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Maths-

General

Easy

Question

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus sin invisible function application x minus 1 over denominator x end fraction$

1
$e^{x}$
X
0

hint Hint:

In this question we will first use the L hospital theorem. Then we will put value of x.

The correct answer is: 0

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus sin invisible function application x minus 1 over denominator x end fraction$
using L hospital theorem,
$limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator d e to the power of x over denominator d x end fraction end style minus begin display style fraction numerator d sin x space minus 1 over denominator d x end fraction end style over denominator begin display style fraction numerator d x over denominator d x end fraction end style end fraction equals limit as x rightwards arrow 0 of fraction numerator e to the power of x minus cos space x over denominator 1 end fraction equals e to the power of 0 minus cos space 0 equals 1 minus 1 equals 0$

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$blank to the power of n C subscript r plus 4 to the power of n C subscript r minus 1 end subscript plus 6 to the power of n C subscript r minus 2 end subscript plus 4 to the power of n C subscript r minus 3 end subscript plus to the power of n C subscript r minus 4 end subscript$ is equal to

$blank to the power of n C subscript r plus 4 to the power of n C subscript r minus 1 end subscript plus 6 to the power of n C subscript r minus 2 end subscript plus 4 to the power of n C subscript r minus 3 end subscript plus to the power of n C subscript r minus 4 end subscript$ is equal to

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$Lt subscript x not stretchy rightwards arrow 0 end subscript invisible function application fraction numerator e to the power of x minus 1 over denominator square root of 1 plus x end root minus 1 end fraction$

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If $a subscript n equals sum from r equals 0 to n of 1 over n subscript C subscript r end subscript text then end text sum from r equals 0 to n of fraction numerator r over denominator blank to the power of n C subscript r end fraction$ equal to

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Match Column-I with Column-II and select the correct option from the codes given below.

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ii) burns more efficiently as compared to petrol and diesel.
iii) is the natural aging of a lake which occurs due to accumulation of __.
iv) _ reduces the number of organisms which are sensitive to high temperature.
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Some statements are given below each with one or two blanks. Select the option that correctly fills up the blanks.
i) High concentration of DDT disturbs _______ in birds, which causes _.
ii) burns more efficiently as compared to petrol and diesel.
iii) is the natural aging of a lake which occurs due to accumulation of __.
iv) _ reduces the number of organisms which are sensitive to high temperature.
v) Irreparable computers and other electronic goods are known as _____.

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