MCQ Bank
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- A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAA+CAYAAADte6/kAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAPRSURBVHhe7ZkB0eIwEEbPABKQgAQs4AALOEABCnCAAQxgAAM4QERvXuf/5nKZtqR/Sumy+2Yy0JKmaV42TcKfJnBJiHdKiHdKiHdKiHdKiHdKiHdKiHdKiHdKiHdKiHdKiHdKiHdKiHfKV4q/3W7NbrdrP4Nuvk785XJp02azCfEDfO1QHxE/jEnxz+ezORwOzWq1atbrdXucE+KHMSke6efzuRWO/C5C/DDmxD8ejzbKh6BD8I6/Xq8/Z4Icc+JPp1MbzX3wO6OA0lBez5gTj0jkBnWYE88wH+LrMSVekznW6UEdpsQzS0d8zNbrMSWeWXqInwZT4jVjtyKejrrf79s9h6VhUnzXTt3SoK5sNC0VU+KPx2MrfumwycQGEp+MTiUdlWUqzzZXZxkUr8mUktC7lrTdbn/Ovh81zm9BBA3LkpBy3rW7x9DOPWgbEt+59yuo01wrlpcRryjL36tIUK+ei1rxXKv3LVEoKVO/OhjmaTdBZyvZe6B+c7XnS/GK+rxxPvF/d634nHetEiiX9qHNSNT7VSTf7/e2E85Fsfi0cfIe3YdEDSXylKIInQpkUAd1aknK65gmCeI7coFRJD0GjZSkrraiHGb8uo5RgWNQvUh65yvvVHOA0eKpsHrz3FCPMR1lCOrPc6RLLQQx1PKp84reFMlXHtqGTlnaJtyD65HINSSeLa2L5HMvmHqV8FK8KiXxPGAa/XMypXjK6WtInlENTp6ufPxOfRBCWaXSgejNnyOVLOgIdJCppcNL8SDxpUO84OG4diiNETk2fx80YhpdKerogmjvez/THuQdGwhck5apTtQFz4v8MR2rhGLxNNSnhnhBPWrFIx1hgudKxSFE92BI5p5dM21kkU9RmUdrH9yLMtN7do0AQF004ox5lZRQLD6v7CeoFY+kfMikvPS5OFbHkCQaPB3pkJyKQFxpUKgzUReVS6JelMt5QLome+SjfB1PQZF4GmPMEP8OeHgaLI3WMWhCRRl5kngt7xS9uoZG1zk+yZNGOb/rXAm0JflpV8rQfdXGyOeYcoE8qvtU8ovELwFF32/FB/8T4p1iTjzDYlCPOfF6Hwd1mBHPEI94TaiCOsyJD6bBlHgtb4J6zIhnzTvlBoZ3zIhnp0y7WsCGDp2B4Z/Pkl2z4B9mxOcTu3TPnZHg0zuL1jAhnrU7EZ/CFqaWdvxO1AflLFa8/pjQkJ6v39M1PZ8hfhyLFa8/Jkhd/4dHxNdh5h2fk77X+R57+OMwK54RQX+Hxqx+PGbFB3WEeKeEeKeEeKeEeKeEeKeEeKeEeJc0zV9hU58DpMes1gAAAABJRU5ErkJggg==
- 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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
Suppose two differentiable functions f(x) and g(x) have the same graph on the interval [a, b]. How their arc lengths are related?
- A) The arc length of g(x) is zero.
- B) The arc length of f(x) is greater.
- C) The arc lengths are equal.
- D) The arc length of g(x) is greater.
