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Maths-

General

Easy

Question

A function f from integers to integers is defined as $f left parenthesis x right parenthesis equals open curly brackets table row cell n plus 3 blank n element of o d d end cell row cell n divided by 2 blank n element of text end text text e end text text v end text text e end text text n end text text end text end cell end table text suppose end text k element of text odd end text close text and end text$ $f left parenthesis f left parenthesis f left parenthesis k right parenthesis right parenthesis right parenthesis equals 27 text end text$ then the sum of digits k is

3
6
9
12

The correct answer is: 6

Related Questions to study

Let f(x) $equals left square bracket n plus p s i n invisible function application x right square bracket cross times stack I with hat on top left parenthesis 0 comma p right parenthesis comma n stack I with hat on top Z to the power of ´ end exponent p to the power of ´ end exponent$ a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )

Let f(x) $equals left square bracket n plus p s i n invisible function application x right square bracket cross times stack I with hat on top left parenthesis 0 comma p right parenthesis comma n stack I with hat on top Z to the power of ´ end exponent p to the power of ´ end exponent$ a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )

If graph of the function y= f(x) is continuous and passes through point (3, 1) then $stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text end text$ is equal

If graph of the function y= f(x) is continuous and passes through point (3, 1) then $stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text end text$ is equal

Let f be twice differentiable real valued function satisfying $f to the power of ´ end exponent left parenthesis x right parenthesis not equal to 0 comma f left parenthesis x right parenthesis plus f to the power of ´ ´ end exponent left parenthesis x right parenthesis equals negative x g left parenthesis x right parenthesis f to the power of ´ end exponent left parenthesis x right parenthesis$ where $g left parenthesis x right parenthesis greater than 0 for all x greater than 0 text .If end text f left parenthesis 0 right parenthesis equals negative 3 text end text$ and $f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 4 text end text$ then
Statement -1: $vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0$
Statement -2: $left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus open parentheses f to the power of ´ end exponent left parenthesis x right parenthesis close parentheses to the power of 2 end exponent$ is decreasing $for all x greater than 0.$

Let f be twice differentiable real valued function satisfying $f to the power of ´ end exponent left parenthesis x right parenthesis not equal to 0 comma f left parenthesis x right parenthesis plus f to the power of ´ ´ end exponent left parenthesis x right parenthesis equals negative x g left parenthesis x right parenthesis f to the power of ´ end exponent left parenthesis x right parenthesis$ where $g left parenthesis x right parenthesis greater than 0 for all x greater than 0 text .If end text f left parenthesis 0 right parenthesis equals negative 3 text end text$ and $f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 4 text end text$ then
Statement -1: $vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0$
Statement -2: $left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus open parentheses f to the power of ´ end exponent left parenthesis x right parenthesis close parentheses to the power of 2 end exponent$ is decreasing $for all x greater than 0.$

parallel

Let $I equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator sin invisible function application x over denominator square root of x end fraction d x text and end text J equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator cos invisible function application x over denominator square root of x end fraction d x text . end text$ Then which one of the following is true ?

Let $I equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator sin invisible function application x over denominator square root of x end fraction d x text and end text J equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator cos invisible function application x over denominator square root of x end fraction d x text . end text$ Then which one of the following is true ?

$text Iff end text text . end text minus y minus e to the power of y end exponent comma g comma negative y minus y comma y greater than 0 text end text$ andE.. $t minus stretchy integral subscript 0 end subscript superscript t end superscript f left parenthesis t minus y right parenthesis g left parenthesis y right parenthesis d y text , end text$ then-

$text Iff end text text . end text minus y minus e to the power of y end exponent comma g comma negative y minus y comma y greater than 0 text end text$ andE.. $t minus stretchy integral subscript 0 end subscript superscript t end superscript f left parenthesis t minus y right parenthesis g left parenthesis y right parenthesis d y text , end text$ then-

If for a non-zero x, af $x plus b f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals fraction numerator 1 over denominator x end fraction minus 5 text , end text$ where $a to the power of not equal to end exponent b text , end text$ then $stretchy integral subscript 1 end subscript superscript 2 end superscript$ f(x)dx=

If for a non-zero x, af $x plus b f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals fraction numerator 1 over denominator x end fraction minus 5 text , end text$ where $a to the power of not equal to end exponent b text , end text$ then $stretchy integral subscript 1 end subscript superscript 2 end superscript$ f(x)dx=

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parallel

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physics-General

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Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.

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