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Mathematics Test 282
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Mathematics Test 282
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  • Question 1/10
    4 / -1

    Domain of definition of the function 

    Solutions

     

  • Question 2/10
    4 / -1

    The domain of the function √(log1/3 log4 ([x]2 - 5)) is (where [x] denotes greatest integer function)

    Solutions

     

  • Question 3/10
    4 / -1

    Solutions

     

  • Question 4/10
    4 / -1

    Solutions

     

  • Question 5/10
    4 / -1

    A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

    Solutions

     

  • Question 6/10
    4 / -1

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  • Question 7/10
    4 / -1

     is real, then the point represented by the complex number z lies :

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  • Question 8/10
    4 / -1

    Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.

    Solutions

    Given:

    Initial ratio = 5 ∶ 6

    Final ratio should be less than 17 ∶ 22

    Calculation:

    Let the least whole number that is needed to be subtracted be a.

    According to the question,

    (5 - a)/(6 - a) < 17/22

    ⇒ 5 × 22 - 22a < 17 × 6 - 17a 

    ⇒ 110 - 22a < 102 - 17a 

    ⇒ 110 - 102 < - 17a + 22a 

    ⇒ 8 < 5a 

    ⇒ 8/5 = 1.6 < a 

    ∴ The least whole number must be 2.

     

  • Question 9/10
    4 / -1

    Given, 6x + 2(6 - x) > 2x - 2 < 5x/2 - 3x/4, then x can take which of the following values?

    Solutions

    ⇒ 6x + 2(6 - x) > 2x - 2

    ⇒ 6x + 12 - 2x > 2x - 2

    ⇒ 2x > - 14

    ⇒ x > - 7     ----(1)

    ⇒ 2x - 2 < 5x/2 - 3x/4

    ⇒ 2x - 2 < 7x/4

    ⇒ 8x - 7x < 8

    ⇒ x < 8     ----(2)

    From (1) and (2),

    - 7 < x < 8

    ∴ x = 5 satisfies the given conditions from the above options.

     

  • Question 10/10
    4 / -1

    The area (in sq. units) of the region {x ∈ R : x ≥ 0, y ≥ 0, y ≥ x - 2 and y ≤ √x) is

    Solutions

     

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