If\,f(x)\, = \,x^2 ,\,\,then\,\,\int\limits_0^2 {\pi \,[f(x)} ]^2 \,dx\,\,is\,\, - - - - - - -
- A) \frac{{32\pi }} {5}
- B) \frac{{7\pi }} {5}
- C) \frac{{23\pi }} {5}
- D) \frac{{17\pi }} {5}
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- A) data:image/png;base64,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
- B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAYCAYAAAA1Zem1AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAJHSURBVGhD7ZaNjeIwEEbphWKohVKohEKog1pyeicemhtsgr1enXbtJ40SJ+P5+2J2D9tiCpbQk7CEnoQl9CQsoSdhCT0JT6Evl8t2OByedjweH2/6OZ1O2/l8fqxeud1uf3Nxjdzv939qGQl90ev/gvzvZlICf2fRW/vLFAl2vV4fq34QmVitTQH7ENv7UcIw5JHxWjF/y0yoVX/u2d/DR0IjWg97J7oEufOvCc96Pz7y+9HATzvR+I/QY1do7nu/oh6hESELXfr4PsE/DT9Z6FF6vBXanwqtVqA/0/hHH4W2OKxUtEIwBP2wvMZAATHuY0yJOTFPgULH3vL/CHFfjF3qh72xnj0RS0K7FzNfrh9zztpersiXTzTvPSFcaUQszIK4OvDYSDxxOQbkmuL7/C6iAPlE88yaFU94J+7nGoesv89yTzFfJguNv8R8wjr2Z45WhgjN+1JzeYhZxNLeT4WOcWvUhFZkIE4WKlvto8i1lvJlYu17+YB17N09rXxZaKB4fLBY5HcJ7T6tRqvQPI/1ZkYLvZcPiNeqR4khQguDiPu/S2hxsNlfek50LRaMFnovH+TenVkrTULHAQnv43OG4f7RQmP45uHWhhUHb434xnqj0IB/rDnuHS00vMsH9i7ODKLfHk+h2UQAzQZI7DMayZCYQvWxaPb7zAG5xixYI0/cg8UBszZ2rvXdYPXJ+YhlXKzUb3ze2k9pVjGGvdTy5XgYZD1cG6/Gy4le/E6W0JOwhJ6EJfQkLKEnYQk9CUvoKdi2Pw2UjGnYC1unAAAAAElFTkSuQmCC
- C) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAXCAYAAADdlHeDAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAKzSURBVGhD7ZaLreIwEEXphWKohVKohEKog1qyOk+c1X0jJ9n1orBPmiNZiT2ej8eXiNPSNBO0cJopWjjNFC2cZooWTjPFN+HcbrfldDr9Hufz+WU5lvv9/pX/aK7X63K5XF6z/x96xJ2tsWf/F4a3Q0Iu7xMomqOFg2jI+ZOEs4U9/LhwjmzoUV8cmvp4PF6zn/fF2ePjwjnqIuWIfM/n8ytHC2eOXeGQmLmD5o7Qx08+A9I/xciFuc7IC6vCyX2ScfO/mIJgkGPUuJpbf4WT9uqPXVv2gn3Eyfz6Ol/7z5j57INzBjFzjf3myZ7W3D6lntu4kD7VNmJXOFAvsmKy9HNu4TQ5G8e7Ng/EEzIf7/UrgF82BLt7eHrozFGxyeYERW8sfLNm1nO/52PwznB/roH5sq8V7BmffFWcxDFWxqvnMT9PYN1zgXYwVp51j7cIB6rP6NCjwozN8NCu4ZMxhDj65ADyZoPWWBNO+ua587JyuL+ej7jY8RPm2aNK7RlzfEQRgPUYD7/aK+z6YGNeh+fnfau2yseEY0z21EvU5qiwlheSeGGOtX01J1DLmnDYt/WLfIdwMh9+znky3xJO7Tdg1wf7Vu692iofEU69tDrPfMTJywTi7B3SmMap1JywJRz38xzxDuGAe+ydNbGWsazHeKM+YVc4xMn7qPxJbclfCydVn1QfDpGFjoTjfuOPhAO811isZSO1k9d184zQRs5sbja/1oEtxQHmzfPBrHCIx7Am41RRWH/tYZ0ziGWczM+7Pa+2Pb511Qtx1ItmmEjSxrCBzhVQ7oFcy/f0ZdT4Hq7GdL3mr/Um7sOHOvVhvfZCAYzqG9WyNSf2Gu41H1iPrPUka7am9Kt1sKfGcr/+WUcy/jk2zQ4tnGaKFk4zRQunmaKF00zRwmmmaOE0EyzLL7YhRyXTWTekAAAAAElFTkSuQmCC
- D) data:image/png;base64,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
Arc length of the curve y=4x from x=0 to x=1 is _____
- A) 0
- B) Sqrt(17)
- C) None of the above
- D) Sqrt(10)
\[ The\,\,bounded\,\,region\,\,between\,\,the\,\,parabola\,\,y = 4x^2 \,\,and\,\,the\,\,line\,\,y = 6x - 2 \]
- A) \[ \frac{1} {{12}} \]
- B) \[ \frac{1} {6}\, \]
- C) \[ \frac{1} {3} \]
- D) \[ None\,\,of\,\,these \]
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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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- A) The area is increased.
