Turito Academy

Test Prep

Global form fields

Two curves are symmetrical about both axes and intersect in four points, so, the circle through their points of intersection will have centre at origin. Solving <img src="data:image/png;base64,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" class="Wirisformula" alt="x to the power of 2 end exponent minus y to the power of 2 end exponent" width="53" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/> = 0 and <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction" width="71" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/>= 1, we get <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAATCAYAAAAwE0VbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAUJJREFUeNpjYCAd/IfiX0B8FIhVGAYG0MQdTECcBcTnGAYW0MQdPxgGB6CaO+yB+OAg8BDV3CEJTctKA+whqrlDDYi3QA0cSEA1d4AM2AbEfIMghgi6IxmIO7CIN0PlYABkkAaNHTwXiMOxiBcAcSup7gAVi+JI/EQgnoKjfkDGhOoSfBgbiAfiLjQxLiC+BcTCpLrDA4j7oGwXIN47QEnLC4hXoYnVA3EtuQbuhhaRF5BChd4AZO8VJL4oEN8FYg5yDSyANj30qNiUITX5gcA3JHYf1F1kAWsgXgM1JHKAS7fD0LpHCRpLTOQYAtK8CZoheYD4zAAmPxBYCMR+QLwUiGPJMUAUWkQie8IHiBcPoKcKoEX7JXI0swHxOiCWxiK3HFoiDgQIgOY5P4ZhBECeOc4wzAAoO1gOJw/pQBuqZAEA5QxVRQ//fbwAAACLdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPj08L21vPjxtc3VwPjxtaT55PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbWF0aD4chRp5AAAAAElFTkSuQmCC" class="Wirisformula" alt="x to the power of 2 end exponent equals y to the power of 2 end exponent" width="53" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»=«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/> = <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD4AAAArCAYAAAAg2jtsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAd1JREFUeNrtWbFKA0EQPSzESrCwEAtBRMQfELGwsbKQtJZpLW0sQpBgb2FnJRYiiFiJnUgKWxFLwVIk2ImEIEKcgSeEZU3ulrlxNtkHD+4WbnZmd2Z2j5dlcaELfhHviQuj5uwYcYf4EMNuleFsJ6Z0lXJ2ndiMJeh+zraRFXkwg7KZjyHofs5y3T/ltLNIvIY98xjkbIV4nnPxboiTFhpWg9hC134kzgU4u0+swdYb+sCdZ6HYzpKFneRdPCJOYREusHtFneXvXoh7PbYOPVnQ9VAd23C4F6fEzQBnn4nLzhhnyIfFuuVUXHXGmp5Uz1Mubc/4hNXA3eOHnz8D7KxgEV3wot5aDPzdeV8LvJVxyZx4xneJdYuBvyIdf8FOXgbY4eZYdcbGca6bPKsPiMdIca7rM3TworhCc9vA+yzGqpYvJjV09jp2v+U5zgaBv9lC8N+4C1SyyDCdJSQkJBhDd0SYkJCQEG2DLl1psSrpqCktViWdztBNlANqSkvZE5lUWsqeyKTSEjpRkeujqtIipZJIBK6qtEipJBKBqyktkiqJROBqSouUSlL0t/evklNTWqRUEokdV1VapFQSicBVlRYplUQicFWlRUolkQhcXWmRUEkk8O9Ky1CpJD9AwOnsDpY8TAAAAPZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1zdXA+PG1pPmE8L21pPjxtbj4yPC9tbj48L21zdXA+PG1zdXA+PG1pPmI8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93Pjxtcm93Pjxtc3VwPjxtaT5hPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bWk+YjwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZnJhYz48L21hdGg+8B+kSAAAAABJRU5ErkJggg==" class="Wirisformula" alt="fraction numerator a to the power of 2 end exponent b to the power of 2 end exponent over denominator a to the power of 2 end exponent plus b to the power of 2 end exponent end fraction" width="62" height="43" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/> Therefore radius of circle =<img src="data:image/png;base64,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" class="Wirisformula" alt="square root of fraction numerator 2 a to the power of 2 end exponent b to the power of 2 end exponent over denominator a to the power of 2 end exponent plus b to the power of 2 end exponent end fraction end root" width="78" height="51" style="vertical-align:-20px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msqrt»«mfrac»«mrow»«mn»2«/mn»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/msqrt»«/math»'/> = <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator square root of 2 a b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction" width="78" height="50" style="vertical-align:-23px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msqrt»«mn»2«/mn»«/msqrt»«mi»a«/mi»«mi»b«/mi»«/mrow»«mrow»«msqrt»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/msqrt»«/mrow»«/mfrac»«/math»'/>

