Maths-
General
Easy
Question
If A is the area between the curve
and x - axis then the number of prime factors of A ![blank to the power of negative 1 end exponent text is end text](data:image/png;base64,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)
- 3
- 4
- 2
- 5
The correct answer is: 5
Related Questions to study
maths-
maths-General
maths-
The value of the definite Integral ![text . end text stretchy integral subscript negative 2008 end subscript superscript 2008 end superscript fraction numerator f to the power of ´ end exponent left parenthesis x right parenthesis plus f to the power of ´ end exponent left parenthesis negative x right parenthesis over denominator left parenthesis 2008 right parenthesis to the power of x end exponent plus 1 end fraction d x text equals end text](data:image/png;base64,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)
The value of the definite Integral ![text . end text stretchy integral subscript negative 2008 end subscript superscript 2008 end superscript fraction numerator f to the power of ´ end exponent left parenthesis x right parenthesis plus f to the power of ´ end exponent left parenthesis negative x right parenthesis over denominator left parenthesis 2008 right parenthesis to the power of x end exponent plus 1 end fraction d x text equals end text](data:image/png;base64,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)
maths-General
maths-
The integral
is equal to
The integral
is equal to
maths-General
maths-
A point P moves in xy – plane in such a way that
denotes the greatest integer function. Area of the region representing all possible positions of the point P is equal to
A point P moves in xy – plane in such a way that
denotes the greatest integer function. Area of the region representing all possible positions of the point P is equal to
maths-General
maths-
The value of ![stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text](data:image/png;base64,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)
The value of ![stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text](data:image/png;base64,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)
maths-General
maths-
If function f(x)
is equal to
If function f(x)
is equal to
maths-General
maths-
If
then
If
then
maths-General
maths-
Statement - I :
attain its maximum value ![text at end text x equals fraction numerator pi over denominator 3 end fraction](data:image/png;base64,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)
Statement - 2:
increasing function in ![open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text](data:image/png;base64,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)
Statement - I :
attain its maximum value ![text at end text x equals fraction numerator pi over denominator 3 end fraction](data:image/png;base64,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)
Statement - 2:
increasing function in ![open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text](data:image/png;base64,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)
maths-General
maths-
denotes the greatest integer function, is continuous and differentiable in (4, 6) then.
denotes the greatest integer function, is continuous and differentiable in (4, 6) then.
maths-General
maths-
denotes greatest integer function)
denotes greatest integer function)
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,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)
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,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)
maths-General
maths-
A function f from integers to integers is defined as
then the sum of digits k is
A function f from integers to integers is defined as
then the sum of digits k is
maths-General
maths-
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
maths-General
maths-
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
maths-General