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Standard XII

Physics

Double Differentiation

Consider the ...

Question

Consider the following statements
$S_{1}$ : A straight line can not have more than one set of direction cosines.
$S_{2}$ : The range of the function $f (x) = ({sin}^{- 1} x) is [0, \frac{π}{2}]$
$S_{3}$ : If ${log}_{10} x = - 2.314$ then characteristics is $- 2$
State, in order, whether $S_{1}, S_{2}, S_{3}$ are true or false

F F T

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F F F

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T F T

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F T T

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Solution

The correct option is B $F F F$
$S_{1}$ : A straight line can have more than one set of direction cosines
$S_{2}$ : The range of $f (x) = {sin}^{- 1} x = [- \frac{Π}{2}, \frac{Π}{2}]$
$S_{3}$ : ${log}_{10} x = - 2.314 = - 2 - 0.314 + 1$
${log}_{10} x = - 3 + 0.686$
so characteristic is $- 3$
Hence, $S_{1}$ , $S_{2}$ and $S_{3}$ all are False.

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Consider the following statementsS1: A straight line can not have more than one set of direction cosines.S2: The range of the function f(x)=(sin−1x)is[0,π2]S3: If log10x=−2.314 then characteristics is −2State, in order, whether S1,S2,S3 are true or false

The correct option is B FFFS1 : A straight line can have more than one set of direction cosinesS2 : The range of f(x)=sin−1x=[−Π2,Π2]S3 : log10x=−2.314=−2−0.314+1 log10x=−3+0.686 so characteristic is −3Hence, S1, S2 and S3 all are False.