The radius of the circle passing through the points of intersection of ellipse <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction" width="71" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/> = 1 and x2 – y2 = 0 is -

Solution for the question - the radius of the circle passing through the points of intersection ofellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 and x2  y2 = 0 is

The radius of the circle passing through the points of intersec-Turito

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If  <img src="data:image/png;base64,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" class="Wirisformula" alt="alpha comma beta" width="28" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mi»§#946;«/mi»«/math»'/> are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -

Solution for the question - if alpha,beta are the eccentric angles of the extremities of a focalchord of an ellipse, then the eccentricity of the ellipse is - (sin alpha+sin beta)/(sin(alpha+beta))

If alpha,beta are the eccentric angles of the extremities o-Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="ϕ" width="13" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#981;«/mi»«/math»'/> is the angle between the diameter through any point on a standard ellipse and the normal at the point, then the greatest value of tan <img src="data:image/png;base64,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" class="Wirisformula" alt="ϕ" width="13" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»ϕ«/mi»«/math»'/> is–

Solution for the question - if phi is the angle between the diameter through any point on a standardellipse and the normal at the point, then the greatest value

If phi is the angle between the diameter through any point on-Turito

when source is fixed and observer is moving towards it <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAAhCAYAAAAiaX7MAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAVrfl2dQAAAdJJREFUeNrtms8rBGEYx98kSVIOc5DkJrlKkvwD2x7c5CS5ODooB22SlBzl4ujgIjlIcpHk5KLNaXN32LYkyUFqfad9NONtZOZ93xmzu99PfQ4zl9n9PtP7ax6l2ou6Ik7phbvwCX7AU9jvuBAdcBNW5RllOMzofxbhHm7DPtgFV2HRcSHO4Z4U2C/KMZxl/AE7ElCaQ9O8BB/mEBYYfzBc1GIOQ9/B/2UU13BKu3fDoSlgAt5mMFm/S9HDL8Ab4w8oyMScdiFq2vW0zEtEGIeVDArhr8a6Q9cleJL3cEbgpfbD06QsK6ZOWTWtyBvrshBb8ECGJH9eOIIXeS6CJ5OYl+Ezh+SZn/ABLqX0nHVZOZXkJavmdfnqr9/P4FibDIueIu3FBlzT7hWbYZJqtWyjtvADsoKwxXRj1SokyvYRDkbMA698oa2Jne1vO8ce+PLPf6Kec+Mcy8TOdlLOV3T885YrDk1WJMp2TjVOF3WWZXNDzEmU7QLcjxjD+DHEnkTZzmjHFKNyvcgcjYdh42z9Lf2zanwWvFP8COKqEMyWEEKaA9M2HOK4CKZtOMQhNm04xBFJ23BISti24RBH2LbhEEfYtuEQh9i04RCHZNWGY8QXKP2r7dCVjQ8AAADGdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDNDNTs8L21pPjxtaT4mI3hCNDs8L21pPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1pPmM8L21pPjxtbz4rPC9tbz48bWk+YTwvbWk+PC9tcm93PjxtaT5jPC9taT48L21mcmFjPjxtbz4uPC9tbz48bWk+JiN4M0M1OzwvbWk+PC9tYXRoPv4eEEEAAAAASUVORK5CYII=" class="Wirisformula" alt="upsilon ´ equals fraction numerator c plus a over denominator c end fraction. upsilon" width="98" height="33" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»υ«/mi»«mi»´«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»c«/mi»«mo»+«/mo»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«mo».«/mo»«mi»υ«/mi»«/math»'/> when source is moving towards observer at rest <img src="data:image/png;base64,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" class="Wirisformula" alt="upsilon &amp;quot; equals fraction numerator c over denominator c minus a end fraction v ´ equals fraction numerator c plus a over denominator c minus a end fraction. upsilon equals c open square brackets fraction numerator 1 plus fraction numerator a over denominator c end fraction over denominator 1 minus fraction numerator a over denominator c end fraction end fraction close square brackets upsilon" width="279" height="60" style="vertical-align:-25px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»υ«/mi»«mo»¨«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»c«/mi»«/mrow»«mrow»«mi»c«/mi»«mo»-«/mo»«mi»a«/mi»«/mrow»«/mfrac»«mi»v«/mi»«mi»´«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»c«/mi»«mo»+«/mo»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«mo»-«/mo»«mi»a«/mi»«/mrow»«/mfrac»«mo».«/mo»«mi»υ«/mi»«mo»=«/mo»«mi»c«/mi»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mfrac»«mrow»«mn»1«/mn»«mo»+«/mo»«mfrac»«mrow»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«/mrow»«mrow»«mn»1«/mn»«mo»-«/mo»«mfrac»«mrow»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«/mrow»«/mfrac»«/mrow»«/mfenced»«mi»υ«/mi»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="equals   c open square brackets 1 plus fraction numerator a over denominator c end fraction close square brackets open square brackets 1 minus fraction numerator a over denominator c end fraction close square brackets to the power of negative 1 end exponent   upsilon almost equal to open square brackets 1 plus fraction numerator 2 a over denominator c end fraction close square brackets upsilon" width="280" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mo» «/mo»«mi»c«/mi»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mn»1«/mn»«mo»+«/mo»«mfrac»«mrow»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«msup»«mrow»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mn»1«/mn»«mo»-«/mo»«mfrac»«mrow»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo» «/mo»«mi»υ«/mi»«mo»≈«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mn»1«/mn»«mo»+«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mi»υ«/mi»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="therefore   capital delta upsilon equals upsilon ´ minus upsilon equals fraction numerator 2 a upsilon over denominator c end fraction equals fraction numerator 2 a over denominator lambda end fraction" width="211" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∴«/mo»«mo» «/mo»«mi»Δ«/mi»«mi»υ«/mi»«mo»=«/mo»«mi»υ«/mi»«mi»´«/mi»«mo»-«/mo»«mi»υ«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»a«/mi»«mi»υ«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«mrow»«mi»λ«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="therefore   a equals lambda fraction numerator capital delta upsilon over denominator 2 end fraction equals fraction numerator 0.5 x 1000 over denominator 2 end fraction equals 250   m s to the power of negative 1 end exponent" width="285" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∴«/mo»«mo» «/mo»«mi»a«/mi»«mo»=«/mo»«mi»λ«/mi»«mfrac»«mrow»«mi»Δ«/mi»«mi»υ«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»0.5«/mn»«mi»x«/mi»«mn»1000«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»250«/mn»«mo» «/mo»«mi»m«/mi»«msup»«mrow»«mi»s«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»'/> = 900 km/hr

