c  a ) is: 31 (1) 0 (2) xabc (3) 2 (4) 1 (1) 0 (3) (5) None of these 28. The expression 1  (2) 1 1 2 (4) am+n (5) None of these 1 1  1  x(ba)  x(ca) 1  x(a b)  x(cb) 1  x(bc)  x(a c) is equal to : (1) xa-b-c (2) 1 (3) 0 (3) 2 34. If m = ax, n = ay and mynx = a2/z then, the value of xyz is: (1) 1 (2) 2 (3) 3 (4) 4 (5) None of these 35. The simplified form of (5) None of these 37/ 2. y 3 35/ 2. y is: 29. If x = ya, y = zb and z = xc, then the value of abc is (1) 4 (2) 3 (3) 2 (4) 1 (5) None of these 1 1 1 30. If 2X =3y =6-z, then  + +  is equal to: y z x (1) 0 (3) 3 2 (2) 1 (4) 1  2 (5) None of these 31. If ax = b, by = c and cz = a, then the value of xyz is: (1) 0 (3) 1 3 (2) 1 (4) 1 2 (1) x2 y (2) x3 y2 (3) x6 y3 (4) xy (5) None of these 36. The solution of :(a) xx x  (x x ) x (b) 33x+5×33x+3= 9 (c) 4X + 2 + 22x + 1 - 36 = 0 are respectively: (1) 9 1 , 1& 4 2 (2) 9 1 , & -1 4 2 (3) 1 9 1, , 2 4 (4) 9 1 1, & 4 2 (5) None of these 37. Consider the following statements: (5) None of these 1 1 1 32. If 2X = 4y = 8Z and 2x  4y  4z  4 , then the value of x is: (1) 7 16 (2) 7 32 (3) 7 48 (4) 3 4 (5) None of these 1   1  33. If   is equal to: n m 1  a mn  1 a (1) if ax = b, by = c, cz = a, then xyz = o (2) if p = ax, q = ay, (pyqx) = az, then xyz = 1 (3) if xa = yb = zc & ab + bc + ca= 0, then xyz = 1. Of these statements (1) 1 & 2 are correct (2) 2 & 3 are correct (3) Only 1 is correct (4) 1 & 3 correct 38. Which of the following is the correct statement? 32 (1) 2 is bigger than (2) 2 is less then (3) 2 and (4) 3 3 3 41. The value of 3  xb   c x  3 3 are equal 2 is equal to 4 3 (5) None of these n4 39. 3 (3)  xc   a  x  (c  a  b)  xa   b  x  (a  b  c) is: (1) xabc (2) xa+b+c (3) xab+bc+ca (4) 1 (5) None of these  2(2 )  2 3 is equat to: n 3 2(2 ) (1) (b  c  a ) n (2) 2n 1 9  2n 8 1/ab  xa  42. The value of  b  x  2n 1  1 8 1/ bc  xb  . c  x  1/ca  xc  . a  x  is: (1) 1 (b) 0 (3) x 1/abc (4) x1/(ab+bc+ca) (5) None of these (4) 1 43. If x, y, z are positive real numbers, the value of (5) None of these   40. If pqr = 1, then   1 1 1    1 1 1  is equal to: 1 q  r 1 r  p  1 p  q 1 pq (1) 0 (2) (3) pq (4) 1 x 1 y. y 1 .z z 1x is: (1) xyz (2) (3) 1 (4) 1 xyz xyz (5) None of these 44. (5) None of these 2, 4 and 3 4 6 is ascending order are: (1) 2, 3 4, 4 6 (2) 4 6, 3 4, 2 (3) 2, 4 6, 3 4 (4) 4 6, 2, 3 4 (5) None of these ANSWERS 1. 2. 3. 4. 5. 6. 7. 8. 5 2 4 4 2 2 3 2 9. 10. 11. 12. 13. 14. 15. 16. 5 4 1 5 3 3 1 4 17. 18. 19. 20. 21. 22. 23. 24. 3 3 1 5 3 4 4 4 25. 26. 27. 28. 29. 30. 31. 32. 2 4 4 2 4 1 2 1 33. 34. 35. 36. 37. 38. 39. 40. 2 1 4 2 2 2 4 4 41. 42. 43. 44. 4 1 3 3 33