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  • Question
  • Which of the following statements is not correct?


  • Options
  • A. log10 10 = 1
  • B. log (2 + 3) = log (2 x 3)
  • C. log10 1 = 0
  • D. log (1 + 2 + 3) = log 1 + log 2 + log 3

  • Correct Answer
  • log (2 + 3) = log (2 x 3) 

    Explanation
    (a) Since loga a = 1, so log10 10 = 1.

    (b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

         ∴ log (2 + 3) ≠ log (2 x 3)

    (c) Since loga 1 = 0, so log10 1 = 0.

    (d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

    So, (b) is incorrect.


    More questions

    • 1. 
      A pipe can fill a cistern in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then third pipe is also opened. In what time is the cistern emptied?

    • Options
    • A. 30 min.
    • B. 33 min.
    • C. 371 / 2 min.
    • D. 45 min.
    • Discuss
    • 2. 
      Two vessels A and B contain milk and water in the ratio 7 : 5 and 17 : 7 respectively. In what ratio mixtures from two vessels should be mixed to get a new mixture containing milk and water in the ratio 5 : 3?

    • Options
    • A. 1 : 2
    • B. 2 : 1
    • C. 2 : 3
    • D. 3 : 2
    • Discuss
    • 3. 
      A shopkeeper buys 26 liter of milk @ Rs. 16 per liter. He also buys from another source an inferior quality of milk @ Rs. 10 per liter. How much quantity of the later should he buy to mix it with the former so that he can sell the mixture @ Rs. 14 per liter without making any loss?

    • Options
    • A. 13 liter
    • B. 12 liter
    • C. 14 liter
    • D. 16 liter
    • Discuss
    • 4. 
      The sum of two number is 216 and their H.C.F is 27. The numbers are?

    • Options
    • A. 54, 162
    • B. 108, 108
    • C. 27, 189
    • D. None of these
    • Discuss
    • 5. 
      The greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m 95 cm, is?

    • Options
    • A. 15 cm
    • B. 25 cm
    • C. 35 cm
    • D. 42 cm
    • Discuss
    • 6. 
      In a class of 30 students , the average weight of boys is 20 kg and the average weight of the girls is 25 kg . The fraction of boys out of the total students of the class is

    • Options
    • A. 4/5
    • B. 5/6
    • C. 3/4
    • D. Data insufficient
    • Discuss
    • 7. 
      The least number which when divided by 12,16 and 18 leaves 5 as remainder in each case. Find the number.

    • Options
    • A. 139
    • B. 144
    • C. 149
    • D. 154
    • Discuss
    • 8. 
      P, Q and R start a business jointly. Twice the capital of P is equal to thrice the capital of Q and the capital of Q is four times the capital of R. Find the share of Q in an annual profit of ? 148500.

    • Options
    • A. ? 54000
    • B. ? 64000
    • C. ? 56000
    • D. ? 55000
    • Discuss
    • 9. 
      The LCM of two numbers is 48. The numbers are in the ratio of 2 : 3. Find the sum of the numbers.

    • Options
    • A. 28
    • B. 32
    • C. 40
    • D. 64
    • Discuss
    • 10. 
      A, B and C enter into a partnership with shares in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs. 21600, then B's share in the profit is?

    • Options
    • A. Rs. 2100
    • B. Rs. 2400
    • C. Rs. 3600
    • D. Rs. 4000
    • Discuss


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