Maths-
General
Easy
Question
In a
as shown in figure given that
, then the value of
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/852998/1/912662/Picture2.png)
- None of these
The correct answer is: ![fraction numerator pi over denominator 4 end fraction](data:image/png;base64,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)
null
![equals fraction numerator fraction numerator y over denominator z end fraction plus fraction numerator x over denominator z end fraction over denominator 1 minus fraction numerator y over denominator z end fraction cross times fraction numerator x over denominator z end fraction end fraction](data:image/png;base64,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)
![equals fraction numerator fraction numerator 3 over denominator 6 end fraction plus fraction numerator 2 over denominator 6 end fraction over denominator 1 minus fraction numerator 3 over denominator 6 end fraction cross times fraction numerator 2 over denominator 6 end fraction end fraction equals 1](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/852998/1/912662/Picture4.png)
![rightwards double arrow blank alpha plus beta equals angle Q P R equals fraction numerator pi over denominator 4 end fraction](data:image/png;base64,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)
Related Questions to study
physics-
A bob of mass M is suspended by a massless string of length L. The horizontal velocity
at position A is just sufficient to make it reach the point B. The angle
at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
A bob of mass M is suspended by a massless string of length L. The horizontal velocity
at position A is just sufficient to make it reach the point B. The angle
at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486040/1/912428/Picture514.png)
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486040/1/912428/Picture514.png)
physics-General
physics-
A bob of mass
is suspended by a massless string of length
. The horizontal velocity
at position
is just sufficient to make it reach the point
. The angle
at which the speed of the bob is half of that at
, satisfies
![](data:image/png;base64,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)
A bob of mass
is suspended by a massless string of length
. The horizontal velocity
at position
is just sufficient to make it reach the point
. The angle
at which the speed of the bob is half of that at
, satisfies
![](data:image/png;base64,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)
physics-General
physics-
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486038/1/912395/Picture512.png)
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486038/1/912395/Picture512.png)
physics-General
Physics-
Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905880/1/912384/Picture507.png)
Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905880/1/912384/Picture507.png)
Physics-General
physics-
A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
![](data:image/png;base64,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)
A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
![](data:image/png;base64,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)
physics-General
physics-
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486034/1/912281/Picture490.png)
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486034/1/912281/Picture490.png)
physics-General
Physics-
A particle is moving on a circular path of radius
with uniform velocity
. The change in velocity when the particle moves from
to
