hamburger menu
All Coursesall course arrow
adda247
reward-icon
adda247
    arrow
    arrow
    arrow
    If 2a×5b=500,2^a × 5^b = 500,2a×5b=500, and a and b are integers, then a + b is ​
    Question

    If 2a×5b=500,2^a × 5^b = 500, and a and b are integers, then a + b is ​

    A.

    5

    B.

    6

    C.

    7

    D.

    Interminable 

    Correct option is A

    Given:
    We are given:

     2a×5b=500,2^a × 5^b = 500,​ where a and b are integers.
    We are to find the value of a + b.

    Solution:
    Step 1: Prime factorize 500
    500 = 2 × 250
    = 2 × 2 × 125
    = 2² × 5³

    So,
    2a×5b2^a × 5^b​ = 2² × 5³

    Thus,
    a = 2, b = 3

    Now:
    a + b = 2 + 3 = 5

    Final Answer:
    S. Ans. (A) 5

    test-prime-package

    Access ‘CSIR NET- GENERAL APTITUDE’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    students-icon
    383k+ students have already unlocked exclusive benefits with Test Prime!
    test-prime-package

    Access ‘CSIR NET- GENERAL APTITUDE’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    students-icon
    383k+ students have already unlocked exclusive benefits with Test Prime!
    Our Plans
    Monthsup-arrow