- B) It doesn't affect the area.
- C) The area is decreased.
- D) The area is undefined.
\[ The\,\,area\,\,bounded\,\,by\,\,the\,\,parabola\,\,y^2 \,\, = \,\,x\,,\,\,straight\,line\,\,y = 4\,\,and\,\,y - axis\,\,is \]
- A) \[ \frac{{64}} {3} \]
- B) \[ \frac{{16}} {3} \]
- C) \[ None\,\,of\,\,these \]
- D) \[ 7\sqrt 2 \, \]
data:image/png;base64,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
- A) data:image/png;base64,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
- B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKQAAAAZCAYAAAC/4YXqAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAQxSURBVHhe7dcNTSVLEAVgLKABC3hAAhqwgAMc4AAFKMAABnCAh3n5svckld7u+bksl+FlTjLZS3d1/Zw61TN7NR04sCMcgjywKxyCPLArHII8sCv8U0G+vb1N9/f30/v7+2llHk9PT9PDw8P08fFxWjnwE9hT3zYJUiLX19fT1dXV9Pj4eFr9g5eXl+n29nb6/Pw8rawDMm5ubhbJeH5+Xk3YXqFW3O0J3923rVjNDjFKQOJ+ewLJEerWooIUNzpvEvknyt+MJUEacgK5FL67b+dglSAFlPiIrLu7uy+LxZRWkf8fsSRIPF6Sgz32bZUgJY3I3jeDtdHeFohh2kYQQ0MDt0k+H5x7fX097fwNA+Ubia2n/V6y75so+3wjWcOCnlisVZv4qXnVIZ4TZGLnqbH8Hvk8F5fq21YsChLhlSjEVCDHeg+aLllnUrhm94hIs0bXv70IUszqMzmMyDXFhMJ3RFNJzN/820cy/1sFyY9Yo7zmBAm9GPhKbmDw5DY3gID7DKHz/NZc5/oWftUCOHG2chYs9W0rFgUJiFZcD22hFciUaAjhR7E9pLAQ36LuZSqrAPnvCTJ+W1R/frd5ybXW1ROLtWqj3tZPjTPKJejFIIzWpzgRSw94cE4N+PeI61ww6htbdnw4Q/jsRv95SU2p8atYJcgIqodRYRUK5GMkRlgqrO4hTUxrGhMCe8jnRu/hbxS3rcvvlgNrbe1qzFlP9Z1YI7QxiKCXmxhzflwebV7s6626pm+49YzECCP+zsWiIDMpo4AKm5tWQMQcgbBUWG8PUQQnvhuhJ8oIcoRR09uGtWIBa9UmDSQY/nIzxbd/53JpY4xyW+LTXh3++JFPsKZvBr3W10NqanM8F4uCXGro0rQiId8yayatklZRi0ZUJRxGt3ia0YoV0cnHfutv6yu7J56vChK2vrITo+bBb2u/1Df1OCP+HBJv1LetWBRk7/qvyA3au50k6WyKQ6QCWoJBI4hqhEpy+w3Jf69xgdie2IvFPiQSH3/8WMt+rTs2cvCopdpEfHIDscSsefvX3+L0IIYztbniJC64HcWtr9+K9EMe/Divh3xXxC6cVMhPXbERCyc927Zv7Of0soRFQSpe0DlIoLWpTYbctC0xgUbMxXE2TYEIwro4c2c1Rly2HrGqKOznFueTb/4qsWz8HRv7rY2BSE7WxfC7zdtaL1/2amn3/a61jgYvSIzkMDpjv82DrfUMRXiZG/bqI3HPxawgQ2htXg8IR1iK2AoTiIhzz38HkPwVYn8CeCTGCkLSwx63e+zbrCBNhwlYA4W3r5s1yAQvif7S+I2ClK+eBRFcK9KKvfVtKMh65a8FAhCy9ozXuFdp79vkp/EbBYl34tI7D8G0r+Qe9tS3xW/IAwcuiUOQB3aFQ5AHdoVDkAd2hUOQB3aFQ5AHdoRp+g+lPoEXFe2UxAAAAABJRU5ErkJggg==
