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Function Test - 3
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Function Test - 3

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  • Question 1/10
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    Find the number of solutions of 2cos x = | sin x | , 0 ≤ x ≤ 4π.

    Solutions

    Given is the graph of y = 2 cosx and y = | sin x |.

    We can see that graphs intersects at 4 points. Hence the equation has 4 solutions

     

  • Question 2/10
    1 / -0

    If the range of the function y =  does not contain any values belonging to the interval  then find the the integral value (s) of ‘a’.

    Solutions

     

  • Question 3/10
    1 / -0

    Solutions

    Range f = { - 1, 0, 1 }

     

  • Question 4/10
    1 / -0

     

    If F (n + 1) =   n = 1, 2,.........and F (1) = 1 then find the value of F (2009).

    Solutions

     

  • Question 5/10
    1 / -0

    Solutions

     

  • Question 6/10
    1 / -0

     then find the range of f (x).

    Solutions

     

  • Question 7/10
    1 / -0

    If f (x) is an even function and satisfies the relation x2 f (x) - 2f  = g (x) where g (x) is an odd function ,then find the value of f(5).

    Solutions


    ... g (x) and x2 are odd and even function respectively .
    So, f (x) is an odd function . But f (x) is given even.
    ... f (x) = 0 ∀x , Hence f (5) = 0

     

  • Question 8/10
    1 / -0

    If [ 2sin x ] + [ cos x ] = - 3 ,then find the range of the function

    Solutions

    [ 2sin x ] + [ cos x ] = - 3 only if
    [ 2sin x ] = - 2 and [ cos x ] = - 1
    ... - 2≤ 2 sin x < - 1 and - 1 ≤ cosx < 0 
    ⇒ - 1≤ sin x < - 1/2 and 
    - 1 ≤ cos x < 0 

     

  • Question 9/10
    1 / -0

    What will be the number of solutions of the equation 2cosx = | sin x |, 
    when x ∈ [ 0, 2π ].

    Solutions

    See the graph y = 2cosx and y = | sin x |. 
    Two curves meets at four points for x ∈ [ 0, 2π ]

    So, the equation 2cosx = | sin x | has four solutions.

     

  • Question 10/10
    1 / -0

    Let A = {1, 2, 3, 4, 5}. If ‘f’ be a bijective function from A to A, then the number of such functions for which f (k) ≠ k, k = 1, 2, 3, 4, 5 is

    Solutions

    The problem is equivalent to derangement . The required number of functions

     

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