# Algebra

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1 1. If  x 2  – 1is a factor of polynomial  f  (  x ) = 2  x 3  + A  x 2  +B  x  + 3 then A 2  – B 2  =?(a)5(b)6(c)–6(d)0 2. If  x  + 1  x  = 2, then find the value of  x 9  + 9 1  x = ?(a)0(b)4(c)2(d)6 3. )1( 132529   x x x  is divisible by:(a)both )1(&)1(    x x (b) )1(    x  but not by )1(    x (c) )1(    x  but not by )1(    x (d)neither )1(    x nor )1(    x 4. If  x 2  – 2  x  + 1 = 0, find the value of  5432  xxxx x    .(a)0(b)2(c)3(d)4 5. Find the number of solution of equation 222 12312231  xxx xx       (a)0(b)1(c)2(d)4 6. If 2 21,0,421  p p pp =¹-+  then the value of 1  p p  is(a)4(b)5(c)10(d)12 7. If 2 13,  x x        then the value of  x 206 +  x 200 +  x 90 +  x 84 +  x 18 +  x 12 +  x 6 + 1 is(a)0(b)1(c)84(d)206 8.  If         ,&           xabcybcazcab , then       333 ?        xaybzc (a) 3()()()     xaybzc (b)3  xyz  (c) ()()()     xaybzc (d)3 abc 9. If  x 4  + 4 1  x  = 119 and  x  > 1, then the value of   x 3  –  3 1  x   is(a)54(b)18(c)72(d)36 10.      2222 ?    abababab (a) 1 ab  (b) 2 ab  (c) 4 ab  (d) 1 ab 11. If    22 2450++++= abba ,   then the value of . abab -+ (a)3(b) –3(c) 13 (d) 13- 12. If HCF of  x 3  – 27 and  x 3  + 4  x 2  +12  x  + k   is a quadratic polynomial. Find the value of k  .(a)27(b)9(c)3(d)4 13. If  x  = a ( b – c ),  y  = b ( c – a ) &  z   = c ( a  –   b ), then thevalue of 333333  xyz abc   is(a) 3 abc xyz  (b) abc xyz  (c) 3  xyz abc (d)1 14. If  x  = 11, find the value of  x 5  – 12  x 4  + 12  x 3    – 12  x 2  +12  x  – 1 is(a)10(b)11(c)12(d)0 15. If  xy yx   = –2, (0)  x,y  , then {  x 3 +  y 3  + 3  xy  (  x + y )} = ?(a)1(b)0(c)–1(d)2 16. If ( a  –1) 2  + ( b  – 2) 2  + ( c  – 3) 2  = 0, then find the valueof a + b + c. (a)–6(b)–3(c)–2(d)6  2 17. If 112323921123239  xyz       , then what is thevalue of 1123239  xyz  xyz  +++++ (a)0(b)1(c)2(d)4 18. The value of .. ?                    abbccaabcbca  xxx xxx (a)0(b)1(c)  x abc (d)  x ( a+b+c ) 19. If  x  = 2 –2 1/3  + 2 2/3 , then find the value of  x 3  – 6  x 2  +18  x  + 18.(a)22(b)40(c)33(d)45 20. The value of  111111 ------ ++++++++ bacaabcbbcac  xxxxxx = ?(a)0(b)1(c)  x a–b–c (d)None of these 21. If 537–43   = 473 ab  , then find a  and b. (a) a  = 3, b  = 5(b) a  = 1, b  = 27(c) a  = 7, b  = 3(d) a  = 2, b  = 7 22. If  p  x  = r   y  = m  and r  w  = p  z   = n ,   then which one of thefollowing is correct?(a)  xw = yz  (b)  xz = yw (c)  x + y = w + z  (d)  x – y = w – z  23. Let 6116)( 23   x x x x f  . Then, which one of the following is not a factor of )(  x f  :(a) 1   x (b) 2   x (c) 3   x (d) 3   x 24. (2 + 1) (2 2  + 1) (2 4  + 1) (2 8  + 1) (2 16  + 1) (2 32  + 1) (2 64 + 1) is(a)2 256  – 1(b)2 256 + 1(c)2 128  – 1(d)2 128  + 1 25. If (3.7)  x  = (0.037)  y  = 10000, then what is the value of  11 –   xy .(a)1(b)2(c)1/2(d)1/4 26. 333 242424............ will be equal to(a)2(b)2 2 (c)2 3 (d)2 5 27. If a  = 3 + 22  ] then the value of 6423 1 aaaa      is(a)204(b)212(c)192(d)240 28. If 21312  xy    = 483  xy    = 4725  xy    then thevalue of (  x  + 2  y ) is equal to :(a)3(b)2(c)7(d)–2 29. If 33 1421++ = 33 42++ abc  and a , b , c  rationalnumbers, then the value of    a + b + c  is(a)0(b)1(c)2(d)3 30. If   and   are the roots of the equation  x 2  – 3 kx  + k  2 = 0 find k   if  2  +  2  = 74 (a) 12  (b) 12 (c) 12  (d)None of these 31. )( nn a x    is divisible by )( a x  :(a)for all values of n (b)only for even values of n (c)only for odd values of n (d)only for prime values of n 32. If    –3 32 a    &    –3 32 b     ,  then ( a  + 1)  – 1  + ( b  + 1)  –1  = ?