is![blank left parenthesis angle P O Q equals 40 degree right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAAQCAYAAADzhpp3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAx5JREFUeNrtWV9km1EU/8RETY2YPsxUmZrZQ4SaqthDmZiZmTG1h5kZMRGzhzIztYcpFXuoPYyYqKopFbOHqlE1MxFlD1M1s5eZPUyNqamIGNm5/MJ1du93z/flJhP640fy5ST3nvu758+9CQI3CsSF4BD/AwtYfzHSxLqnwS8err8zMA6Iv5lINegggjLOeJjMM+Iqe9YktkE10TXitGXTVIh7cGaZeDZkrBzxDbGBMd5bftc3LsMXE44RnxO3wTKe6VC+jRJP4XUHE/DBiQwE6wZqUhvEL8Qx7fk48aP2Pkm8QPzKxJgjviaeIybAq8RvxElLCuH2VyB2todiDRM/hQi2hXno4m4xmwOsyxgTLIBgE65JlIjFLpwYhRNqYin2mVr0l4bv3CHO4vUj7EQTppngCvcc9vUeClbG3E2CXUeG4Vgk3tDe54n7ECtv8M3ZR6i0cj6mA1ns6gp2OcdjTRgeIWqTnCZ+tnxXTyEpbXPsOuz3Ecm+kdWixSRYFWnatImqwjGmDBFpXJA4Dt5E7ZgNsVljKUJhBKnzOPGpILo3tQ01L7Q31eO2gDao9dnR0r3J9pdlHZPY1BIkDWnyH/yJ2YY2DGJwKGFOsMJa05qDXVbzTPiuFW6Jvap7R3vQdheZ+FHWsRVhrJZPwYZR7H8IimMCv93G7lNCPdEETED0MBxBiotj7wtpQ1MWVbCmT8GkKfEkGoAdFjU2qO7ubZfhrwr5iiaGy/4ajgOBx5S4ja7OJdieZR2HfKfETUErPIlBNxBlEqjOaMkRgS1HA1FjbX1DYJ/xHGFSkauWS4Oc76bD1dbPIKQXYxyi8w6bdeJty2cPDe37ssO+1KfbirYlul8Yni+xtj4MRYkPYQfnOUyuEMOpV8RLDptxtPW3kPI681mxnLXOoAnR7dOwn+/j9ZItfaoScB9zS+KM+S7C74oOzgEOm/wea1WY9ztcN7S5Q8KDdwX2P3HQnhLUxqZ27VUI+gubYCn40kT6LkcoIeKrqc4urQeDiRl0rR9wCzEyoH5EuvxVuBsM7t8rahc/wBVZbgDnX+L1/i98NeQJ0OsyBwAAALV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4QTA7PC9taT48bW8+KDwvbW8+PG1pPiYjeDIyMjA7PC9taT48bWk+UDwvbWk+PG1pPk88L21pPjxtaT5RPC9taT48bW8+PTwvbW8+PG1uPjQwPC9tbj48bW8+JiN4QjA7PC9tbz48bW8+KTwvbW8+PC9tYXRoPq760RIAAAAASUVORK5CYII=)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905851/1/912216/Picture489.png)
A particle is moving on a circular path of radius
with uniform velocity
. The change in velocity when the particle moves from
to
is![blank left parenthesis angle P O Q equals 40 degree right parenthesis](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905851/1/912216/Picture489.png)
Physics-General
Physics-
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905855/1/912209/Picture487.png)
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905855/1/912209/Picture487.png)
Physics-General
physics-
A string of length
is fixed at one end and carries a mass
at the other end. The string makes
revolutions per
around the vertical axis through the fixed end as shown in figure , then tension in the string is![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486030/1/912200/Picture486.png)
A string of length
is fixed at one end and carries a mass
at the other end. The string makes
revolutions per
around the vertical axis through the fixed end as shown in figure , then tension in the string is![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486030/1/912200/Picture486.png)
physics-General
physics-
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
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b9qL8Xf8S4+jBBwsZ17cQEuBUlYDkEsjABdXmiYfGf+wew2yh9t++2C772bmNan7mTd7bHgwuYeI3lY84V+Wb0IIyZIfdF7niQbfHeF9qAyPFz0M86Z+X/4w0tcaKOX5d/KvDp+Tz04cQ9ytXtMjmqKRi/U9wsU4M9WlWb4gXUWxUcoj1Vtjg1E1RJ346JIJxacRZtUAqdurqngNFz1mYwsEFwwPmichcwDN/wwaoA2jn/vW8ZzlxnXVJIar5GfuN9piuPMIOBHROOZlYJFGzqlHbBmN+25TiElOGUVhTFohViYXXe/QBaGDCVGzweozZk6jQ2/h34FCPJRh10P0btV7D4SeFtqn4FfNT8QD5iUhzEdI5eU+NT5251+0Y9AfSJtfVkaQVdvamzDUGP2XR/PBsrX7YXwLPUGpsVepZGwQ/S6bTye6hraUuaLrB26mJV+ZfR5MeChHbNx3OM1EcsS6ZYiZiJVn4sSrZ+9iRf48QKzFIXZXtxUTVDxhkqxin5NL23h18krRoEa1U+ip39GKMGQf62AMEVrRqE9/RIx9HZw/M/RLrUxd9Mq8MG30eytMvwuuwSq2Ufol01I91OR3IBriMs5PI+Q0tj6+ayh+dnt08aahhpEH0praqZZoZg2JPbyT7ZxY0L2lzrX8zZj5WujYHbQibIWJ1POxD+TN8jkMeJ2z/PQ9MThpMEbWupfTES0KfqXuCJbEOwC0rafgZaoCRLZUU1XJg6TdY+ldc2PD+W07+yWziJqCSUnaxik8QSsvf62QAGm0gjfudywQ3oTgtGbjjjPJlpd9kznPzq6MAlP3Qxin3iwRCGddgwYroypvmpaxBaZKfooUmGzddhiCfM6Td7WP1SaHE9SvHilFGPQ/SQqMyQ6Jb8U+qKkI7GVo5CjSKt/jF9eby4g9NxF+AXwI1unHBhWo14fH5JHlM+vDHm2SJ4Tu5040T4+/7Rj+3yRXsDZv/LQ6836bOfV0Y1+ZrIbwfDng1NLJPbfbfUlZFE0doHmsL2FhQYwQ6uF9Df47YfK4vrsYRTHfdOe+05tYAwGewqL57bTSO57m4vleEMTfUytr28AuAy0X9WrN8JNggtdIWIWkttj/QhuO/HgrFsb39nuls/ujOvioyi9aufn0HHiJG7xUZwb5RXlu7/SHTwW+LI7zVThs3KauYLGjIdB/SywVENp3txX7Y/wA+EPRlJ/w1UfiwXjYK+i8T1jyE5GKMvqsU5aSL7MmG0l03o4DpVieMUbqs64NsxT4Q6x8b7scAY8MR1NLRbCXHOXWEe03lbsKE4ntuLcpswIVC49XkvuKRCMOr3uR+B9o/hrNjZwEzYPulhqlT5Hb5LQE8AUidLLdDfUjyPWkY2YxK/oyVIVL4EpUtld99y6Kwg8BCFypLEjqirfo2uhlMW7RUjdjka670CVvinKSi/DIhPgG1p3q5j953vrreeBhPTRDB9pLJdagatFCNQhiSMiYTGI0+wFEtboTfIi2WFx3wNgtg5scQpVBUJru4RLDGtKVGVSt/Z1Rbh6mBjivqoNUsomgcp42JP8TW87/E1Jva5tiEvs4OTLBjpbAFI6UZLPLizL2kNDqFcWneGB/edeHD6za10Zwpf9Gfe/OBZGADd5efMU/vY1liT43f5NJErzk9SSD7dVTetuGFN7NuxfJ/nyVUorSUITSgrokJTQra74nhQodB7FAYXucvu/GBbZ1C41u6gUOj4uxReADwL91rjxVSb3AXUDnt/y5h8486s1q4aQW583l6s8wQvSxqdHZcwmrZjzKN4r6CkO3T9030gvEgPaX1TARWJX75Vm6NTjT4Vt5wDz1SG09+3j8z3/eCZT0TOqkN95r8Dp1+Z+1Wl8i8C/j9UXMgyF5fAM/dmTgf/nfUZ/rfM1QGzk4EHmS+r5UId3QptJvGSx74b6in4/ZVG1S76SuNdTc2AoPd0ZLq9H1umSIGXtD5bAKfoVsm2WWA+nSGjafUSanJhjZtAGKF4aIWrOV8KpbfOFfHeyOAQUVl/liVwim4RJ9O3HA0V+DannrKOkvidrcvp290MRLqaVdifeuQuAa+xwA2rtq2V2nCcdfl/alGJdLnLqAu84D4/Nvxv23jbOPreyPk9uM703A3uKz3x+bHwcQ7gXQ8A4N1Hhm6jmKT/21+lndF9k9AvJsRMklEKP/4ZWhndtwGdO6eS7CfuFv/XuLfLJ/qwlab+5Wj/FNzPK1gZgORxoTKzauPIABUi7TFRVffMxcoVXH9uewQv3JrCykPQaNdeJ/iGsGmfvtIXnkd9om2HP1EhNCvktMHEj6w+7KN8rC7BiwnX8WsSuF9yWhkf26kCWRmF8ne3aFlZWRkN7npXr4xPthkrU3DlAmD/twp2EvhSEwt+PatcV1ZW/hxB8D/ky/bs/LU/gwAAAABJRU5ErkJggg==)
physics-General
physics-
A frictionless track
ends in a circular loop of radius
figure. A body slides down the track from point
which is at a height
cm. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
A frictionless track
ends in a circular loop of radius
figure. A body slides down the track from point
which is at a height
cm. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
physics-General
Physics-
The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through
, where
equals
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905679/1/912154/Picture483.png)
The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through
, where
equals
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905679/1/912154/Picture483.png)
Physics-General
physics-
The time taken by the projectile to reach from
to
is
then the distance
is equal to
![](data:image/png;base64,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)
The time taken by the projectile to reach from
to
is
then the distance
is equal to
![](data:image/png;base64,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)
physics-General
physics-
Two identical discs of same radius
are rotating about their axes in opposite directions with the same constant angular speed
. The discs are in the same horizontal plane. At time
, the points
and
are facing each other as shown in figure. The relative speed between the two points
and
is
as function of times best represented by
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486055/1/912010/Picture480.png)
Two identical discs of same radius
are rotating about their axes in opposite directions with the same constant angular speed
. The discs are in the same horizontal plane. At time
, the points
and
are facing each other as shown in figure. The relative speed between the two points
and
is
as function of times best represented by
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486055/1/912010/Picture480.png)
physics-General