Applications Of Integrals Test

Applications Of Integrals

This is Applications of Integrals Test-03 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The area of the smaller segment cut off from the circle \({x^2} + {y^2} = 9\) by x = 1 is
  • A
    \(\frac{1}{2}(9{\sec ^{ - 1}}(3) - \sqrt x )\)
  • B
    \(9{\sec ^{ - 1}}(3) - \sqrt 8 \)
    Correct
  • C
    \(\sqrt 8 - 9{\sec ^{ - 1}}(3)\)
  • D
    none of these
2
The area enclosed by the curve \(x{y^2}\; = {\text{ }}{a^2}\left( {a{\text{ }}--{\text{ }}x{\text{ }}} \right)\) and the y – axis is
  • A
    \(\Pi {a^2}\)
    Correct
  • B
    \(\Pi \)
  • C
    none of these
  • D
    \(2\pi \)
3
The area bounded by the curves \({y^2} = {x^{3\;\;}}and\;\left| y \right| = 2x\) is given by
  • A
    2
    Correct
  • B
    \(\frac{{32}}{5}\)
  • C
    \(\frac{{32}}{3}\)
4
The area bounded by the curves \({y^2} = 4x\;and\;y = x\) is equal to
  • A
    none of these
  • B
    \(\frac{{35}}{6}\)
  • C
    \(\frac{8}{3}\)
    Correct
  • D
    \(\frac{1}{3}\)
5
The area included between the curves \(\sqrt x + \;\sqrt {\left| y \right|} = 1\;and\;\left| x \right| + \left| y \right| = 1\) is equal to
  • A
    \(\frac{2}{3}\)
    Correct
  • B
    \(\frac{1}{6}\)
  • C
    \(\frac{4}{3}\)
  • D
    none of these
6
The area of the figure bounded by y = \({e^x}\;,\;y = {e^{ - x}}\) and the straight line x = 1 is
  • A
    e – 1/e
  • B
    none of these
  • C
    e + 2/e
  • D
    e + 1/e - 2
    Correct
7
The area enclosed between the curves y = \(\sqrt {x\;\;} ,\;x = 2y + 3\;\)and the x-axis is
  • A
    27
  • B
    none of these
  • C
    18
  • D
    9
    Correct
8
The positive value of the parameter a for which the area of the figure bounded by y = sin ax , y = 0 , x = \(\frac{\pi }{a}\;\;and\;x = \frac{{\pi \;}}{{3a}}\) is 3 is equal to
  • A
    \(\frac{{2 + \sqrt 3 }}{3}\)
  • B
    \(\frac{1}{2}\)
    Correct
  • C
    2
  • D
    none of these
9
The area bounded by the parabola \({y^2} = 4x\) and the line x + y = 3 is
  • A
    \(\frac{{64}}{3}\)
    Correct
  • B
    \(\frac{{32}}{3}\)
  • C
    \(\frac{{16}}{3}\)
  • D
    none of these
10
The area bounded by the curve\(y = {x^2} + 1\) and the line x + y = 3 is
  • A
    \(\frac{{35}}{3}\)
  • B
    \(\frac{9}{2}\)
    Correct
  • C
    \(\frac{{32}}{3}\)
  • D
    \(\frac{{16}}{3}\)
11
The area of the region bounded by y = \(\left| {x - 1} \right|\) and y = 1 is
  • A
    2
  • B
    \(\frac{1}{2}\)
  • C
    none of these
  • D
    1
    Correct
12
The area of bounded by the curve \(\sqrt x + \sqrt y = 1\) and the coordinate axes is
  • A
    \(\frac{1}{2}\)
  • B
    \(\frac{1}{6}\)
    Correct
  • C
    none of these
  • D
    1
13
The area bounded by the curves \({x^2} = 4y\;and\;x = 4y - 2\;\)is
  • A
    \(\frac{9}{4}\;sq.unit\)
  • B
    \(\frac{9}{8}\;sq.units\)
    Correct
  • C
    \(9\;sq.units\)
  • D
    \(\frac{9}{2}\;sq.units\)
14
If the area bounded by the curve \({y^2} = 16x\;\)and the line y = mx is \(\frac{2}{3}\)2/3 , then m is equal to
  • A
    1
  • B
    4
    Correct
  • C
    2
  • D
    3
15
The area of the region bunded by the curves y = \(\left| {x - 2\;} \right|\;,\;x = 3\;,x = 1\;\)and the x – axis is
  • A
    2
  • B
    1
    Correct
  • C
    4
  • D
    3