A radar operates at wavelength 50.0 cm. If the beat freqency between the transmitted singal and the singal reflected from aircraft (<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAH5JREFUeNpjYMANmIB4LwMJoB6IfwGxOTGKdYD4OFRTMyHFIKecAWI1IDYG4kuENNQCcSUS/zkQq+Bzyhk0sdlAXITPKVpo4n5AfBCXU6qxiLMA8Q8gFibkFGSwAYjjCTkFGaQB8RoYpxrqHHxAEhqJIOcxfADi/0RiNgZSAQDENx9+HtbufQAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4Mzk0OzwvbWk+PC9tYXRoPmeV+VYAAAAASUVORK5CYII=" class="Wirisformula" alt="capital delta" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»Δ«/mi»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAKCAYAAABmBXS+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAGpJREFUeNpjYICAICBeyoAJ9gKxF4yjAsQX0BTYA/FJdF3fgJgJiX8ciF3QFYEE9aBsDyA+iMV6hoVAHAplg6y2xKYoC4i7gDgAiHcz4AAgX6wD4itAbIBLERcQ/wDiTQwEwAcg1mEgBwAA5+gQxmAj9O8AAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnY8L21pPjwvbWF0aD476OiVAAAAAElFTkSuQmCC" class="Wirisformula" alt="v" width="9" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»v«/mi»«/math»'/>) is 1 kHz, then velocity of the aircraft will be

Solution for the question - a radar operates at wavelength 50.0 cm. if the beat freqency between thetransmitted singal and the singal reflected from aircraft (

A radar operates at wavelength 50.0 cm. if the beat freqency be-Turito

The locus of P such that PA2 + PB2 = 10 where A = (2, 0) and B = (4, 0) is

Solution for the question - the locus of p such that pa2 + pb2 = 10 where a = (2, 0) and b = (4, 0) is nonex2 + y2  6x +5 = 0

