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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1$ observe the following
$text l) end text delta f equals 2.11$
$text II) end text d f equals 2.1$
$text III) Relative error in end text x text is end text 1$
The true statements are

only I, III
only II, III
only I, II
I, II, III

The correct answer is: only I, II

Related Questions to study

Statement I : $f colon A not stretchy rightwards arrow B text is one - one and end text g colon B not stretchy rightwards arrow C text is a one-one function, then gof end text colon A not stretchy rightwards arrow C$ is one - one
Statement II : $text If end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A$ are two functions such that $g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals$ $g to the power of negative 1 end exponent$
Staatement III : $f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text then end text f equals g$
Which of the above statement/s is/are true.

Statement I : $f colon A not stretchy rightwards arrow B text is one - one and end text g colon B not stretchy rightwards arrow C text is a one-one function, then gof end text colon A not stretchy rightwards arrow C$ is one - one
Statement II : $text If end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A$ are two functions such that $g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals$ $g to the power of negative 1 end exponent$
Staatement III : $f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text then end text f equals g$
Which of the above statement/s is/are true.

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter $2 cross times 1 0 to the power of negative 5 end exponent$ m. The tube is immersed vertically into a liquid of surface tension $5.06 cross times 1 0 to the power of negative 2 end exponent$ N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter $2 cross times 1 0 to the power of negative 5 end exponent$ m. The tube is immersed vertically into a liquid of surface tension $5.06 cross times 1 0 to the power of negative 2 end exponent$ N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?

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