Maths-
General
Easy
Question
If a, b, c are in A.P then
,
are in
- A.P.
- G.P.
- H.P.
- A.G.P
Hint:
If a, b , c are in AP. We know that in AP
2
second term = first term + third term
The correct answer is: A.P.
Given : a, b , c are in AP.
We know that in AP
2
second term = first term + third term
2b = a + c
Now,
(1)
=
=
Let ![1 over b plus 1 over c space plus space 1 over a space equals space m](data:image/png;base64,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)
![rightwards double arrow a open parentheses m space minus space 1 over a close parentheses space equals space a m space minus space 1
rightwards double arrow space T e r m space 1 left parenthesis t subscript 1 right parenthesis space equals space a m space minus space 1 space........... space left parenthesis 1 right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAREAAABUCAYAAACldgPlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAqG59bSAAABx5JREFUeNrtnV+EVnkYx3/GSDJiJBkrkTVWVoa9SDKyd5mLZG8yF3uxYiRZexFjJElirJWVRDKSJEa6SpYkI1lLkqwkki6SxEiSjOHd5/E+u/vO6Zzz/n7nPe/5934+fNX8znvOvL/nec5zfn/POFctjojOu8HinNUbAHpkUvRYNDxg9db6PhHtJQQAsrNB9FI00ZD6jItOWFL04Vur/wihAJCN06ILDarPVdGMqBXYrTlNKACEs1n0XvRVA+sWkkTGRB/MHgAQwHF7cjeRVuDnF6wbBAABPHXtQVWSiHN7RM8ICQB/dADyXYPr18pwzlvRN4QGgB8/ia6RRNZwzewCAB5cER0miazhkNkFADy4JZoiiaxhn+g2oQHgh46HNHlKM0sSGXHNHicCyJVPoiGSyBqGzC4A0KebrC71iiqEFUKjJ0K3HQBJBLvAGrJsOwBuFuwC2LEOHBNtDOjbn3LtxVMr1rTcFujkk6JZ0RbX3qCm13rj/p/RGRWdFS279r6TOYI/Mz7+qps/SCIVRPe5vHLt5dnduGWBNmoBuig6EOjkRQvch6Jp1373hga2bpvXDWtLooNWvlX02QJ8UJJIy0O++Pirbv4giZRoeB+dcckzK9MWcJ1ccV+uCenm5OeiuxbYnbwWXUooH6MlEoyvv+rmD5JIhVkwByUtWb8n2h0pWwrszvw71bkhsLzoJ3gro6oU/D7+qos/SCI1aonMp7REous/9P8fA528y4K713K6M93x8Vcd/UESqfGYSHTFpX7+UaCTtYl9OYdyujPd8fFXHf1BEqkgOjvj8x5Q7Quv7/hZF/7cCHSyDvLN5FBOEsnHX3X0B0mkxui7Qi9as3ibjZ3cDnTyTRe/OS+0nCSSj7/q6A+SSAO6Pov2VNOnnK4piE4Zrqacvxx5OmYtryMrFfRXnfyR18AsVIy43bpN34CXhWFXjQ14vDAaaoH2xUcxwxo2OV4FAOCNrpLc17A6+SwfT2PK8VIiAG90CrBp7xP1WT6exoxrzlQ1QN/50TXrb874Lh9P47rjRc0A3oxbs78p+C73T0PHQ/iTEQABPIm58eqK73L/JL53/PEqgGB0FexCQ+riu9w/Ce3azRESAGHolGZT/qC373L/OLZaq2UTIQEQjr7o5nwD6uG73D8OfR/HKUIBIBv6LooXop0NqIvPcv8oE679drARQgEgOzp+oAuzhhtWr27Lx9e59uDyJCEA0Du60OrCgNVZu3GHcT0AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFMQR0XyP15i36wBUMWaJzz6yU/RnTtd6YNcDqGLMlhKfQ6IVUStFK/a5KjIuOiF63MWwEzn9vu9E94nxQvw2yCTFbDe7VSI+x2vm2KuiGUt2cUyYQ6J8nVDuw31zFvTPb4PMREps+tit9Pj8QXSthoZPMuqvoqM51/Nn1/v4CqT7bZBJillfu2WOz2OijTlU4JRdK4ktohuiz6JXor2R4ydFs6LDoof2udnIMb3GOdFb0RvRlB0fFZ0VLYs+iOZyCMY/RJMx37GzuzYbaKPdorslBNeQ+eetdTG1xbgtwf79sDFJpBjiYjbEbpnj87jd1Ht6rIAmiP0JxzRJPek4vkP0d+Qzi6LXot9E22OOnbTkMi0atpvgpWhMtCQ6aOVbLQFt6TEY9UZZF1Ou3+VARhuts+v6fq9u8uWWJYZRSyhxdeinjUkixZAUs752S43PlqfOuOwDoS8s2JKaWXMxgd1Z4efWVYjjuWXI0Ui5Jp1LCeVjPQbjakL5s5ineAgrBQfWtCWITq50tDCKsDFJpBhWc7BbT/G5YL8gS39fn04fU5rS70WbI2UfOhKW/vsp5Xw9tiGw3PUhiYReuwpJ5J41UztZiiTCfto4zxYVSaTEJOLbEpnP2BLZbcEax66E3/Ug8pm08+/lUJ5Hd2aX3YBZKaM78yni06GYhN9vG9MSaUB3pt9jItpkvpxwbH9Mczrk/KRjoeWhRr0TY5Np6wok0W0uvoyB1XeRn7VOjwq2MUmkGO543Md9GVjVGZWRHr+8DtodSvlif/Vwvh6byaE81Khx02W/u/QptG5z8UftukWiYxfrO37WJHejYBuTRIqh1yneMuLzP266LwfqOnkq+sWa