The locus of p such that pa2 + pb2 = 10 where a = (2, 0) and b -Turito

Let L = 0 is a tangent to ellipse <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent over denominator 9 end fraction" width="64" height="38" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«msup»«mrow»«mo»)«/mo»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»9«/mn»«/mrow»«/mfrac»«/math»'/> + <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator left parenthesis y minus 2 right parenthesis to the power of 2 end exponent over denominator 4 end fraction" width="62" height="38" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»2«/mn»«msup»«mrow»«mo»)«/mo»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«/math»'/> = 1 and S, <img src="data:image/png;base64,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" class="Wirisformula" alt="straight S to the power of straight prime" width="12" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»S«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«/math»'/> be its foci. If length of perpendicular from S on L = 0 is 2 then length of perpendicular from <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAYAAADpPU2iAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAJJJREFUeNpjYCAe2AJxJQnqGbqAWJIUDRmkKGYCYmF0gVYgfgnEv4D4MBD74DOhB4iLgJgFioOAeD8+DV8YSAQPgdiaFA3JUFvKgZiNWE0gTx4E4qdAnEOKbZFA/AGIjwOxKCnhDkoGG0iNrB+kaBAE4se4JEExmwjE0lC+LBBvAeI0XBosgXgd1AmwpBHEQA0AALEbGUuuYmjkAAAAkXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5TPC9taT48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjAzMjs8L21pPjwvbXN1cD48L21hdGg+yy73eAAAAABJRU5ErkJggg==" class="Wirisformula" alt="straight S to the power of straight prime" width="12" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»S«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«/math»'/>  on L = 0 is

Solution for the question - let l = 0 is a tangent to ellipse ((x-1)^(2))/(9) + ((y-2)^(2))/(4) = 1 ands,5 be its foci. if length of perpendicular from s on l =

Let l = 0 is a tangent to ellipse ((x-1)^(2))/(9) + ((y-2)^(2))-Turito

The condition that the line <img src="data:image/png;base64,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" class="Wirisformula" alt="ell" width="12" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#8467;«/mi»«/math»'/>x + my = n may be a normal to the ellipse <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction" width="27" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/>+ <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction" width="27" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/> = 1 is

Solution for the question - the condition that the line in x + my = n may be a normal to the ellipse(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 is none of these

The condition that the line in x + my = n may be a normal to th-Turito

Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (<img src="data:image/png;base64,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" class="Wirisformula" alt="m divided by s to the power of 2 end exponent" width="44" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«mo»/«/mo»«msup»«mrow»«mi»s«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/> ). (g is acceleration due to gravity). Normal reaction (in N) acting on block A. <img src="https://mycourses.turito.com/pluginfile.php/1/question/questiontext/472067/1/944861/Picture150.png" alt="" />

Solution for the question - two blocks a and b of equal masses m kg each are connected by a lightthread, which passes over a massless pulley as shown in the fig

Two blocks a and b of equal masses m kg each are connected by a-Turito

Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (<img src="data:image/png;base64,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" class="Wirisformula" alt="m divided by s to the power of 2 end exponent" width="44" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«mo»/«/mo»«msup»«mrow»«mi»s«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/> ). (g is acceleration due to gravity) Normal reaction (in N) acting on block B is <img src="https://mycourses.turito.com/pluginfile.php/1/question/questiontext/472059/1/944859/Picture121.png" alt="" />

A light inextensible string connects a block of mass m and top of wedge of mass M. The string is parallel to inclined surface and the inclined surface makes an angle <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»θ«/mi»«/math»'/> with horizontal as shown in the figure. All surfaces are smooth. Now a constant horizontal force of minimum magnitude F is applied to wedge towards right such that the normal reaction on block exerted by wedge just becomes zero. The magnitude of acceleration of wedge is <img src="data:image/png;base64,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" 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Solution for the question - a light inextensible string connects a block of mass m and top of wedge ofmass m. the string is parallel to inclined surface and the

