Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

61. find the value of the k so that the given function is continuous at the indicated point:

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight k space cos space straight x over denominator straight pi minus 2 straight x end fraction comma space if space straight x not equal to straight pi over 2 end cell row cell space space space space space space space 3 space space space space space space comma space if space straight x equals straight pi over 2 end cell end table close at space straight x equals straight pi over 2

116 Views

Here space straight f left parenthesis straight x right parenthesis equals open curly brackets table row cell 1 space space space comma space space space space space straight x less or equal than 3 end cell row cell ax plus straight b comma space space space space 3 less than straight x less than 5 end cell row cell 7 space space space comma space space space space straight x greater or equal than 5 end cell end table close

∵ f is continuous at x = 3 and x = 5

∴ f is right continuous at x = 3 and left continuous at x = 5

therefore space Lt with straight x rightwards arrow 3 to the power of plus below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 3 right parenthesis space space space space space space space space space space space rightwards double arrow space 3 straight a plus straight b equals 1 space space space space space space space.... left parenthesis 1 right parenthesis space Lt with straight x rightwards arrow 5 to the power of minus below space space space space straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 5 right parenthesis space space space space space space space space space space space space rightwards double arrow space 5 straight a plus straight b equals 7 space space space space space space space.... left parenthesis 2 right parenthesis

Subtracting (2) from (1), we get,
– 2 a = – 6, ⇒ a = 3
Putting a = 3 in (1) we get,
3 x 3 + b = 1, ⇒ b = – 8
∴ a = 3, b = –8.

83 Views

63. If the function

straight f left parenthesis straight x right parenthesis equals open curly brackets table row cell space space space 3 ax plus straight b space space if space straight x greater than 1 end cell row cell space space space space space space 11 space space space space space space space space if space straight x equals 1 end cell row cell space space 5 ax minus 2 straight b space space if space straight x less than 1. end cell end table close

is continous at x=1, find the values of a and b.

73 Views

64. For what value of k is the following function continuous at x = 2?

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell table row cell 2 straight x plus 1 comma space space space space straight x less than 2 end cell row cell space space space straight k space space space space comma space space space space space space straight x equals 2 end cell end table end cell row cell space 3 straight x minus 1 comma space space space space space straight x greater than 2 end cell end table close

92 Views

65. Given that

straight f left parenthesis straight x right parenthesis equals open curly brackets table row cell fraction numerator 1 minus cos space 4 straight x over denominator straight x squared end fraction space space space space space space space space space space comma space if space straight x less than 0 end cell row cell space space space space space space straight a space space space space space space space space space space space space space space space space space space space space space space space comma space if space straight x equals 0 end cell row cell fraction numerator square root of straight x over denominator square root of 16 plus square root of straight x end root minus 4 end fraction space space comma space if space straight x greater than 0 end cell end table close

If f(x) is continous at x=0, find the value of a.

76 Views

66. Determine the value of a, b_y c for which the functions

straight f left parenthesis straight x right parenthesis equals open curly brackets table row cell fraction numerator sin left parenthesis straight a plus 1 right parenthesis straight x plus sin space straight x over denominator straight x end fraction space space space comma space straight x less than 0 end cell row cell space space space space space space space space space space space space space space space space space space space space straight c space space space space space space space space space space space space space space space comma space straight x equals 0 end cell row cell fraction numerator square root of straight x plus bx squared end root minus square root of straight x over denominator bx to the power of begin display style 3 over 2 end style end exponent end fraction space space space space space space space comma space straight x greater than 0 end cell end table close

is continous at x=0.

75 Views

67. Is the function defined by f(x) = | x |, a continuous function ?

86 Views

68. Discuss the continuity of the function f given by f(x) = x³ + x ² –1.

89 Views

69. Discuss the continuity of the function f defined by

straight f left parenthesis straight x right parenthesis equals 1 over straight x comma space straight x not equal to 0

105 Views

70. Examine the following functions for continuity :
f(x)=x-5

117 Views