- C) data:image/png;base64,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
- D) data:image/png;base64,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
\[ Evaluate\;\frac{d} {{dx}}\int_2^x t dt \]
- A) \[ x \]
- B) \[ x^3 \]
- C) None of these
- D) \[ x^2 \]
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- A) data:image/png;base64,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
- B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAABFCAYAAACsXs9eAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAASzSURBVHhe7ZqBTeswFEX/AozACIzACmzACmzABEzABizAAizAAt2AIfp1ql7JshzHbl8Tu7pHsiAlsePn42cn5d/RmEAslAnFQplQLJQJxUKZUCyUCcVCmVAslAnFQplQLJQJxUKZUCyUCcVCmVAslAnFQplQLJQJxUKZUCyUCeXuhPr5+Tk+PDycj8zW3JVQh8Ph+Pb2ZqF25K6Eenl5Of79/VmoHZlKKGRRBnp8fDwdi/f399NyB/yd33VstmMqoZDp8/OzmIU4zouF2p5phGJ/RFZqAZnMPkwj1MfHx2mPtMb39/dJqJZzTTzTCIUgSGWWYStAjMjkTKo94jWNUATJQtVhz/j6+nr6XZl6a6YQSpvwr6+v8ydmDfaceyz7UwjFzEMoP7W1wxMxUm3NFEIpfc8klCaBSuu9s2Sl15UKS396nMM7ud/f3/PRtkwhlAI4o1C99/z8/Hz+bR3FJSWVid+3Ziqh0jfjo3OJUJzLUtVKLhR7TI7TsjVTCMVM2yM413CJUPST5b2VUobqhY07dfSIXKMolIKhIrSXofSk5mtRpyOgb+k+hbpvsd+4RChi2pOFI4QC6oh6gl7MUMoKeUAYgKenp02fIKKEoi+8z1KfEIlj6o+mVyhE6p2kkUJFjeeiUApIPmOQqTVIUURmqJxbLae9QpEhEKSHCKE0qaJYFSoNCB1oeXKQALXSkxWYuZGdTmHvkGYGAsykKd0zhftON7/ae2gZ1XFNqNISy3X6vKV+uEQo2lBd9JP6OIbWdms0C6VA7/GkxX3cYlmiT9StgaRvTBgtP/qcz/KAKvg6h8FNzykJxR5UA5SLRmxT1uqHXqH0HxvUQx8pXM+/BImWdmssCqXG1HECnAdhK7iPaKHoH8ElgDn6m2CwS+cxEJxXCnpJKO1TqE9ZARi80qDV6odeoWgzj2Mqj1hrt8aiUKCAUHHLUie4aa6tlR5Bes9fA2Gob2mCkEnUHhLQ/tKmlfMIPnWmlIQSygKqkwEsCQtL9UOvUJybtoNIS9fX2q2xKhSd3WupE9yHBvha6EeebdNsAcxKBgsYgHw5EvyNcynUmcaoJhQwWJqk9K0U31r90CNU6X5KGQvW2q2xKlQtKFvBPUQJRRDTWUqwGFyhY/WZQaNtZjOTS1CHROSafBkrDWAK9dIOWYpBy1mrH3qEUqalD9SHzNobpn1rabdGVSgC2bPU3QI6RSCUMa4hfTGbF0F/U8F0TZpFCD6fKXMxIFzDZwr+mlDUxTWlGLfUDz1CAe1wviaI+qb2W9utURVqBDQwEUJtyZpQQHZYO6dGr1BbYKFuRItQLENpNuzFQl2ABob0PBMtQl2LhbqALQbmFlioQVHQ2CDOhIRSiRRLMVEZiWmEMnMwhVB6jDXjM7xQvDPpebFm9mV4oXiLrLe4wKO23t/wyD3b09+9M7xQiJNuyFkCJRhveMlgZhyGForsU/qeS/C9E4KZcRhOKH0hyU+yz9LjNn/33mo8hhNKX0hS0v8KSEEm9lH8NGMx/B4qJ5cp/6be7Mt0QukJT8Wb8rGYTigzNhbKhGKhTCgWyoRioUwoFsqEYqFMKBbKhGKhTCgWyoRioUwgx+N/tl+v7K8uz00AAAAASUVORK5CYII=