A light inextensible string connects a block of mass m and top -Turito

The vector <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAARCAYAAAAL4VbbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAHZJREFUeNpjYECA/3jwKMALkoG4A4t4M1QOA5wDYnEkfiIQT8FlugcQ90HZLkC8l5BzdgOxPRBfAGJhQooLgPgXEOsRUmgNxGugTonEp1AJiDcBMRcQ8wDxGVzOEAXibWiSPkC8GF0hGxCvA2JpLIYsh4YQ6QAAzWsXE43U1c8AAABwdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPng8L21pPjxtbz4tPC9tbz48L21vdmVyPjwvbWF0aD42Ly94AAAAAElFTkSuQmCC" class="Wirisformula" alt="stack x with minus on top" width="11" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mover accent=¨true¨»«mrow»«mi»x«/mi»«/mrow»«mo»-«/mo»«/mover»«/math»'/> which is perpendicular to (2,-3,1) and (1,-2,3) and which satisfies the condition <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAAeCAYAAACrDxUoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA7FJREFUeNrtXNFnm1EUPyIqZkZUxcyMqImp2dtMH6ZMTM3U2ENFHmbUniZm7GFqD1X6MFUxpapq+hBmomb2UlMxM2VmZg9V9gf0pWZmZkZ2jpxYltzv++79vu/eL1nOjx/Jzdfk+H3nO/ecc+8tgFukkVXkLAhsYZY1TosUvXiOvCoyWEcRWRcZ/kUFuSgyOMMCay5AjCH3kRmRwhlI6wPkqEgB8BA5LzKI7kmBot9pkcE5TnEUHGqcRX4UX0gMn5CFYRaghFz3+bzpwyTRr3aZYg1ZHmYHXB92ARJGOSAA/PfYBun9JYlpGPKe4GdkXvxACpGkcp7vIMtCSYL6gV+HWYCf4gNyD5LEb7n/ieOXOKBAHHBAwv8PZMqSLZPQ2pHzjW8KNchLfWBX0zAHN7XF1hRMiwzz4L/QcAK5itxjrvGYM5gUIePQ6tzbQgNa++WO8/tzyLcQvD/Rtl1euAm9PTxTW2wWIVvIuYBC9TXyesf7azzmDC7aMFEq9TMJOVcQcsg30LuDaAZZM/geF22Yps8DVFWMr6ge+tvIJcXFC/xZWJg0oh8hHzh2QJ0pKqxdUfACeSHAFppZnkKr2ewFF41oL/0p3Skqxqf4sx584CevjVvIJxGNM1mKe8ZPuEsHvMTTsA27wuIOeG+jatuS4ddTAd/ltxTXBPP800T/I+SIYpzGDlV/QJFqmV9fiWmuDtqM0IkDnjJcOWCGE+NJS3aFTQn2fPJmsmWCI+RFzQBQsmxzM0QHxLMy30Fe5somjt20utuxUlzdxVE16jhkltODYsB1acd2NXyiWlujd+yEOiDtC33ogJ5pT4W987zGD1Nu+KVr2g4bQehp3nVUhOTZ+cY1p+hdcANK2l9paEQJ/EYMBYjtKfjQYwrOeE3B7T7ZMugdnbzPXxS021lnazj93qYDByzwtHRM8/oodpmAotu+R+GhsuUx54pRdbddhKgK0KKqCMlzXkE3hvpk7yG+Ay2jEHwoqRqh2tZ1wBwn7iabI8iuOQc3cYanXxNbdnzyV5eHkrz0v+GR/292B7gxDv2dxlLDcCtGI++C/7HMekA7IQ4HfBkiH9qOYJcJatx1AAONslywnFRcu8iaQ4IOCJwyVPihH+Go3OguieseOVoN4t1M6ncw/QjsH9sMk+u4sKudL2UDrlHZMsHdis7xaY70kICeqmJvg4sOKqDW4O9KlHPQU7ACg/OvOXIweKfKSNtVsLduLXCEFCf690QKgUuUebqgTRRLIodd/AFIEAtiFbpr3wAAAVl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+eDwvbWk+PG1vPi08L21vPjwvbW92ZXI+PG1vPiYjeDIyQzU7PC9tbz48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+aTwvbWk+PG1vPi08L21vPjwvbW92ZXI+PG1vPis8L21vPjxtbj4yPC9tbj48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+ajwvbWk+PG1vPi08L21vPjwvbW92ZXI+PG1vPi08L21vPjxtbj43PC9tbj48bWk+azwvbWk+PC9tcm93PjwvbWZlbmNlZD48bW8+PTwvbW8+PG1uPjEwPC9tbj48L21hdGg+GQzvgQAAAABJRU5ErkJggg==" class="Wirisformula" alt="stack x with minus on top times open parentheses stack i with minus on top plus 2 stack j with minus on top minus 7 k close parentheses equals 10" width="160" height="30" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mover accent=¨true¨»«mrow»«mi»x«/mi»«/mrow»«mo»-«/mo»«/mover»«mo»⋅«/mo»«mfenced separators=¨|¨»«mrow»«mover accent=¨true¨»«mrow»«mi»i«/mi»«/mrow»«mo»-«/mo»«/mover»«mo»+«/mo»«mn»2«/mn»«mover accent=¨true¨»«mrow»«mi»j«/mi»«/mrow»«mo»-«/mo»«/mover»«mo»-«/mo»«mn»7«/mn»«mi»k«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mn»10«/mn»«/math»'/>