0jpAp4Osk57nJx0LLQ81atzCnfM2dpT1mmUs5jktumi213EQHfO6XbCNy04icd2/ppR1i9kQu5W62Gw58rSLst2+4KollEMB5ycdCy33GXOIonsQOvcT7LAne6tL3zPuWmUuKz5uXcoTZhtdA3KgABv3K3mEjg0NShKJi1lfu7Eto09k3cwU5+gqbcDbjGuJ2QrHZ+PQFbShS4FbMX3VGUwJFY1Z4rOCMOgHACQRACgneeSxGhOgVP4BUtDB/JkLPTkAAAM0dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDIxRDI7PC9tbz48bWk+YTwvbWk+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1pPm08L21pPjxtbz4mI3hBMDs8L21vPjxtbz4tPC9tbz48bW8+JiN4QTA7PC9tbz48bWZyYWM+PG1uPjE8L21uPjxtaT5hPC9taT48L21mcmFjPjwvbXJvdz48L21mZW5jZWQ+PG1vPiYjeEEwOzwvbW8+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtaT5hPC9taT48bWk+bTwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPi08L21vPjxtbz4mI3hBMDs8L21vPjxtbj4xPC9tbj48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PG1vPiYjeDIxRDI7PC9tbz48bW8+JiN4QTA7PC9tbz48bWk+VDwvbWk+PG1pPmU8L21pPjxtaT5yPC9taT48bWk+bTwvbWk+PG1vPiYjeEEwOzwvbW8+PG1uPjE8L21uPjxtbz4oPC9tbz48bXN1Yj48bWk+dDwvbWk+PG1uPjE8L21uPjwvbXN1Yj48bW8+KTwvbW8+PG1vPiYjeEEwOzwvbW8+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtaT5hPC9taT48bWk+bTwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPi08L21vPjxtbz4mI3hBMDs8L21vPjxtbj4xPC9tbj48bW8+JiN4QTA7PC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4mI3hBMDs8L21vPjxtbz4oPC9tbz48bW4+MTwvbW4+PG1vPik8L21vPjwvbWF0aD45LJenAAAAAElFTkSuQmCC)
(2) Term2 (
) = ![b open parentheses 1 over c plus 1 over a close parentheses](data:image/png;base64,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)
Term2 (
) = ![b open parentheses 1 over c plus 1 over a space plus 1 over b space minus space 1 over b close parentheses space left curly bracket space a d d i n g space a n d space s u b t r a c t i n g space 1 over b space o n space b o t h space s i d e s right parenthesis](data:image/png;base64,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)
Term2 (
) = ![b open parentheses m space minus space 1 over b close parentheses](data:image/png;base64,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)
Term2 (
) = ![b m space minus space 1](data:image/png;base64,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)
Similarly,
(3) Term3 (
) = ![c m space minus space 1](data:image/png;base64,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)
Let
,
,
be in AP
We can check if they satisfy the condition 2b = a + c
2
=
+ ![t subscript 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAQCAYAAADJViUEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAALV/ZLFgAAAI1JREFUeNpjYEAAFSA+ykAmCALipeRorAfi/0i4nFQDVgFxALnOvgHE8uRoZALib+Taag7EB8nVHAnEC3HIwQLxFxBfAGI3dAUTgDiHCEs0gPghuuAUIJ5LZNi8QxfUAuKnUOex4dAoDLUkkdQwgfk7ltxA5QPiViBOY6AA/CBXoy0QnyHHvyAbdyAnYQCPfx8hqGB5+QAAAGB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+dDwvbWk+PG1uPjM8L21uPjwvbXN1Yj48L21hdGg+nujX7AAAAABJRU5ErkJggg==)
Substituting the values
2 ![cross times](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==)
