\[ {\text{Definite integral indicating the arc length of the curve }}y = x^2 {\text{ between }}x = 0{\text{ and }}x = 2{\text{ is }}......... \]

• A) None of these.
• B) \[ L = \int\limits_0^2 {\sqrt {1 + 2x^2 } dx} \]
• C) \[ L = \int\limits_0^2 {\sqrt {1 + 4x^2 } dx} \]
• D) \[ L = \int\limits_0^2 {xdx} \]

To Find the arc length, why might piecewise functions be more challenging than smooth functions?

• A) Piecewise functions have more complicated shapes.
• B) Piecewise functions have smoother curves.
• C) Piecewise functions are not defined on intervals.
• D) Piecewise functions may have discontinuities.

Distance between the points (-2,-3) and (-4,-1) using the distance formula is.........

• A) Sqrt(8)
• B) None of these
• C) Sqrt(10)
• D) 0

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• A) data:image/png;base64,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
• B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMwAAABICAYAAAC6Axo8AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAcxSURBVHhe7ZqNUes6EIVpgRpogR4ogRpogQ7ogA6ogApogAbogB5y57sv5719GiuxbEeS5fPNeIh/I+/u2V0p3J2MMbOxYIwpwIIxpgALxpgCLBhjCrBgjCnAgtmA5+fn093dnbeJbTQsmA14eno6fX19nffMyFgwG2DBHAcLZgMQjDkGFswGjNirm2ns6Q2wYI6DPb0B9/f3509mdCyYlfz+/noOcyAsmJWwOmbBHAcLZiUWzD/IDsznHh4eTj8/P+czY2HBrIRAeXl5Oe8dF8Ty/f39b4v69vZ2PjMWXQqG7EQQ7sHoHx8fwwbHUvDdqD/kdicYshQByP9n7SEQGaMF8x/47/X19bw3Ht22ZHsJxD0KRv8YSXXcktHFAs0EQ69L6cZx/I7BfmRPgvn8/Dzv7QPaJey+5cQ8igVf7i2JzKWZYBDL+/v7X+PivJS9CIbWcW/9OuNlJWtLeJ4qF5sFsyFktmu/jhOIeyjvrAj1JhiS0aXqQaLCvnOhevBM00gwZJ/cbxdqF+LWM70JRpU7Qsv4+Pj415aMly1ew1yGBMY1Qn7QMZ47atUooUk04rBRjJ8TfgsQRjoejhH4Eoj2qRqguaQEEsWf+om2q6fk0IImgiGbjSKYXv7xksBnLBKCSG1NwOfGjCDitVSXuBjDvbEKHZHqgtEkf+slzVbwLj1AoKfVRVUjzmeoNLmqyLxGcxv8M+UjRDWK75ZQ3dty4iilvZcKwzjS5W1EFAVNskqrSAQxqarkJvm65qhUF4x66FEE08McRpP2FI5ja9o0qgyrjoxX1SP1gZIZYsmtsnFczzwi1QWjrDeCYHiHHgQTW6kIlYLxSQTsIxrElWuruDZ3TlBhRv9FP0czweC8vdOLYBBAXCZeCkLJtWIRxHLUtqy6YDA2ghkBBDMnwG4JrdEWFRvBzX0XhLWlD5VEmV/1TvXIVYuwFnppHEx2lbHTSe+t4ftyE2gqKG3SkjGV2Edzwtyc4xpq0XLvMQXi5DvXijRCXLROPnPYrWB4htoQgpMWAcfXbPUIsqlAI4gl5CVBVWIfZeeaaOK/ZYIiLq7NnXpgt4JJUabdMutdY0owOF3Hlo6nxD4tBAN8Z/ruayDB7GHlrbqlVQm2Rn21KgzGp03j2NSmFkD7ym6qDHOyHQFzSRA859aCoe3jXWrDGJcKBh+pnWZTWxjRXJe/IH+2btuqCwYjbO1gHIAxY4uGofmLQJW5OJYanH3uldBKWgPubS0Yxrs3weATNs27+ByXxfEXvlQSZJ93lI9aMoRgeN5U5sHAMXMhjCkx4CycxjPmigX43rWC4TzXXdtyz2EMOXtOPWfplsKxJYJBCPgkBj/jV7KLcA3fg396EAvsXjAE+ZSxgXmNvksT1anVJAmrdFxcr+o1Bd/nCvN/GGua3LB9zk4ksqWV7BbsWjAYPhoT4UTDx/NUDirMFBKdqsxcrr1HDcGoOtZmqWDS+7B77n3ls9iutWa3gsHQaXDzXAWoqob2cRLn1R8LiQU4x/ji+UvEdi9F7URJiydyATQF71Vy/VbwnUsEEwWAnXmG5pCa4AN2wzda/eR8STK7FVUtrSBaYugIbRXByrPSTQLB+DGgZXhEwzgAx3FMjsBJes4c0XBdiiaocXzslwhn6rk5Wghmze8w2AHbIBLuly/lFz1b4uEY13LNpfa3FlUtTTBjjLWC6QUceQtKBKBEMDU3y0Fwcs/SjC0/KjkdCQtmBQRea9RGlgYv9yxpF0GV+Ig0EcySUt4bvEsPggHaldIkhB9KqlKEdqnFQkMPNBFMaTbskZ4Ew1ysZCWJqoTIloJY4gT9SFQVjCaoPUze1oJgegkaTaRzYG8tcDDvYu4SBcbEWvMaVX89M23bNCkfwYdLaCKYESCwepqLEdxTra5WoRAJwmDDB3EVkM8IgGsQDiLJLQhw7VHbMagumFutLNWGd+lJMIxlqkWkkqTHcxUCwSGuS5UT/6VV50hUFQyOK+m1e4AMzZjTIOlNMFQOgj2dHyKOOHaEkqvyqj65OSbPOXJ1gaqCwdixFSCT4SCyVo89MWPVihBjJKAEYult8YIKEasJ40sFMFVxBG0Y7xl9JHh3zvX2zrWpKhicJ2GQreS43vtiBV6sKARXj8HDuBTwmqCzT8AjfjauwQ9RGBzDJ0oQul5wvqeK2opqgiH7RVGQ6eQAtQI9w3hpefTbBWLvNdsS3BonQY9tGS8iwQ/sSwyIhPdS28Y7sS/RAPfwTHNjwaiM8zcNMPZjxupdMMrWChwFoDkWN41SAopsFTOY2FuFAcbLOBE+gjHHo1mU0j8TdIhFn3uHsSJ+xspfczyaCUZtGhm711WyKaiUjHkPFdFsj72+AC0zm+NhwSzAc5jjYsEYU4AFY0wBFowxBVgwxhRgwRhTgAVjTAEWjDEFWDDGFGDBGFOABWNMARaMMQVYMMYUYMEYM5vT6Q8obu5S3pcy8AAAAABJRU5ErkJggg==
• C) data:image/png;base64,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
• D) data:image/png;base64,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

