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Question

If F left parenthesis alpha right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell c o s alpha end cell cell negative s i n alpha end cell 0 row cell s i n alpha end cell cell c o s alpha end cell 0 row 0 0 1 end table close curly brackets a n d G left parenthesis beta right parenthesis equals open square brackets table row cell c o s invisible function application beta end cell 0 cell s i n invisible function application beta end cell row 0 1 0 row cell negative s i n invisible function application beta end cell 0 cell c o s invisible function application beta end cell end table close square brackets, then left square bracket F left parenthesis alpha right parenthesis G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent equals

  1. F left parenthesis alpha right parenthesis minus G left parenthesis beta right parenthesis    
  2. negative F left parenthesis alpha right parenthesis minus G left parenthesis right parenthesis    
  3. left square bracket F left parenthesis alpha right parenthesis right square bracket to the power of negative 1 end exponent left square bracket G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent    
  4. left square bracket G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent left square bracket F left parenthesis alpha right parenthesis right square bracket to the power of negative 1 end exponent    

The correct answer is: left square bracket G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent left square bracket F left parenthesis alpha right parenthesis right square bracket to the power of negative 1 end exponent

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Matrix A is such that A to the power of 2 end exponent equals 2 A minus I, where I is the identity matrix The for n greater or equal than 2 comma A to the power of n end exponent equals

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Statement‐I:: If f left parenthesis x right parenthesis is increasing function with concavity upwards, then concavity of f to the power of negative 1 end exponent left parenthesis x right parenthesis is also upwards
Statement‐II:: If f left parenthesis x right parenthesis is decreasing function with concavity upwards, then concavity of f to the power of negative 1 end exponent left parenthesis x right parenthesis is also upwards.

Statement‐I:: If f left parenthesis x right parenthesis is increasing function with concavity upwards, then concavity of f to the power of negative 1 end exponent left parenthesis x right parenthesis is also upwards
Statement‐II:: If f left parenthesis x right parenthesis is decreasing function with concavity upwards, then concavity of f to the power of negative 1 end exponent left parenthesis x right parenthesis is also upwards.

maths-General
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Statement‐I:: fraction numerator 2 e to the power of x subscript 1 end subscript end exponent plus e to the power of x subscript 2 end subscript end exponent over denominator 3 end fraction greater than e left parenthesis fraction numerator 2 x subscript 1 to the power of plus X end exponent 2 end subscript over denominator 3 end fraction right parenthesis , where e is Napier’sconstant.
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Statement‐I:: fraction numerator 2 e to the power of x subscript 1 end subscript end exponent plus e to the power of x subscript 2 end subscript end exponent over denominator 3 end fraction greater than e left parenthesis fraction numerator 2 x subscript 1 to the power of plus X end exponent 2 end subscript over denominator 3 end fraction right parenthesis , where e is Napier’sconstant.
Statement‐II:: If f e subscript i left parenthesis x right parenthesis end subscript and f C C left parenthesis x right parenthesis is positive for all x element of R, then f left parenthesis x right parenthesis increases with concavity up for all x element of R and any chord lies above the curve.

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The beds of two rivers (within a certain region) are a parabola y equals x to the power of 2 end exponent and a straight line y=x-2 These rivers are to be connected by a straight canal The coordinates of the ends of the shortest canal can be:

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If f(x) equals x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d comma 0 less than b to the power of 2 end exponent less than c, then f(x)

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The set of value (s) of a’for which the function f left parenthesis x right parenthesis equals fraction numerator a x to the power of 3 end exponent over denominator 3 end fraction plus left parenthesis a plus 2 right parenthesis x to the power of 2 end exponent plus left parenthesis a minus 1 right parenthesis x plus 2 possess anegative point of inflection‐

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The greatest, the least values of the function, f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x to the power of 2 end exponent end root comma x element of left square bracket 21 right square bracket are respectively

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Hence the final answer is (2,0)

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Hence f(2)=4 is the suitable option

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