- C) data:image/png;base64,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
- D) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIUAAAA8CAYAAABIH3mBAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAARESURBVHhe7ZnbTewwFEVvA5RACZRAC3RAC3RABVTAD980QAM0MA3QAUUMWtFs3SPbmVcck4P2kqyZPPzKWXEc59/emAJLYSoshamwFKbCUpgKS2EqLIWpsBSmwlKYCkthKiyFqbAUpsJSmIo/JcXn5+f+5ubmsGWu5c9I8fX1tX96erIUHfgzUjw8POy/v78tRQdSSUHQNRrc3t5O2/D8/Dw9OoBj/Ne2uZxUUiDE6+trNSLwv0yW4nrSSMGcgdHhFAhhlpFGipeXl2necIyPj49JilPnmeOkkYJAI4ZZnzRS8OiwFGNIIYUmlu/v74c9Zk1SSKGVSr9RjCGFFJpAZpbi8fFx6sOptAVSSMFcgguWWYr7+/vDv+2TSgqtYGYDmVl4y0IKKVjG3srQeg20n0fgtWhORWIRb22aUqgBJA3ZegNQGnnXskZBnddAOxlp7u7upjJ+49WWR8fS66U+jKAphSZ25cXTMD762b5ECvIydCso+qA2qg/U22M+wbUf9QiafXxw4cohj0aNvstgiRQlBImyRvWDtZUedfH2wsfAERyVInaGO+sc48lD3lPpEqj3nI9h58Azmfqj8JqzzKW3t7epfv5rCCdAcRt2u93h33+4keL++BhjPyluC66jzqUM/sfjyEYexQTZuXlie67lLCmosGzUSGgLHe4BdxxJEFyERxLt12gSJ3X0nSDobtVNwrnKS57ysVQGifPJF+sqry2SUpfK0rYgD/ui4FyfXvGZlYKGSwoaEEeN0fSSgj4okCX0UQHnLmzdcVx02kI5tEflSB7yROE4vzUPkAgcK4OpOqJc1BfLjdAfUi8hYFYKGktjdEecC3no1Kl0CZy/VAoCTRBaQgB9VCA4rxVMUP/KEQGog2OSBMnY14L8nEt5EbZLIRGiPE8gc48bJnJUCiosh7bfYKkUBCbmpz/xImsYFvS5FUzyUQ7BLucAgv1cN+DcloTs4xh1cH6si/1lW+ck5Bgyx0dLD45K0TL5N1gihS5cDA59iv3ifyxfQSC4yleWw92LPGXQKYsgIVprhOV89ksoBKM+bTNCqVzaoOOUV7aHNkto5hXUrVFqCbNSUEGrU6PhItDpGMRLoA/kL5PK4yISRM0ngDzxDiYA5GGfgkfgtC9Ce9lHwDRiRDhGPpWNBGoTZZMom/PURtrDvlg35UsQBI1lLmVWiq0w9+zdMgp0a8jPgKVYAY0+WUkjRVxsMuuSRoqsQ3FGNi8Fjw2k0CTLrE8aKcw4UkjBK5gZx+al4H18bt3frMPmpWDhRgtLLNYwcmgBKNNraiY2L0WcZPIGolGDV1TPNdZh01IQ+LmldhaI4vcK04/NScEjgoklvwR9bn2CpeQeH39Mzeak4FHBnIE094GHD01et1iPzc8pSqIQra+QZjmppGDkYHIZk+lPupHCrI+lMBWWwlRYClNhKUyFpTAVlsIU7Pc/7l/VB6bmjJUAAAAASUVORK5CYII=
Which mathematician introduced the concept of arc length and formulated the integral for its calculation?
