Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

31.

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

  • 7

  • 1

  • 3

  • 3

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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 

  • 5/3

  • 1/3

  • 2/3

  • 2/3


D.

2/3

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



The space required space area space equals space 2 integral subscript 0 superscript 1 space left parenthesis 1 minus 3 straight y squared right parenthesis space minus space left parenthesis negative 2 straight y squared right parenthesis
space equals space 2 integral subscript 0 superscript 1 space left parenthesis 1 minus straight y squared right parenthesis space dy space equals space 2 space open square brackets straight y space minus space straight y cubed over 3 close square brackets subscript 0 superscript 1
space equals space 2 space straight x space 2 over 3 space equals space 4 over 3

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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
98 Views

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