The volume of the solid generated by the region enclosed between y = \sqrt x x=1 , x=3 and x-axis is resvolved by y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) V = \int\limits_1^3 {2\pi x\sqrt x dx}
• B) V = \int\limits_1^x {2\pi x\sqrt x dx}
• C) V = \int\limits_1^3 {2\pi {x^{\frac{3}{2}}}dx}
• D) Both b and c

Integral of (1-2x) from [0,1] is ……….

• A) 0
• B) 3
• C) 2
• D) 1

The volume of the solid generated by the region enclosed between y = \sqrt x x=1 , x=4 and x-axis is revolved about y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) \frac{{114\pi }}{5}
• B) \frac{{124\pi }}{5}
• C) 77.91
• D) Both a and c

If integral of ‘f(x)’ from [-1,2] = 4 and integral of ‘g(x)’ from [-1,2] = 8 ,then integral of (2f(x) +3g(x)) from [-1,2] =……..

• A) 38
• B) 36
• C) 32
• D) 30

Arc length of the curve y=10 from x=0 to x=2 is _____.

• A) 8
• B) 4
• C) $\sqrt[2]{2}$
• D) 2

The volume of the solid generated by the region enclosed between $y = \sqrt x $ x=1 , x=3 and x-axis is resvolved by y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.

• A) Both b and c
• B) $V = \int\limits_1^x {2\pi x\sqrt x dx} $
• C) $V = \int\limits_1^3 {2\pi x\sqrt x dx} $
• D) $V = \int\limits_1^3 {2\pi {x^{\frac{3}{2}}}dx} $

\[ Area\,\,between\,\,the\,\,x - axis\,\,and\,\,the\,\,curve\,\,y = \,\cos x;\,\,when\,\,0 \leqslant x \leqslant 2\pi \,\,is\, \]

• A) \[ \,4 \]
• B) \[ \,0\, \]
• C) \[ \,2 \]
• D) \[ None\,\,of\,\,these \]

Arc length of the smooth curve x=g(y) for y=a to y=b is…………………

• A) L = \int\limits_a^b {\sqrt {1 + (\frac{{dy}} {{dx}})^2 } } dx
• B) L = \int\limits_a^b {\sqrt {1 + (\frac{{dx}} {{dy}})^2 } } dy
• C)
• D)

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• A) data:image/png;base64,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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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

If f is a smooth function on [a, b] then arc length of the curve y=f(x) from x=a to x=b is ……………

• A) L = \int\limits_a^b {\sqrt {1 + \frac{{dy}} {{dx}}} } dx
• B) L = \int\limits_a^b {\sqrt {1 + (\frac{{dy}} {{dx}})^2 } } dx
• C)
• D)

Area\,\,lying\,\,between\,\,the\,\,parabola\,\,y^2 = \,\,4ax\,\,and\,\,its\,\,latus\,\,rectum\,\,is\,

• A) None\,\,of\,\,these
• B) \frac{8} {3}a^2
• C) \frac{4} {3}a
• D) \,\frac{8} {3}a\,

If the radii of the top and bottom circles of a frustum are 6 cm and 3 cm respectively, and the slant height is 10 cm, what is the lateral surface area?

• A) 90π cm²
• B) 30π cm²
• C) 60π cm²
• D) 120π cm²

Arc length of the curve y=1 from x=a to x=b is ............

• A) b-a
• B) a-b
• C) 0
• D) 2(b-a)

The\,\,area\,\,bounded\,\,by\,\,the\,\,parabola\,\,y^2 \,\, = \,\,x\,,\,\,straight\,line\,\,y = 4\,\,and\,\,y - axis\,\,is

• A) 7\sqrt 2 \,
• B) \frac{{16}} {3}
• C) None\,\,of\,\,these
• D) \frac{{64}} {3}

If integral of ‘f(x)’ from [3,4] = - 8 ,then integral of ‘f(x)’ from [4,3] is …………

• A) 9
• B) -6
• C) -8
• D) 8

{\text{Length of the curve y = sin(x) from x = 0 to x = }}\pi {\text{ is }}.........

• A) \int\limits_0^\pi {\sqrt {\cos x} } dx
• B) \int\limits_0^\pi {\sqrt {1 + \cos x} } dx
• C) None of these.
• D) \int\limits_0^\pi {\sqrt {1 + \cos ^2 x} } dx