- A) Archimedes
- B) Isaac Newton
- C) Pierre-Simon Laplace
- D) Euclid
Arc length of the curve y=7 from x=0 to x=1 is _____.
- A) 2
- B) -2
- C) 1
- D) -1
The volume of solid obtained when the region under the curve y = {x^3} over the interval [1,3] is revolved about the x-axis is
- A) V = \int\limits_1^3 {\pi {x^3}dy}
- B) V = \int\limits_1^3 {{x^6}dx}
- C) V = \int\limits_1^3 {\pi {x^3}dx}
- D) V = \int\limits_1^3 {\pi {x^6}dx}
Arc length of the curve y=x from x=0 to x=2 is _____.
- A) \int\limits_0^2 {\sqrt {1 + {{[\frac{d}{{dx}}(x)]}^2}} } dx
- B) \int\limits_0^2 {\sqrt {1 + {{[1]}^2}} } dx
- C) \int\limits_0^2 {\sqrt {1 + {{[\frac{{dy}}{{dx}}]}^2}} } dx
- D) All of the above
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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,iVBORw0KGgoAAAANSUhEUgAAAX0AAAAdCAYAAABG+ry/AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAcoSURBVHhe7ZiJbVw5EAWVi4NxLA7FkTgQx+FYtFuLLeH5mZw/Y0Ow5v8ugBgezT45rePldRiGYbgM0/SHYRguxDT9YRiGCzFNfxiG4UJM0x+GYbgQ0/SHYRguxDT9YRiGCzFNfxiG4UK8Nf1v3769vry83Bzfv3//T5Y58mfm8+fPb3E/EuvXr19fP3369P/q+fnx48dbHhjD34X3dasO1svv6vB7kL/OI9/rL1++/L96Xt5eD4+JIR0g8/zBcOamT6zmgvm9Tdwv5JmaPvHQSJznGxk+FvkDepr+72PDP2sef2r6STd9HpSNnmT8zabPb+HvyZ8UmzyepelT46NYyNOZfhC899t6D9Lns/6mTy/yl48VnGW/+lNs/L+bx4/8jrZ/J3bTT/5m03/vpvqnX5ozNf17YuH8LE2fN03tn4mu0Rmbvg34VtOnyX6Upo8fp236nDPvgvjwHLcSZ9NIWRPuMIFpj2GzecQeYFPZLE764dg9NO4p0zrQnz5lHnexQTad1Tl0DhySMWQzWNG+5A/yzBGj/YA8Z5ir9PEoPnOT9hLW3EOP51mTW7VH571vq2uf9syLPmY9Weddfcv7KZ9knrBhfhj65Z615E7OlWfgh/kgzvRhh/IZg2RNOJf0ibk5dz9rYhySdoxD8owBmRNG64P0k9H+9P6OlNeXvOO+mH8+GZA5Z6ATco8h99SLM/eVlcx1n+3YvgYSaSCNBgwIWZOBE1lME8l+k8VKUp8BGwz7qf8Re4CsfgOy+ZBM4q3kIW9ulFenj0Wf9Ed2sSnn6HNQt+BHxs65uoHzjC1Rt2g/c4Ou1L8i4wHykjo4dw/9Dsg968VcfZ4xzAH69OlW7dn3bsK++ju/3k9YZzxZe/WnD4CMOgGZzFGC7ry/en/a47PtdY28nzqYZwySsv1O0Mk5KKcO7aWv5o7hOfusjZ3PzEO+z46DuXGrR39WZF2g84p+fV2h/4K+lGfO0H/2tdd32c989lo9mX9G2ko7rI0dXZn/jFE/buUJfn7hQSa9QTEGJBNucnukfIIdA2wMgmFCkF0Vs8fKHnt5F0yq