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NDA I 2020 Mathematics Test - 1
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NDA I 2020 Mathematics Test - 1

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  • Question 1/10
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    If y2 - 4y + log0.5 β = 0 does not have two different real roots, then the maximum value of β is

    Solutions

    If y2 - 4y + log0.5 β = 0 does not have two different real roots it means this quadratic equation will have either real & equal roots or imaginary roots.

     

  • Question 2/10
    1 / -0

    Solutions

    Now substitute this value on the given expressions

    Then

     

  • Question 3/10
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    The maximum or minimum value of 3y + 7 - 2y2 on R is:

    Solutions

     

  • Question 4/10
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    If x,y,z and k are different positive numbers in H.P., then

    Solutions

     

  • Question 5/10
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    If log x , log y and log z are in A.P. then x,y and z are in :

    A.

    Solutions

     

  • Question 6/10
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    Solutions

     

  • Question 7/10
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    For real numbers a and b we write a R b if f a - b + √2 is an irrational number. Then the relation R is :

    Solutions

     Given that in the set of real numbers R,

    aRb if f a - b + √2 is an irrational number

    Reflexive : Reflexive relation on a set is a binary element in which every element is related to itself.

    x - x + √2 = √2(irrational) for every x

    So R is a reflexive relation.

    Symmetric : Let a= √2

     , b = 1 so a- b + √2 = √2 - 1 + √2 = 2√2 - 1 which is an irrational number 

    For symmetric relation: (a,b) ∈R which implies that (b,a) ∈R

    So if (√2,1) ∈R then (1,√2) should also belong to R

    ⇒ a= 1 , b=√2

    ⇒ a - b + √2 = 1 - √2 + √2 = 1 which is not an irrational number 

    ⇒ (1,√2) does not belong to R

    So R is not symmetric relation.

     

  • Question 8/10
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    Let A= {α,β,γ}, B = {x,y} . Then the number of relations from A to B is what times to the number of relations from B to A :

    Solutions

    So the number of relations from A to B is the same as the number of relations from B to A

     

  • Question 9/10
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    Solutions

    The above condition is true for all real values of y. you can visualize it by putting y = 1,2,3,-1,-2,-3 and so on…..

     

  • Question 10/10
    1 / -0

    Solutions

     

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