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# JEE Mathematics 2008 Exam Questions

#### Multiple Choice Questions

31.

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

• 5/3

• 1/3

• 2/3

• 4/3

D.

4/3

Solving the equations we get the points of intersection (–2, 1) and (–2,  1)The bounded region is shown as shaded region

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32.

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

• 7

• 1

• 3

• 5

B.

1

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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33.

The value of

C.

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34.  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

B.

I < 2/ 3 and J < 2

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