Physics-
General
Easy
Question
Match the List I with the List II from the combinations shown
![](data:image/png;base64,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)
- I-A; II-C; III-B; IV-D
- I-B; II-D; III-C; IV-A
- I-D; II-B; III-A; IV-C
- I-D; II-A; III-C; IV-B
The correct answer is: I-D; II-B; III-A; IV-C
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physics-
A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true
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)
A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true
![](data:image/png;base64,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)
physics-General
physics-
In the given figure, what is the angle of prism
![](data:image/png;base64,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)
In the given figure, what is the angle of prism
![](data:image/png;base64,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)
physics-General
physics-
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P as shown in the figure. The ray will suffer
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)
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P as shown in the figure. The ray will suffer
![](data:image/png;base64,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)
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,iVBORw0KGgoAAAANSUhEUgAAAOYAAADMCAMAAABQgy/ZAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///0JCQoyMlGtra+be3s7Ozubv762cznuczikpIebOc+Zr5uZac+ZaMebOMeYp5ua15hlrWuaUMeaUc3spWuactUIIGebOUuZK5uZaUuYI5hlKWuaUUnsIWuaclL3FxRAhEEop3krvGUqtnEqtGa0plK3vGa2tGa0pGXvvnHta73sZ7xApUnvvWnutWhBrGXsplHvvGXutGUIIUq3OWkrO3kpK3krOWq1KlEqM3kqMWq2MWq1KGUJKGUrOnEoI3krOGUqMnEqMGa0IlK3OGa2MGa0IGRAIUnvOWnuMWhBKGXsIlHvOGXuMGff379bW3gAAAEpKUqWUlK2trUpjUq2c760pWubOtXulnHuc7+b3va0IWubOlKWllGNaY4SEhOYpEBlrjBkpjITO7+YIEBlKjBkIjITOztZaENbOENaU5taUELW9tXtze0IpY63vrbXF5q1rzkprjEopjK0pznvOrXtrznspzntSpa3FlK3vjK1KzkpKjEoIjK0IznvOjHtKznsIzntShBAhIToxOrVrWkopGeYpMeZrteYpc+YptRlrrRkprYTv7xnv7xlr7xnvaxmt7xmta3trKRnvrRkp7xnvKRmtrRmtKXspKZRrWuZKteYIc+YItRnO7xlK7xnOaxmM7xmMa3tKKRnOrRkI7xnOKRmMrRmMKXsIKbVKWuYIMeZrlOYpUuYplBlKrRkIrYTvzhnvzhlrzhnvShmtzhmtSntrCBnvjBkpzhnvCBmtjBmtCHspCJRKWuZKlOYIUuYIlBnOzhlKzhnOShmMzhmMSntKCBnOjBkIzhnOCBmMjBmMCHsICOb3jOb3OvdaEPfOEPeU5veUEOb3Y+b3EBAIGbXv73NSSrXvzq1r763va0rv70pr70rva0prra1rpUqt70qta62ta0opra1rKa0p70JrKUrvra1K763vSkrvzkprzkrvSkpKra1rhEqtzkqtSq2tSkoIra1rCK0I70JrCErvjHtzpUpra3NzUq2Mre/W9973///v/wAAAJiSX+MAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAMN0lEQVR4Xu2dWW7juhJATXEAuIb