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Very short answer question:
Give an example in which packaging could have been reduced?
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Very short answer question:
Give an example in which packaging could have been reduced?

Answer

Packaging could be reduced if we carry our own carry bags (made of jute and cotton) instead of getting the polythene bags from the shopkeeper.
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Long answer question:
Describe how packaging increases the amount of garbage.
If \( f\left(x\right)=\left[\begin{array}{cc}\frac{a{e}^{sinx}+b{e}^{-sinx}-c}{{x}^{2}} ;& x\ne\;0\\ 2& ; x=0\end{array}\right.\) is continuous at \( x=0;\) then
(a) \( a=b=c\)
(b) \( a=2b=3c\)
(c) \( a=b=2c\)
(d) \( 2a=2b=c\)
A person holds a bundle of hay over his head for \(30\) minutes and gets tired. Has he done some work or not ? Justify you answer.
Short answer question:
Do you think it is better to use compost instead of chemical fertilizers? Why?
If \( f\left(x\right)=\sqrt{\frac{1+{sin}^{-1}x}{1-{tan}^{-1}x}};\) then \( {f}^{\prime }\left(0\right)\) is equal to :
(a) \( 4\)
(b) \( 3\)
(c) \( 2\)
(d) \(\frac12\)
Let \(\begin{array}{cc}f(x)=\left\{\begin{array}{cc}\frac{x\left(3 e^{2}+4\right)}{2-e^{1 / x}} & , & x \neq 0 \\ 0 & , & x=0\end{array}\right.\end{array} \quad x \neq \frac{1}{\ln 2}\)
which of the following statement(s) is/are correct?
(a) \( f\left(x\right)\) is continuous at \( x=0\)
(b) \( f\left(x\right)\) is non-derivable at \( x=0\)
(c) \( {f}^{\prime }\left({0}^{+}\right)=-3\)
(d) \( {f}^{\prime }\left({0}^{-}\right)\) does not exist
A twice differentiable function \( f\left(x\right)\) is defined for all real numbers and satisfies the following conditions:
\( f\left(0\right)=2, {f}^{\prime }\left(0\right)=-5 and \;{f}^{\prime \prime }\left(0\right)=3\)
The function \( g\left(x\right)\) is defined by \( g\left(x\right)={e}^{ax}+f\left(x\right)\forall\;x\in\;R,\) where \( {a}\) is any constant. If \( {g}^{\prime }\left(0\right)+{g}^{\prime \prime }\left(0\right)=0\) then \( {a}\) can be equal to
(a) \( 1\)
(b) \( -1\)
(c) \( 2\)
(d) \( -2\)
An electric heater is rated \(1500\ W\). How much energy does it use in \(10\) hours?
If \( f\left(x\right)\) be a differentiable function satisfying \( f\left(y\right)f\left(\frac{x}{y}\right)=f\left(x\right)\forall\;x,y\in\;R,y\ne\;0\) and \( f\left(1\right)\ne\;0\) \( {f}^{\prime }\left(1\right)=3,\) then :
(a) \( sgn\left(f\right(x\left)\right)\) is non-differentiable at exactly one point
(b) \( \underset{x\xrightarrow{}\;0}{lim}\frac{{x}^{2}(cosx-1)}{f\left(x\right)}=0\)
(c) \( f\left(x\right)=x\) has 3 solutions
(d) \( f\left(f\right(x\left)\right)-{f}^{3}\left(x\right)=0\) has infinitely many solutions
Let \( f\left(x\right)=\left[\begin{array}{c}{x}^{2}+a;0\le\;x<1\\ 2x+b;1\le\;x\le\;2\end{array} and\;g\left(x\right)=\left[\begin{array}{c}3x+b;0\le\;x<1\\ {x}^{3};1\le\;x\le\;2\end{array}\right.\right.\)
If derivative of \( f\left(x\right)\) w.r.t. \( g\left(x\right)\) at \( x=1\) exists and is equal to \( \lambda \), then which of the following is/are correct ?
(a) \( a+b=-3\)
(b) \( a-b=1\)
(c) \( \frac{ab}{\lambda }=3\)
(d) \( \frac{-b}{\lambda }=3\)

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