Applications Of Integrals Test

Applications Of Integrals

This is Applications of Integrals Test-05 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 region bounded by the parabola \({(y - 2)^2} = x - 1\;,\)the tangent to yhe parabola at the point ( 2 , 3 ) and the x – axis is equal to
  • A
    9 sq. units
    Correct
  • B
    12 sq. units
  • C
    none of these
  • D
    6 sq. units
2
The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and \(x = \frac{\pi }{2}\)is equal to
  • A
    \(2(\sqrt 2 + 1)\)sq. units
  • B
    \(2(\sqrt 2 - 1)\)sq. units
    Correct
  • C
    \(\left( {4\sqrt 2 + 1\;} \right)\) sq. units
  • D
    \(\left( {4\sqrt 2 - 1\;} \right)\) sq. units
3
The area bounded by the parabola y = \({x^2}\) and the line y = x is
  • A
    \(\frac{1}{2}\) sq. units
  • B
    \(\frac{1}{6}\) sq. units
    Correct
  • C
    none of these
  • D
    \(\frac{1}{3}\) sq. units
4
Let y be the function which passes through ( 1 , 2 ) having slope ( 2x + 1 ) . The area bounded between the curve and the x – axis is
  • A
    6 sq. units
  • B
    \(\frac{5}{6}\) sq. units
  • C
    none of these
  • D
    \(\frac{1}{6}\) sq. units
    Correct
5
The area bounded by the curves \(y = \sqrt {5 - {x^2}\;} \;and\;y = \;\left| {x - 1} \right|\) is
  • A
    \(\frac{{5\pi + 2}}{4}\) sq. units
  • B
    \(\frac{{5\pi - 2}}{4}\) sq. units
    Correct
  • C
    \(\frac{{5\pi - 5}}{4}\) sq. units
  • D
    \(\frac{{\pi - 5}}{4}\) sq. units
6
The area of the region bounded by the curves y\( = \left| {x - 2} \right|\) , x = 1 , x = 3 and the x – axis is
  • A
    3
  • B
    4
  • C
    1
    Correct
  • D
    2
7
The area enclosed between the curve \(y = {\log _e}(x + e)\) and \(x = {\log _e}\frac{1}{y}\) and the x- axes is
  • A
    none of these
  • B
    3 sq. units
  • C
    1 sq. units
  • D
    2 sq. unit
    Correct
8
The area bounded by y = \(\left| {\sin x} \right|\) , the x – axis and the line \(\left| x \right| = \pi \) is
  • A
    2 sq. units
  • B
    6 sq. units
  • C
    none of these
  • D
    4 sq. units
    Correct
9
The area bounded by the curves \(y = \sqrt x \;,\;2y + 3 = x\)and the x – axis in the first quadrant is
  • A
    36
  • B
    9
    Correct
  • C
    18
  • D
    none of these
10
The area bounded by the curve \(y = x\log x\;and\;y = 2x - 2{x^2}\) is
  • A
    none of these
  • B
    \(\frac{1}{2}\) sq. units
  • C
    \(\frac{7}{{12}}\) sq. units
    Correct
  • D
    \(\frac{3}{{12}}\) sq. units
11
The area bounded by the curves \(y = \left| {x - 1} \right|\;\) and y = 1 is given by
  • A
    2
  • B
    \(\frac{1}{2}\)
  • C
    1
    Correct
  • D
    none of these.
12
The area bounded by the lines y = 2 + x , y = 2 – x and x = 2 is
  • A
    3
  • B
    8
  • C
    4
    Correct
  • D
    16
13
Ratio of the area cut off from a parabola by any double ordinate is that of the corresponding rectangle contained by that double ordinate and its distance from the vertex is
  • A
    1 : 1
  • B
    2 : 3
    Correct
  • C
    1 : 3
  • D
    1 : 2
14
If the area cut off from a parabola by any double ordinate is k times the corresponding rectangle contained by that double ordinate and its distance from the vertex , then k is equal to
  • A
    \(\frac{1}{3}\)
  • B
    \(\frac{2}{3}\)
    Correct
  • C
    3
  • D
    \(\frac{3}{2}\)
15
The larger area bounded by \({y^2} = 4x\;and\;{x^2} + {y^2} - 2x - 3 = 0\;\) is equal to
  • A
    \(\;2\pi - \frac{4}{3}\)
  • B
    \(2\pi + \frac{8}{3}\)
    Correct
  • C
    \(2\pi + \frac{2}{3}\)
  • D
    \(2\pi + \frac{4}{3}\)