7Ia9I5mDg9Y/NDVALuN/RGrUXJxeNR0q0rdiaVbQUIwfotByk0yoVa2CxSO1+WQTzEBY+vS2m3Jcl5zp8fFcyJc4ZkUKFz+9KsneaJBy9+bjF/L/djpYyfHxTWHF0I9cIEz6/KZobQg16cyl3RpS8LGz49K4wiXaZLRANn98UynP3VQtnoO+M2fvxmor3drTZ2YeTnX1zMSnH7itB4p19kE/yckKtLHEWvvWOUMRLvuccv7mfrfLYv9XlL7/88svrqCpAFQf3x314t4jixKPUqjzPMZISuT8Suw/KUi9u+KGfjZPQJviMeIETlZxoShP5L01PiTKXghdHoywh4Wd/KoRYhVGBlW5IciruqQHRBhcIO1F/rFIZ1V7EpoQVujiEqwBJLoXMLf2BtsqIzRFSDwJV0NOz5jJqEDIp+VmSEqokMhNNjuZO9fTnDF6S4gLPmWYx7R7ODxHUj1Y1e/ARjJIfICizGKn+26RJ72j+AYJm1AkZrjtRvM0xNSCfSG05lBIlzbAeNB+cUhMs7VYFdeP1Mube7IhHsbPSbLO+4FT5FS4hyHL5lFisD7MSA98VBf+Ni3ERL0I90hztplwuMZ/jHzwZf+/63JIYrgbN8YRa3QhPe+OAp6aM8bDnJFyNIhmKm01YvhUDnWqWdtqNJ8ctRBamYj9uPWsaAIyOP6h0vracTpcvcIVr65OpUendd8j0+YfGesXAkqk5q3dJo+Q1FopXbH3T5znP+DQhbt6w641bPWPEOrSc88++1loRpec0XE1jZp09euBq5+XmYvIV3BDJX96MtoKczPgeplnMboxmny/vwLVy9pPVaK6RpecXu1sq5/s9NSeg1JhX5Fx3Mjxp6vUdjSZMxB7AyQvldJnsgjWdw4KRRz9f6N7pbOtazNfroifDK+45uLwsjullvZNskT5ojBJiG0TOS/Ku2GXuMh9TtF9OlvhG0QWoZW3uRL7ECy32P+qfZXONl+Tw2eJclg6sfw5ynL9KPBqLVm+DsOf5+cVI2JL8BwoZPahQgP1ri39D9KIpA5hlLrZNp87I1kmL5cpM5s9Qrpwiq1MtjJmeBROxKyxu7ATJ2VOAWkfUekm2MJuFg6GI6mSvSpuHuSTRnFBGABwQEDpidTr5DBeLoBDLPhEHFpB/a3ZHzwdHm4/RAsQeAOKmI9qoXTzRDEzsPeggixU6CZA5/IUZbedI+fuG/KznFGnUahQutgFZUPjvgRmgUTKhma2X4QblOUCZ5k4tWFxogqMYJ+FAppnwZQXQK3FCCljaDhNQdrvDwnpxK2CmOX8Z9xEZwTg3NDu5cowgJgHJREExEUolhENN8MgB6Dc1CnzMAKV+aREuFmNntT+1kF6uPogZ8Qlj8KdzuFgMQMmr5rY0R7AQs/rqnknAikwa7EAkdKr+SlEhBMwQAVyhPlioszpCumfyfF8CifmaVcVphHSP7GSBEUiuEGk+sIzrwjUtE5KD3B+BO2EM7qSDa1H6U6Q7mG3ZgNmBzaGiuqn34jAuoWI641D3BhdQdqp+YIkA8xuHfbhYysGgDyinfcLVzBVBTRHdoAX6VUQKIUqgp19ne2kJN7+mPFws5OSkFAKoGa5utpd7uCCQApX1TCWmgJnVVd32zgGBjdkdBcrcg5hiD7EhqpoEGMgD+yiQbdIPL+RRS1Eu31lSVYMQXAxwrqMMFwthOqTZXtB8YYLmWxBsCVlDIGDPjOCyVqM+Cr5s6PrmWp8BwTE1oGRpZ9BQN89oSvGxRKN/ckZKmPWrAJuY7JGi0zWfgjadoWIjBZ9vowY7BwQ6c5qauivReWx78nHT5mdloxzP1KgxGYJdv5pYvzwgIbqGuSqvUuV+wGWVoLM0ihNdwrYQThQzEfwDddxBcrVNfQyLKXM1KjVkBuTJJhXdqcQSnYp253y1TZLfngObp1FpOPD+GzapjY2eDkjuTu0rX1dtft8iNEOjmeQl9HFuelrmyFDnom9tm8w8LGj9nSwowVBzgDsTpyikR0yvTYqfize1MxpvbBqJuoIJyMTyQZ+YpdL4fDtrhDRLo5M0qvfl+GcykomBs0fMREic34K6xfmlIWftjMb9VzjCyymyy6R0o0fMk2gczeY39aaXpo+th+4YjUrYDKiCJfkUp3bo0ebHvdjoHJEftt8j7EiNkiLGjjw7aWLdp81bFuQDrJMme2qWGKVRE+UtQKQj2rfTZ5v3zCXL/Q7t1k0fwxqVYpwJT2PaKkrPoFW3GYqLUtzZada6DFUP3W6NUn6EzYBqsmTK3vhx2tQoz48Yd2itP47iCA7IM2nbVK9t3rSZYKe0BHUuwTLbqdGsiDJm3Z1PKSD0edq7NvOq1wj3DJN66LYkxy76xhiz7vk1w/gQPdq8zzd3xouZfvaqpSO8HKO9bU1dwsUIxmnT+DdtVd62jzZBUw6f6AWmhJRx2jw5qxxzgNSzoFgcI+QGFVP6D8Z5WmbOLTOVNu6Cpt5QSRHJz3r6G4cz/7bJ6zb4cdrckWT0YnrtdWm9VV6V0casv/f2ekANUwgVRUhoxtmmY