If the L.C.M. and H.C.F. of two expressions are (x2 + 6x + 8) (x

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Two numbers are in the ratio 5 : 6. If their LCM is 120, their HCF will be

  • 12

  • 10

  • 8

  • 4

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2.

The least among  and 1 is

  • e
143 Views

3.

The sum of two numbers is 45 and their H.C.F. and L.C.M. are 3 and 168 respectively. The sum of the reciprocals of the numbers will be

  • 15/57

  • 3/11

  • 15/56

  • 5/56

334 Views

4.

The ratio of two numbers is 3 : 4 and their LCM is 180. The second number is

  • 60

  • 45

  • 90

  • 90

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5.

The greatest perfect square number of 6 digits is:

  • 999001

  • 998001

  • 998009

  • 998009

301 Views

6.

The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator 7+C (C > -7) is a constant, then the minimum value of the fraction is

  • 5

  • 1 fifth
  • -5

  • -5

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7.

If the L.C.M. and H.C.F. of two expressions are (x2 + 6x + 8) (x + 1) and (x + 1) respectively and one of the expressions is x2 + 3x + 2, find the other.

  • x2 + 5x + 4

  • x2 - 5x + 4

  • x2 + 4x + 5

  • x2 + 4x + 5


A.

x2 + 5x + 4

x2 + 6x + 8 = x2 + 4x + 2x +8 = x(x + 4) + 2(x + 4) = (x + 4) (x + 2)

x2 + 3x + 2 = x2 + 2x + x +2=  x(x + 2) + 1(x + 2) = (x + 2) (x + 1)
Now, 
First expression x Second expression = LCM X HCF
⟹  (x2 + 3x + 2) x Second expression = (x2 + 6x + 8) (x + 1) x (x + 1)
⟹ (x + 2) (x + 1) x Second expression = (x + 4) (x + 2) (x + 1) (x + 1)
rightwards double arrow space space Second space expression space equals space fraction numerator left parenthesis straight x plus 2 right parenthesis thin space left parenthesis straight x plus 4 right parenthesis thin space left parenthesis straight x plus 1 right parenthesis thin space left parenthesis straight x space plus 1 right parenthesis over denominator left parenthesis straight x space plus space 2 right parenthesis thin space left parenthesis straight x plus 1 right parenthesis end fraction space equals space left parenthesis straight x space plus space 4 right parenthesis thin space left parenthesis straight x space plus space 1 right parenthesis
⟹ (x + 4) (x + 1) = x2 + 4x + x + 4 = x2 + 5x + 4
 




 
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8.

Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.

  • 183
  • 243

  • 483

  • 483

265 Views

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9.

Three man step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. The minimum distance each should cover so that all can cover the distance in complete steps is

  • 9630 cm

  • 9360 cm

  • 6930 cm

  • 6930 cm

174 Views

10.

Find the greatest number which will exactly divide 200 and 320.

  • 10

  • 20

  • 16

  • 16

290 Views

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