MCQ Bank
A plane curve (not line) is a curve that lies in a ............ plane.
- A) None of these
- B) Two dimensional
- C) Three dimensional
- D) One dimensional
Arc length of the curve y=x from x=0 to x=1 is .........
- A) \sqrt 2
- B) 2\sqrt 2
- C) 0
- D) None of these.
If a function is continuous on a given interval then it is called....
- A) Discontinuous function.
- B) Smooth function.
- C) Piecewise function.
- D) Step function.
\[ \begin{gathered} If\,the\,curve\,\,y\, = \,f(x)\,\,over\,\,[a,\,b]\,is\,\,revolved\,about\,x - axis,\,then\,the\,volume\,is\,calculated\,by\,the\,formula\,\, - - - - - - - \ \end{gathered} \]
- A) \[ \int\limits_a^b {\pi \,[f(x)} ] \,dx \]
- B) \[ \int\limits_a^b {\pi \,[f(x)} ]^3 \,dx \]
- C) \[ \int\limits_a^b {\pi \,[f(x)} ]^4 \,dx \]
- D) \[ \int\limits_a^b {\pi \,[f(x)} ]^2 \,dx \]
Length of the curve y=3x from x=0 to x=1 is........
- A) Sqrt(10)
- B) Sqrt(5)
- C) 0
- D) None of these.
\begin{gathered} Find\,\,the\,\,area\,\,of\,\,the\,\,region\,\,to\,\,the\,\,left\,\,of\,the\,\,parabola\,\,x = 2y^2 ,\,\,to\,\,the\,\,right\,\,of\,\, \hfill \ the\,y - axis\,\,and\,\,between\,\,y = 1\,\,and\,\,y = 3 \hfill \\ \end{gathered}
- A) None\,\,of\,\,these
- B) \frac{{10}} {4}
- C) \frac{1} {3}
- D) \frac{{52}} {3}
If the function f(x) is not differentiable on the interval [a, b], what impact does it have on the calculation of the arc length?
- A) The arc length is approximated.
- B) The arc length is infinite.
- C) The arc length cannot be determined.
- D) The arc length is zero.
What happens to the arc length as the number of divisions of the interval increases?
- A) It becomes less accurate.
- B) It becomes more accurate.
- C) It decreases.
- D) It remains constant.
Find\,\,the\,\,area\,\,between\,\,y = x\,\,and\,\,y = \,\, - x(x - 4)
- A) None\,\,of\,\,these
- B) \frac{9} {2}\,
- C) 0
- D) \frac{7} {2}\,
The\,\,bounded\,\,region\,\,between\,\,the\,\,parabola\,\,y = 4x^2 \,\,and\,\,the\,\,line\,\,y = 6x - 2
- A) \frac{1} {6}\,
- B) None\,\,of\,\,these
- C) \frac{1} {{12}}
- D) \frac{1} {3}
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- B) data:image/png;base64,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
- C) data:image/png;base64,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
- D) data:image/png;base64,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
By using cylindrical shells to find the volume of the solid when the region R in the first quadrant enclosed between y=x and y = {x^2} is revolved about the y-axis is ______.
- A) V = \int\limits_0^1 {2\pi (x - {x^2})} dx
- B) V = \int\limits_0^1 {2\pi x(x - {x^2})} dx
- C) V = \int\limits_0^1 {\pi x(x - {x^2})} dx
- D) V = \int\limits_0^3 {2\pi x(x - {x^2})} dx
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- C) data:image/png;base64,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- C) data:image/png;base64,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
- D) data:image/png;base64,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
Arc length of the curve y=1 from x=0 to x=1 is.........
- A) 1
- B) 2
- C) 0
- D) -1
The\,\,area\,\,of\,\,the\,\,ellipse\,\,\frac{{x^2 }} {{a^2 }}\,\, + \,\,\frac{{y^2 }} {{b^2 }}\,\, = \,\,1
- A) \pi (a + b)
- B) \frac{1} {4}\,\pi (a^2 + b^2 )
- C) None\,\,of\,\,these
- D) \pi ab
Use cylindrical shells to find the volume of the solid generated when the region ‘R’ enclosed between y = 2x + 1 and y = - 2x - 3 in the interval [1,3] is revolved about the y-axis is ______.
- A) V = \int\limits_1^3 {2\pi x\left( {(2x + 1) - ( - 2x - 3)} \right)} dx
- B) V = \int\limits_1^3 {2\pi x\left( {(2x + 1) + ( - 2x - 3)} \right)} dx
- C)
- D)
A ………… function is a function that has continuous derivatives up to some desired order over some domain.
- A) Smooth
- B) Non smooth
- C)
- D)