(a) 482 (b) 503 (c)1(d)5 33. If 2  s  = a + b + c , then the value of (  s – a ) 2  +(  s – b ) 2  + (  s – c ) 2  +  s 2  – a 2  – b 2  – c 2  will be :(a)–1(b)1(c)2(d)0 34. If 28633 ab    , then ( a  – b ) = ? (where a , b  are rational number)(a)–2(b) 2(c)4(d) –1 35. If 2  x  = a  + 33 43 baa   and 2  y  = a  – 33 43 baa   ,then find  x 3  +  y 3 .(a) a (b) b (c) a 3 (d) b 3  3 36. If 3  pqr  x     , then find (  x–p ) 3 + (  x–q ) 3 + (  x–r  ) 3  – 3(  x–p ) (  x–q )(  x–r  ) .(a)  pqr  (b)  p + q + r  (c)0(d)3 37. If ( a  + b +c )  p  = ( b +c – a ) q = ( c +a – b ) r = ( a +b – c )  s , then find 1111 –. qrsp   (a)1(b)2(c)0(d) a  + b +c 38. If a  + b  = 5 and a 2  + b 2  = 13, then find a  – b , where ( a > b ).(a)1(b)– 3(c)2(d)– 1 39. If 41553  x   , then 20122012  xx xx    = ?(a)1(b)2(c)3(d)4 40. If  x  = 32,then the value of 11– 111–1–   x x xx   is(a) 13 (b) 23 (c) 3 (d)2 41. If  xy + yz + zx =  xyz  , then find the value of  (1)(1)(1)  xyyzzx xyzyzxzxy       .(a) 32  (b) 12 (c)0(d)1 42. If  76711774711  pqrs      ,then  pqrs    = ?(a)6(b)4(c)9(d)8 43. If 123  x     , then the value of ( 432 285  xxx     2628  x   ) is(a)0(b) 66 (c) 36 (d) 6 44. Thevalue of  24816 ...       ppppp (a) 522      p (b) 352      p (c) 1   p p (d) 512      p 45. If 222 4()  xaxbxcabcbccaab          ,then thevalue of  x  is equal to :(a)( a  + b  + c ) 2 (b) a 2  + b 2  + c 2 (c) ab  + bc   + ca (d) a 2  + b 2  + c 2  – ab – bc – ca 46. Find the value of 26153.523853   (a) 3 (b)2(c) 13 (d)3 47. If 444 444..32 a  x     , then a  = ?(a) 152 (b) 154 (c) 52 (d) 51 48. Find the value of          4444444 abcbccaababcabc             (a)3 abc (b)4 abc (c)6 abc (d)12 abc 49. The solution to the inequality 11  x  – 61   5 is(a)–6     x     6(b) –6     x     0(c)  x  6(d) 0     x     6 50. If  x  + 1  x  = –  3 , then the value of  x 67  +  x 53  +  x 43  +  –  x 29  +  x 24  +  x 12  +  x 6  + 3 is :(a) 3 (b)0(c)    223  (d)    223   4 51. If ( ab  – b  + 1) = 0 and ( bc – c  + 1) = 0, then ( a – ac )is equal to(a)–1(b)0(c)1(d)2 52. If a  + b + c = 20 and 11130 abc    , then find thevalue of abbccabacbac         .(a)597(b) 600(c)599(d) can't find 53. If a  x  = bc , b  y  = ac, c  z   = ab, then   111  xyz  xyz      = ?(a)0(b)1(c)2(d)3 54. If  x 2  (  x + y + z  ) = 36,  y 2 (  x + y + z  ) = 46,  z  2 (  x + y + z  ) = 63,  xy (  x + y + z  ) = 111,  yz  (  x + y + z  ) = 99,  zx (  x+ y + z  ) = 82, then  x  = ?(a)6(b)7(c)2(d)4 55. If  xz  yw  , then  –  mmmmmmmm  xyzw xyzw          = ?(a)  y x (b) 1(c)(  xyzw ) m /2 (d) (  xyzw ) m 56. If )( t  x   is a factor of both )( 2 q px x    and ),( 2 mlx x    then the value of 't'   is:(a) qm  (b)  pl   (c) qm pl   (d)  pl qm  57. If a  + b  + c  = 0 , then 444222222 2()()    abcabbcca = ?(a)1(b)2(c)3(d)4 58. If a , b , c  and d   are four positive number such that a  + b  + c  + d   = 4, then what is the maximum valueof ( a  + 1) ( b  + 1) ( c  + 1)( d   +1).(a)32(b)8(c)16(d)81 59. What should be added to the  x (  x + a )(  x  + 2 a )(  x +3 a ), so that the sum be a perfect square?(a) 2 9 a (b) 2 4 a (c) 4 a (d)None of these 60. If 1(1)(2)0(1)  xx xx     , then find  x 2 +  x .(a)4(b)1(c)9(d)0 1. (a) 2. (c) 3. (b) 4. (d) 5. (b) 6. (c) 7. (a) 8. (a) 9. (d) 10. (c)11.(c) 12. (b) 13. (c) 14. (a) 15. (b) 16. (d) 17. (b) 18. (b) 19. (b) 20. (b)21.(b) 22. (a) 23. (c) 24. (c) 25. (c) 26. (a) 27. (a) 28. (c) 29. (a) 30. (a)31.(b) 32. (c) 33. (d) 34. (c) 35. (d) 36. (c) 37. (c) 38. (a) 39. (b) 40. (b)41.(d) 42. (d) 43. (b) 44. (b) 45. (a) 46. (c) 47. (a) 48. (d) 49. (c) 50. (d)51.(c) 52. (a) 53. (c) 54. (c) 55. (c) 56. (d) 57. (d) 58. (c) 59. (c) 60. (b) Answer

Sep 22, 2019

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