Applications Of Integrals Test

Applications Of Integrals

This is Applications of Integrals Test-02 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 bounded by the curve y = 4x - \({x^2}\) and the x- axis is equal to
  • A
    \(\frac{{31}}{7}{\text{ }}sq.{\text{ }}units\)
  • B
    \(\frac{{32}}{3}{\text{ }}sq.{\text{ }}units\)
    Correct
  • C
    \(\frac{{34}}{3}{\text{ }}sq.{\text{ }}units\)
  • D
    \(\frac{{30}}{7}{\text{ }}sq.{\text{ }}units\)
2
The area bounded by the curve \({y^2} = x\;,\;line\;y = 4\) and y – axis is equal to
  • A
    none of these
  • B
    \(\frac{{64}}{3}\)
  • C
    \(\frac{{16}}{3}\)
    Correct
  • D
    \(7\sqrt 2 \)
3
The area bounded by y = log x , the x – axis and the ordinates x = 1 and x = 2 is
  • A
    log ( \(\frac{2}{e}\) )
  • B
    \(\log \left( {\;\frac{4}{e}\;} \right)\)
    Correct
  • C
    none of these
  • D
    log 4
4
Area lying in the first quadrant and bounded by the circle \({x^2} + {y^2} = 4\) and the line x = y\(\sqrt 3 \)is
  • A
    \(\begin{array}{*{20}{l}} \pi \end{array}\)
  • B
    none of these
  • C
    \(\frac{\pi }{2}\)
  • D
    \(\frac{\pi }{3}\)
    Correct
5
The area common to the circle \({x^2} + {y^2} = 16\) and the parabola \({y^2}\) = 6x is
  • A
    none of these
  • B
    \(\frac{{4(4\pi + \sqrt 3 )}}{3}\)
  • C
    \(\frac{{4(8\pi - \sqrt 3 )}}{3}\)
    Correct
  • D
    \(\frac{{4(4\pi - \sqrt 3 )}}{3}\)
6
Area bounded by the curves satisfying the conditions \(\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{36}} \leqslant 1 \leqslant \frac{x}{5} + \frac{y}{6}\) is given by
  • A
    30 ( - 1 ) sq. units
  • B
    15(\(\pi /2\) - 1 ) sq. units
    Correct
  • C
    \(\frac{{15}}{2}\) (\(\pi /2\) - 1 ) sq. units
  • D
    \(\frac{{15}}{4}\) (\(\pi /2\) - 1 ) sq. units
7
The area bounded by the parabola y = \({x^2}\) + 1 and the straight line x + y = 3 is given by
  • A
    \(\begin{array}{*{20}{l}} {\frac{9}{2}} \end{array}\)
    Correct
  • B
    \(\begin{array}{*{20}{l}} {\frac{{25}}{4}} \end{array}\)
  • C
    \(\begin{array}{*{20}{l}} {\frac{{45}}{7}} \end{array}\)
  • D
    none of these
8
The area bounded by the curves \({y^2}\) = x andy = \({x^2}\) is
  • A
    none of these
    Correct
  • B
    1 sq. units
  • C
    1/2 sq. units
  • D
    2/3 sq. units
9
The area common to the circle \({x^2} + {y^2} = 16{a^2}\) and the parabola \({y^2}\) = 6ax is
  • A
    none of these
  • B
    \(\frac{{4{a^2}}}{3}(4\pi + \sqrt 3 )\)
    Correct
  • C
    \(\frac{{4{a^2}}}{3}(4\pi - \sqrt 3 )\)
  • D
    \(\frac{{4{a^2}}}{3}(8\pi + \sqrt 3 )\)
10
The area of the region bounded by the curves y = \(\left| {x - 1} \right|\) and y = 3 - \(\left| x \right|\) is
  • A
    4 sq. units
    Correct
  • B
    3 sq.units
  • C
    2 sq. units
  • D
    6 sq. units
11
The area bounded by the curves y = \(\left| x \right|\) - 1 and y = -\(\left| x \right|\) + 1 is
  • A
    4
  • B
    1
  • C
    2\(\sqrt 2 \)
  • D
    2
    Correct
12
The area bounded by the parabola \({y^2}\) = x and the straight line 2y = x is
  • A
    \(\frac{1}{3}sq.{\text{ }}units\)
  • B
    1 sq. units
  • C
    \(\frac{2}{3}sq.{\text{ }}units\)
  • D
    \(\frac{4}{3}sq.{\text{ }}units\)
    Correct
13
The area bounded by the ellipse \({x^2} + 9{y^2} = 9\) and the straight line x + 3y = 3 is
  • A
    \(9\pi \)
  • B
    \(6\pi \)
  • C
    \( \Rightarrow \frac{3}{4}(\pi - 2)\)
    Correct
  • D
    \(4\pi \)
14
The area between the hyperbola \(xy = {c^2}\) , then x – axis and the ordinates at a and b with a > b is :
  • A
    \({c^2}\log \left( {\frac{b}{a}} \right)\)
    Correct
  • B
    \({c^2}\log \left( {ab} \right)\)
  • C
    none of these
  • D
    \({c^2}\log \left( {\frac{a}{b}} \right)\)
15
The area of the smaller portion of the circle \({x^2} + {y^2} = 4\)cut off by the line x = 1 is
  • A
    \(\frac{{4\pi - 3\sqrt 3 }}{3}\)
    Correct
  • B
    \(\frac{{4\pi + 3\sqrt 3 }}{3}\)
  • C
    none of these
  • D
    \(\frac{{4\pi - \sqrt 3 }}{3}\)