0KQqjVKpEtlpajP0XBfJvyCkQwcRXLIxV4FTY3U5kS8RgskjOV+zFKMiS87gRup7R21u/Tu5Pu1OV8DjMq94LzkdMdyIVKCBPypMwNlTPNxe7BxtOk1WFQLh34nHD2VJlEpvMd1WWa4asNZTbiaYJsTSTHOjTahlCH34MWgCoZ61EkbTQCxtFm7HBP6nhb+qm76yrXJ/v6fjoubM7nNCQFbZb7TU/nKZKOzuF+bC4PAtbsr0+Xsg9MG8MWbdui+0XIbyzY9t8NX9EEeI70Au1udOoygSlXxbNMbjpeM5sZmztdGOiy8a3sjw3XB+lA5v4jaDNubUmky9zTBGgAf6NpERXgtGKl0GlGbuK6kZtVojfc6J93a70ixm84TkuJLNYhiZUG+TL/UUY+jtRBHzogjjLEs6jEdT5vYjdWXkLacMsNSeqA2TWk4Mbk3bv4vXM1BR5tOP9EdVG4Mrm/OhB0hX9PRDxleNorlafNJKzkLSQe3Q/TaZu80pxc94RUWy8kGi3y9tjlbm/QcKYftYLD61TNoG1X3qcQ7uqKDoQNq+7Q5u6X/Ja8E+M5AZ0m/bc7bPWVffdiwY+DojgielqxyUn/We0h2jzZn2iZ70RmfjzSa0Z4B16aT8oURs8kBdxecwOPmKofX19Du9+tAe1oTa145hm7fB6zNsBtsLWxXDwSsbcbY+j8J25F+gXra1aX0VYNWOSG1uaL3uUNb01s423TxeQNSejlb8gQwT0vwNqR0d2Ke2wd6Bu0UbWbpZZ3cpw2WPM1X+rQ5wTaVtCvlPq3Yx0NtYGwzf1GxcjQUf58LQnhaKrfzVsorxHw7KW153GQ52tI7Rq80X3RMUi/moV1r4zytlevmd90QhcLhuMTkUtKOI8XG2CbJ5Zpv9RsgzcM60p8ScdlxtsSwbTK1QatswrSsuhMIEqKxRP+NIW0yhfCmwkgbRMuq20yIrqOJ+7VZCbnd8XqnEvTAO1/02+dpnXnjzb5N/hGijwXqLPx1elpm5bMmM8w5dxMxzD/Wn449QmiCUMe7FTpsk+SFVC0vWiVY+CbwtAQ6IRSWjFhcIPN830SK4mF7DWM2dz/bbEsjp5vKq6NBmVzy6rKoMKqN5BdFm82g5Ohb7hpTt4yqcyGNfVipV/w6ATN++Q1P2uzzahihCrsQihMdNoY5F+wovOj+MeCCI6zp8xFVLOH8q/ouRmSn+5rotgE7pFrhi5PnKCX25wU5St8sui/r6w/nZSo+3De5+1i6K+4ib5U9IrljMU71jIFvMrFfWp9c3uAlO+bYfJ1OWrlvaaW+/qjkK1FKnRLlPqo/6itBojpuJEP5bnBzw6bwYzCt+mExexqlD5BjmVdDmfAk5gsWYpFKUQ5nrAzjYK8pvySbN8wWMvLscJ65qfuL8zUW/F6NaUaf9wUDvNJrHUaM2TtjRvgmsT8kCC7D8t5NO28CQeMqez8bptAWj7qFRp+SzrrC+2DxX7P+GzxjQ/EfKrf1lpwIsBydpTiGT2+LMiyjCOwg/G3CtG9tTjn8KT8bgtGj3xFIcvgDuLYEyaU0GUuklPHetrgBWJY58dwX/9cvv/wCwbunLTVgb0rbHrvd/wFN4GiiMh2tJQAAAABJRU5ErkJggg==)
Physics-General
maths-
The foot of the perpendicular on the line drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is
The foot of the perpendicular on the line drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is
maths-General
maths-
(where a, b are integers) =
(where a, b are integers) =
maths-General
maths-
maths-General
maths-
is equal to
is equal to
maths-General
maths-
Let denotes greatest integer function, then is equal to
Let denotes greatest integer function, then is equal to
maths-General
maths-
The value of is equal to
The value of is equal to
maths-General
Maths-
The value of
(where {x} is the fractional part of x) is
The value of
(where {x} is the fractional part of x) is
Maths-General
Maths-
The shortest distance between the two straight line
and
is
The shortest distance between the two straight line
and
is
Maths-General
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