Solution for the question - the vector x which is perpendicular to (2,-3,1) and (1,-2,3) and whichsatisfies the condition bar(x)*( bar(i)+2 bar(j)-7k)=10 7i+5j+k

The vector x which is perpendicular to (2,-3,1) and (1,-2,3) an-Turito

Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is

Solution for the question - let f : r r be a differentiable function satisfying f (x) = f (x y) f (y) " x, y  r and f  (0) = a, f  (2) = b then f  (-2) is (b)/(a) '/>

Let f : r r be a differentiable function satisfying f (x) -Turito

Four identical metal butterflies are hanging from a light string of length <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAANCAYAAACgu+4kAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ9JREFUeNpjYICA/3gwLvANiJkYkAwgBagA8SVkAVINCADi5ZQYUA/E5ZQYsArqChQDfgHxJyDeBsRFQMyDx4BbQCyNTYIFiI2BuBaIbwCxBhY1TNAYIAjcgPggFnFzIN5PrF9/YBGLBOL5xGjWAeK7WMQnAXEauuA6ILaE+g+EPaCag7AYAFLrhS4YCg3ZP0D8DhpNpjhcBpLnYKAWAABXlSXBtkRwTgAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+NTwvbW4+PG1pPmw8L21pPjwvbWF0aD6k6MhDAAAAAElFTkSuQmCC" class="Wirisformula" alt="5 l" width="16" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»5«/mn»«mi»l«/mi»«/math»'/> at equally placed points as shown in the figure . The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle <img src="data:image/png;base64,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" class="Wirisformula" alt="theta subscript 1 end subscript" width="19" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="theta subscript 2 end subscript" width="19" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/math»'/> is given by <img src="data:image/png;base64,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" alt="" />

Solution for the question - four identical metal butterflies are hanging from a light string of length51 at equally placed points as shown in the figure . the e

Four identical metal butterflies are hanging from a light strin-Turito

F - Kx = mb and kx = ma <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/471944/1/944733/Picture170.png" alt="" width="136" height="129" /> Hence m (b – a) = F – 2kx

Initially the spring is undeformed. Now the force 'F' is applied to 'B' as shown in the figure . When the displacement of 'B' w.r.t 'A' is 'x' towards right in some time then the relative acceleration of 'B' w.r.t. 'A' at that moment is: <img src="https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471906/1/944733/Picture147.png" alt="" />

Solution for the question - initially the spring is undeformed. now the force 'f' is applied to 'b' asshown in the figure . when the displacement of 'b' w.r.t '

Initially the spring is undeformed. now the force 'f' is applie-Turito

Initially the block is at rest under action of force 2T upward and mg downwards. When the block is pulled downwards by x, the spring extends by 2x. Hence tension T increases by 2kx. Thus the net unbalanced force on block of mass m is 4kx <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/471932/1/944732/Picture169.png" alt="" width="103" height="108" /> \ acceleration of the block is = m/4kx

Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light &amp; smooth and strings light. <img src="https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471932/1/944732/Picture146.png" alt="" />

Solution for the question - mass m shown in the figure is in equilibrium. if it is displaced further byx and released find its acceleration just after it is rel

Mass m shown in the figure is in equilibrium. if it is displace-Turito

The FBD of blocks is as shown From Newton's second law 4mg – 2T cosq = 4 mA .... (1) and T – mg = ma .... (2) <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/471896/1/944729/Picture168.png" alt="" /> cosq = 5/4 and from constraint we get a = A cosq (3) Solving equation (1), (2) and (3) we get acceleration of block of mass 4m, a = 11/5g

In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses theta equals s i n to the power of negative 1 end exponent invisible function application fraction numerator 3 over denominator 5 end fraction close parentheses" width="103" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«mi»θ«/mi»«mo»=«/mo»«msup»«mrow»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»⁡«/mo»«mfrac»«mrow»«mn»3«/mn»«/mrow»«mrow»«mn»5«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«/math»'/> <img src="https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471896/1/944729/Picture145.png" alt="" />

Solution for the question - in the figure shown, the pulleys and strings are massless. the accelerationof the block of mass 4m just after the system is released