Wednesday, October 15, 2014

  1. Some Basic Formulae:
    1. (a + b)(a - b) = (a2 - b2)
    2. (a + b)2 = (a2 + b2 + 2ab)
    3. (a - b)2 = (a2 + b2 - 2ab)
    4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
    5. (a3 + b3) = (a + b)(a2 - ab + b2)
    6. (a3 - b3) = (a - b)(a2 + ab + b2)
    7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
    8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.
  2. 1. 
    5358 x 51 = ?
    A.273258B.273268
    C.273348D.273358

    2. 
    The sum of first five prime numbers is:
    A.11B.18
    C.26D.28

    3. 
    The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
    A.240B.270
    C.295D.360

    4. 
    (12)3 x 64 ÷ 432 = ?
    A.5184B.5060
    C.5148D.5084
    E.None of these

    5. 
    72519 x 9999 = ?
    A.725117481B.674217481
    C.685126481D.696217481
    E.None of these

    6. 
    If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
    A.0 B.1
    C.2D.None of these

    7. 
    The smallest 3 digit prime number is:
    A.101B.103
    C.109D.113

    8. 
    Which one of the following numbers is exactly divisible by 11?
    A.235641B.245642
    C.315624D.415624

    9. 
    (?) - 19657 - 33994 = 9999
    A.63650B.53760
    C.59640D.61560
    E.None of these

    10. 
    The sum of first 45 natural numbers is:
    A.1035B.1280
    C.2070D.2140

    11. 
    Which one of the following is not a prime number?
    A.31B.61
    C.71D.91

    12. 
    (112 x 54) = ?
    A.67000B.70000
    C.76500D.77200

    13. 
    It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
    A.(216 + 1)B.(216 - 1)
    C.(7 x 223)D.(296 + 1)

    14. 
    What least number must be added to 1056, so that the sum is completely divisible by 23 ?
    A.2B.3
    C.18D.21
    E.None of these

    15. 
    1397 x 1397 = ?
    A.1951609B.1981709
    C.18362619D.2031719
    E.None of these

    16. 
    How many of the following numbers are divisible by 132 ?
    264, 396, 462, 792, 968, 2178, 5184, 6336
    A.4B.5
    C.6D.7

    17. 
    (935421 x 625) = ?
    A.575648125B.584638125
    C.584649125D.585628125

    18. 
    The largest 4 digit number exactly divisible by 88 is:
    A.9944B.9768
    C.9988D.8888
    E.None of these

    19. 
    Which of the following is a prime number ?
    A.33B.81
    C.93D.97

    20. 
    What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
    A.0 B.2
    C.3D.5

    21. 
    Which of the following number is divisible by 24 ?
    A.35718B.63810
    C.537804D.3125736

    22. 
    753 x 753 + 247 x 247 - 753 x 247= ?
    753 x 753 x 753 + 247 x 247 x 247
    A.
    1
    1000
    		B.
    1
    506
    C.
    253
    500
    		D.None of these

    23. 
    (?) + 3699 + 1985 - 2047 = 31111
    A.34748B.27474
    C.30154D.27574
    E.None of these

    24. 
    If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
    A.2B.5
    C.6D.7
    E.None of these

    25. 
    The difference between the local value and the face value of 7 in the numeral 32675149 is
    A.75142B.64851
    C.5149D.69993
    E.None of these

    26. 
    The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
    A.
    3
    5
    		B.
    3
    10
    C.
    4
    5
    		D.
    4
    3

    27. 
    On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
    A.4B.5
    C.6D.7

    28. 
    If n is a natural number, then (6n2 + 6n) is always divisible by:
    A.6 onlyB.6 and 12 both
    C.12 onlyD.by 18 only

    29. 
    107 x 107 + 93 x 93 = ?
    A.19578B.19418
    C.20098D.21908
    E.None of these

    30. 
    What will be remainder when (6767 + 67) is divided by 68 ?
    A.1B.63
    C.66D.67
    31. 
    On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
    A.0B.1
    C.2D.4

    32. 
    How many 3-digit numbers are completely divisible 6 ?
    A.149B.150
    C.151D.166

    33. 
    How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
    A.8B.11
    C.12D.13
    E.None of these

    34. 
    How many of the following numbers are divisible by 3 but not by 9 ?
    2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
    A.5B.6
    C.7D.None of these

    35. 
    (963 + 476)2 + (963 - 476)2= ?
    (963 x 963 + 476 x 476)
    A.1449B.497
    C.2D.4
    E.None of these

    36. 
    How many 3 digit numbers are divisible by 6 in all ?
    A.149B.150
    C.151D.166

    37. 
    A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
    A.10B.11
    C.12D.15

    38. 
    8597 - ? = 7429 - 4358
    A.5426B.5706
    C.5526D.5476
    E.None of these

    39. 
    The smallest prime number is:
    A.1B.2
    C.3D.4

    40. 
    (12345679 x 72) = ?
    A.88888888B.888888888
    C.898989898D.9999999998
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