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JEE Mathematics Solved Question Paper 2008

Multiple Choice Questions

31.

How many real solutions does the equation x⁷+ 14x⁵+ 16x³+ 30x – 560 = 0 have?

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32. $Let space straight I space space equals space integral subscript 0 superscript 1 space fraction numerator sin space straight x over denominator square root of straight x end fraction dx space and space straight J space equals space integral subscript 0 superscript 1 space fraction numerator cos space straight x over denominator square root of straight x end fraction space dx$ then which one is true?

I > 2/ 3 and J > 2

I < 2/ 3 and J < 2

I < 2/ 3 and J > 2

I < 2/ 3 and J > 2

I < 2/ 3 and J < 2

straight I equals space integral subscript 0 superscript 1 fraction numerator sin space straight x over denominator square root of straight x end fraction space dx space less than space integral subscript 0 superscript 1 space fraction numerator straight x over denominator square root of straight x end fraction dx space equals space integral subscript 0 superscript 1 square root of straight x dx space equals space 2 over 3 straight x to the power of 3 divided by 2 end exponent space left enclose space subscript 0 superscript 1 end enclose space equals space 2 over 3 rightwards double arrow straight l space less than space 2 over 3 straight J space equals space integral subscript 0 superscript 1 fraction numerator cos space straight x over denominator square root of straight x end fraction space dx space less than integral subscript 0 superscript 1 fraction numerator 1 over denominator square root of straight x end fraction space dx space equals space 2 square root of straight x vertical line subscript 0 superscript 1 space equals space 2 therefore space straight J less or equal than 2

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33.

The area of the plane region bounded by the curves x + 2y²= 0 and x + 3y²= 1 is equal to

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34.

The value of $square root of 2 space integral fraction numerator sin space straight x space dx over denominator sin space open parentheses straight x minus begin display style straight pi over 4 end style close parentheses end fraction space is$

$space straight x plus space log open vertical bar cos space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus space straight C$
$straight x space minus log space open vertical bar sin space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus straight c$
$straight x space plus space log space open vertical bar sin space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus straight c$
$straight x space plus space log space open vertical bar sin space open parentheses straight x minus straight pi over 4 close parentheses close vertical bar space plus straight c$