+i2E60b5He2f8l2IVWzuSfvSj6flsavOHCvQ03nPBwUdywrOU8/KvjqO4oOVPu6J+eQTOeY9lG9dib4wdvmH1Af51qHPjalH1i3pHLjWBuvUf1Sje3KarOSZs9dDn5iv9K3yl/7ymfocwGf6kOgPvu7oumAr8wbI7OrQ8tpMn1gb9+pc8GNlx1ynnqN6oWdXO/bVl6PjbtYd4V8wnElMWnEmnM+dkysyQPHxoKuTgix35BF7fRfUbzyrIiT6tqNt+DjQC7dia9193rrQkY8rz45Y5Z112l/lq0k9+rvjKD5ovzi3NpB3jmq/ivGR/EPbz7cOfY6uo5w1qRN/0w/WWVPkUj/nub4np8lKHvv5rhp0cYeRtlf5S/84y1hk5UPC/u6uHNUFOndJy2szfWKdecQme4y0zTzzZ3zaznqsYs/znDfY2Z3dYvsNxVgGkuBkJqgf7a0H03RQnYReI8sdecQesujKx3Nkr2G/dSTtX8of2eovzcoX8syeI8FuP/QdyHbeVrnN9QrOkZP2N7knvpW+1ZeRu8jdqn3rejT/0PbzrUOfq5PPe0m76lZv+g+c36pRxwSdh2Qlb46P0G9rkHEI/nqOH5mrhHu7M/25ldNVXXIN6UuDfOZIm5mXlhH05lnb6fzn+qheHVeCzC6eW2wri+GdMZzMAqVjBpFBEtCuoJ0Q7yvPZyYFWe44f9Qest4H7mXiVkVouJ86wPjTP0AP+tB7FJtraV84zzgbzrQluxpqK/Xht75Bx7KCc+TwkYG9jAH04Sg+UJ9wnvV55K21rkfy773Ujxxrhj4wV5/gY+dtVwdRp7Vj3v6D+8K5a+b35DRZyQN3Mu9gDGmf2JUzf+ajdeMDa2MEdfK5OzPvnO3i8F0gg31tZW3Sl6btu847zLXPnv4Bc8+YmxP2yJey6E89rtOvrFfnFDjjXusC9KTsil+avkZymAiNOAzItYFiOOX68UjKdAJz3zm+pW79utee7GSJJ8/ycTcZNwPSV0bnEj93sbW+vsu6/XOgR1Y+7FjZkPYnH1aivcwj87xL3O37ynaujcm5+13bXe1zb5efnGM/3zd6If1GN4N7q+9C0vnzre5QtxhX3kt/fZsZ/705lc4d8kmeMST9yH3tdV6TvpvnfWYNYCWfWCfzAv3mUt8K8q+svnjHfQZ62U9/s3bmgdFr/NNOv5GUY6C/7zPyrXUN049eyy9Nf/i4UPxV8+iGcyZ4uMQ9fHxsTsPHZir0JPibZTd91v5GcEam6T8P0/Sfg6nQE+GXKkf+OXsm/CHnOPNfM2eg/5Wy+ot0+BhM0x+GYbgQ0/SHYRguxDT9YRiGCzFNfxiG4UJM0x+GYbgQ0/SHYRguxDT9YRiGy/D6+g8Oy3oICd+MNQAAAABJRU5ErkJggg==
The volume of the solid generated by the region enclosed between $y = \sqrt x $ x=0 , x=1 and x-axis is revolved about y-axis.Which of the following equation gives the volume of solid by cylindrical shell ____.
- A) $\frac{{12\pi }}{5}$
- B) None of the above
- C) $\frac{{4\pi }}{5}$
- D) $\frac{{124\pi }}{5}$
The volume V of a cylinder with base area A and height h is calculated by ---------.
- A) V = A h^3
- B) V = A h
- C) V = 2A h
- D) V = A h^2
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) Both a and c
- C) 77.91
- D) \[\frac{{124\pi }}{5}\]