Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If A is a 3x3 non- singular matrix such that AAT = ATA, then BBT is equal to

  • l +B
  • l
  • B-1

  • B-1

284 Views

22.

If g is the inverse of a function f and f'(x) = fraction numerator 1 over denominator 1 plus straight x to the power of 5 end fraction comma then g'(x) is equal to 

  • 1+ x6

  • 5x4

  • fraction numerator 1 over denominator 1 plus space left curly bracket straight g left parenthesis straight x right parenthesis right square bracket to the power of 5 end fraction
  • fraction numerator 1 over denominator 1 plus space left curly bracket straight g left parenthesis straight x right parenthesis right square bracket to the power of 5 end fraction
178 Views

23.

If f and ga re differentiable  functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

  • 2f'(c) = g'(c)

  • 2f'(c) = 3g'(c)

  • f'(c) = g'(c)

  • f'(c) = g'(c)

149 Views

24.

If fk(x) = 1/k (sink x + cosk x), where x ε R and k ≥1, then f4 (x)-fo (x) equal to 

  • 1/6

  • 1/3

  • 1/4

  • 1/4

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25.

Let A and B be two events such that straight P left parenthesis space stack straight A space union straight B right parenthesis with bar on top space equals space 1 over 6 comma space straight P space left parenthesis straight A space intersection straight B right parenthesis space equals space 1 fourth space and space space straight P space left parenthesis straight A with bar on top right parenthesis space equals space 1 fourth where straight A with bar on top. Then, the events A and B are

  • independent but not equally likely

  • independent and equally likely

  • mutually exclusive and independent

  • mutually exclusive and independent

158 Views

26.

If =-1 and x =2 are extreme points of f(x) =α log|x| + βx2 +x, then

  • α = -6, β = 1/2

  • α = -6, β = -1/2

  • α = 2, β = -1/2

  • α = 2, β = -1/2

307 Views

27.

The integral integral open parentheses 1 plus straight x space minus 1 over straight x close parentheses straight e to the power of straight x plus 1 over straight x end exponent dx is equal to 

  • left parenthesis straight x minus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
  • xe to the power of straight x plus 1 over straight x end exponent plus straight C
  • left parenthesis straight x plus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
  • left parenthesis straight x plus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
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28.

The Integral integral subscript 0 superscript straight pi square root of 1 plus 4 space sin squared straight x over 2 minus 4 sin straight x over 2 dx end root is equal to

  • π-4

  • fraction numerator 2 space straight pi over denominator 3 end fraction minus 4 minus 4 square root of 3
  • 4 square root of 3 minus 4
  • 4 square root of 3 minus 4


D.

4 square root of 3 minus 4

By using the formula, vertical line straight x minus straight a vertical line space equals open curly brackets table attributes columnalign left end attributes row cell straight x minus straight a comma space space space space space space space space space straight x greater or equal than straight a end cell row cell negative left parenthesis straight x minus straight a right parenthesis comma space space space straight x less than straight a end cell end table close
It breaks given integral in two parts and then integrates separately.

integral subscript 0 superscript straight x square root of open parentheses 1 minus 2 sin straight x over 2 close parentheses squared end root dx space equals space integral subscript 0 superscript straight pi vertical line 1 minus 2 space sin straight x over 2 vertical line dx
equals integral subscript 0 superscript straight pi over 3 end superscript open parentheses 1 minus 2 space sin space straight x over 2 close parentheses dx space minus integral subscript straight pi over 3 end subscript superscript straight pi open parentheses 1 minus 2 space sin space straight x over 2 close parentheses dx
equals space open parentheses straight x plus 4 space cos space straight x over 2 close parentheses subscript 0 superscript straight pi over 3 end superscript space minus space open parentheses straight x plus 4 space cos space straight x over 2 close parentheses subscript straight pi over 3 end subscript superscript straight pi
equals space 4 square root of 3 space minus 4 minus straight pi over 3

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29.

The area of the region described by A = {(x,y): x2 +y2 ≤ 1 and y2 ≤1-x} is

  • straight pi over 2 plus 4 over 3
  • straight pi over 2 minus 2 over 3
  • straight pi over 2 minus 2 over 3
  • straight pi over 2 minus 2 over 3
145 Views

30.

Let the population of rabbits surviving at a time t be governed by the differential equation.fraction numerator dp left parenthesis straight t right parenthesis over denominator dt end fraction space equals space 1 half straight p left parenthesis straight t right parenthesis space minus 200 If p(0) = 100 then p(t) is equal to 

  • 400 minus 300 straight e to the power of straight t over 2 end exponent
  • 300 minus 200 straight e to the power of negative straight t over 2 end exponent
  • 600 minus 500 straight e to the power of straight t over 2 end exponent
  • 600 minus 500 straight e to the power of straight t over 2 end exponent
147 Views

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