Applications Of Integrals Test

Applications Of Integrals

This is Applications of Integrals Test-01 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 ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) is
  • A
    \(\frac{{\pi ({a^2} + {b^2})}}{4}\)
  • B
    \(\Pi \left( {a{\text{ }} + {\text{ }}b} \right)\)
  • C
    \(\pi ab\)
    Correct
  • D
    None of these
2
The area of the loop between the curve y = a sin x and the x – axis and x= 0 , \(x = \pi .\) is
  • A
    a
  • B
    none of these
  • C
    3a
  • D
    2a
    Correct
3
The area enclosed between the curves y = \({x^3}\) ,x- axis and two ordinates x = 1 to x = 2 is [ in square units ]
  • A
    \(\frac{5}{3}\)
  • B
    \(\frac{{12}}{5}\)
  • C
    \(\frac{{15}}{4}\)
    Correct
  • D
    \(\frac{5}{4}\)
4
Area of the region bounded by the curves y = \({e^x}\), x = a , x = b and the x- axis is given by
  • A
    \({e^b} - {e^a}\)
    Correct
  • B
    none of these
  • C
    \({e^{b - a}}\)
  • D
    \({e^b} + {e^a}\)
5
AOB is the positive quadrant of the ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) in which OA = a and OB = b . The area between the arc AB and chord AB of the ellipse is
  • A
    \(\frac{1}{4}ab(\pi - 2)\)
    Correct
  • B
    \(\frac{1}{2}ab(\pi + 2)\)
  • C
    \(\frac{1}{4}ab(\pi - 4)\)
  • D
    none of these
6
The area lying in the first quadrant and bounded by the curve y = \({x^3}\) , the x – axis and the ordinates at x = - 2 and x = 1 is
  • A
    6.
  • B
    3
  • C
    \(\frac{{15}}{4}\)
    Correct
  • D
    2
7
The area bounded by the curve y = \({x^3}\) , the x – axis and two ordinates x = 1 and x = 2 is
  • A
    \(\frac{{17}}{4}\) sq. units
  • B
    \(\frac{{15}}{2}\)sq. units
  • C
    \(\frac{{15}}{4}\) sq. units
    Correct
  • D
    \(\frac{{17}}{2}\) sq. units
8
If A is the area between the curve y = sin2x , x – axis and the lines x = \(\frac{\pi }{4}\) and x = \(\frac{{3\pi }}{4}\)is :
  • A
    3
  • B
    none of these
  • C
    1
    Correct
  • D
    2
9
The area bounded by y = 2cosx , x = 0 to x =2π and the axis of x in square units is
  • A
    8
    Correct
  • B
    7
  • C
    4
  • D
    6
10
The area of the figure bounded by the curve \(y = {\log _e}x\) , the x – axis and the straight line x = e is
  • A
    1
    Correct
  • B
    5 - e
  • C
    none of these
  • D
    3 + e
11
The area enclosed by the curve \(y = 2\sqrt {1 - {x^2}} ,x \in \left[ {0,1} \right]\) is
  • A
    \(\frac{\pi }{2}\)
    Correct
  • B
    \(\frac{\pi }{4}\)
  • C
    none of these
  • D
    \(\pi \)
12
The area of the region between the curve y = 4 – \(x{\;^2}\;,\;0 \leqslant x \leqslant 3\) and the x –axis is equal to
  • A
    \(\frac{{23}}{3}\)
    Correct
  • B
    \(\frac{7}{3}\)
  • C
    3
  • D
    \(\frac{{16}}{3}\)
13
The area bounded by the curve \(\left| x \right| + y = 1\) and the x –axis is
  • A
    1
    Correct
  • B
    4
  • C
    2
  • D
    \(\frac{1}{2}\)
14
The area enclosed by the curve \(\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1\)is equal to
  • A
    20\(\pi \;sq.units\)
    Correct
  • B
    none of these
  • C
    \(10\pi \;sq.units\)
  • D
    \(5\pi \;sq.units\)
15
The area of the curve \({x^2} + {y^2} = 2ax\) is
  • A
    \(2\pi {a^2}\)
  • B
    \(3\pi {a^2}\)
  • C
    \(\pi {a^2}\)
    Correct
  • D
    \(4\pi {a^2}\)