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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?

7

1

3

3

x⁷+ 14x⁵+ 16x³+ 30x – 560 = 0
Let f(x) = x⁷+ 14x⁵+ 16x³+ 30x
⇒ f′(x) = 7x⁶+ 70x⁴+ 48x²+ 30 > 0 ∀ x.
∴ f (x) is an increasing function ∀ x.

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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

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

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