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Algebra Test 476
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Algebra Test 476

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  • Question 1/10
    1 / -0.25
    The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144 . Find the positive difference between the squares of these two given numbers.
    Solutions
     Let, two natural numbers = a & b

    According to question,

     ….(i)

    (a – b) = 18

    ab = 144 ……(ii)

    We know,

    And,

    (a + b) = 30

    Also,

    Now,

     = (30)(18) = 540

    Hence, option B is the correct answer.

  • Question 2/10
    1 / -0.25
    Simplify the given expression.

    Solutions
    Given expression,

    We know,

    Here, a = (326+222) & b = (326 – 222)

    So,

    =

    =

    Hence, option B is the correct answer.

  • Question 3/10
    1 / -0.25
    Which of the following numbers is divisible by 24?
    Solutions
    We know, if a number is divisible by both 8 & 3 then it is divisible 24

    Divisibility of 8 - A number is divisible by 8 if the last three digits of the number are divisible by 8.

    Divisibility of 3 - A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

    Take, 52668 -

    Last three digit 668 is not divisible by 8.

    Take 49512 -

    Last three digit 512 is divisible by 8

    And the sum of digits (4+9+5+1+2=21) is also divisible by 3.

    Hence, 49512 is divisible by 24.

    Hence, option B is the correct answer.

  • Question 4/10
    1 / -0.25
    If = 7, and 0 < x < 1, find the value of
    Solutions
    Given,

    Add 2 on both sides

    According to question,

    Now,

    Hence, option D is the correct answer.

  • Question 5/10
    1 / -0.25
    If x +  = 7, then the value of  is :
    Solutions

    Squaring on both sides

    Now, cubing on both sides

    Hence, option B is the correct answer.

  • Question 6/10
    1 / -0.25
    If  then what is the value of ?
    Solutions
     x2 + 1/x2 = 7

    ⇒ (x + 1/x)2 – 2 = 7

    ⇒ (x + 1/x)2 = 9

    ⇒ (x + 1/x) = 3

    ∴ x3 + 1/x3 = (3)3 – 3(3)

    = 27 – 9 = 18

    Hence, option B is the correct answer.

  • Question 7/10
    1 / -0.25
    If x = 7 and y = 2 then, what is the value of ?

    Solutions

    x = 7 and y = 2

    ∴ [x3 – y3]/[x2 – y2] – [3xy]/[x + y]

    = [(x-y)(x2+y2+xy)]/[(x-y)(x+y)] – [3xy]/[x+y]

    = [x2+y2+xy]/[x+y] – [3xy]/[x+y]

    = [x2+y2-2xy]/[x+y]

    = [x-y]2/[x+y]

    = [7-2]2/[7+2]

    = 25/9

    Hence, option C is the correct answer.

  • Question 8/10
    1 / -0.25
    If a +  = P2, then a2 + .

    Solutions
     We know that, if x + 1/x = n, then x2 + 1/x2 = n2 – 2

    Now, a + 1/a = P2

    ∴ a2 + 1/a2 = (P2)2 – 2

    = P4 – 2

    Hence, option C is the correct answer.

  • Question 9/10
    1 / -0.25
    If 2p + q = 19 and 8p3 + q3 = 361, then find the value of pq.
    Solutions

  • Question 10/10
    1 / -0.25
    If a − b = 8 and ab = 9, then the value of a + b is ______.
    Solutions

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