= ![a m space minus space 1 space plus space c m space minus 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAANCAYAAAB7LIZDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAbVJREFUeNrtmLFLQzEQxoMUERGhg0iH4uY/ICLif1Ac3KSz4OwgiEgREUEcHLqJg4i4FOkkbiLFVaQ4iYtTkVLoIFJEhPoFvsLjeInte6U0fTn4De9ylNyXSy6pUqNp86AAqsqb168LuwKboO3X3uvXi7WH5DdGUr8xcADq4IfH0ZyI2Qc7YBYUGfsBchxPg1PQBJ9g1xeMmgInoEZdy9TJBT2tud9y0mkWTwmsiZgSk3wCeZBiUb2DDKiAdfqz4JtiJLVgdLE8gyMwDcbBNlh1RE9j7nlOPmiXgUrv2Bu4D+yQjundc27wZxJcMMfchCYbdj2NuT+AZeGriJakT50WmAxpZTZ/txP7j0Etdr/movNvhCy6S3oa41qcUHByXyJmiYWlYvqTcsIsgkfLuAt6GnNviO8V9l7Zti4M7awXf1IKJscLru0aMOx6GnPXvXEi8K3/tLkRMUW+zVVMf1IKZgG8WsZd0NOY+yE4YyvS95ZrcCdiyiGX4Cj+JF16q3whpfhK2uLp7Yqe1tz3+FIq8LSpi2d1U5xCUf2DSrQfl+a4luXj4Re8gA1H9Iyk34zy5k3YHw+mrmsJDHV0AAAA5HRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5hPC9taT48bWk+bTwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPi08L21vPjxtbz4mI3hBMDs8L21vPjxtbj4xPC9tbj48bW8+JiN4QTA7PC9tbz48bW8+KzwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pPmM8L21pPjxtaT5tPC9taT48bW8+JiN4QTA7PC9tbz48bW8+LTwvbW8+PG1uPjE8L21uPjwvbWF0aD4XYesUAAAAAElFTkSuQmCC)
= ![a m space plus space c m space minus space 2](data:image/png;base64,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)
= ![a m space plus space c m space](data:image/png;base64,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)
Taking m common and cancelling out from both sides
= ![a space plus space c space](data:image/png;base64,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)
Thus, a, b, c are in A.P then
,
are in A.P.
Related Questions to study
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The ultimate source of organic evolution is
The ultimate source of organic evolution is
biologyGeneral
Maths-
If
are in A.P with common difference
then sind
terms] ![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
If
are in A.P with common difference
then sind
terms] ![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
Maths-General
Maths-
The sum of all integers between 50 and 500 which are divisible by 7 is
The sum of all integers between 50 and 500 which are divisible by 7 is
Maths-General
Maths-
digits )=
digits )=
Maths-General
maths-
In a
as shown in figure given that
, then the value of
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486056/1/912662/Picture2.png)
In a
as shown in figure given that
, then the value of
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486056/1/912662/Picture2.png)
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
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,iVBORw0KGgoAAAANSUhEUgAAANwAAADpCAMAAAB4M6mtAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///2trY+be3s7OztbW3gAAAISclKWUlCEhGff370JCQrWttUIZY7Wc5koZEISc74ScxZRjWq0QWq1jEBAZQmNaWkpKUubOc+Zz5uZac61jpeYx5uZaMebOMea15hlrWuaUMeaUc3sxWntjMebOUuZS5uZaUq1jhOaU5uaUUubv70pjUq2tWkoZra0Z760xlEop3krvGUqtGa0xGa3vGa2tGRBrGXta73sZ73sxlITvnITv3nvvWnutWnvvGXutGa3OWkpK3krOWkqMWq2MWkoI3krOGUqMGa3OGa2MGXvOWnuMWnvOGXuMGRAZGXtjpbW9tbVjWq0xWubOta1jMRAZY+acteb3xebOlOaclK2tnHtze73FxWtzc4SEjOYQteYpEBlrjBkpjHsQKeYQlOYIEBlKjBkIjHsQCNYQ5tZaENbOEAhKWtaUEGsQWmtjEISEhDopMTo6Meb3EEJrKa1rzkprjEopjK0pzq0Qpa0QKRBKKXtrznspznsQpYTOrYTO70JCEEJrCK1KzkpKjEoIjK0Izq0QhK0QCBBKCHtKznsIznsQhITOjITOzpylnAgZCFLv71Kt71LvrVKtreYxteYpMeZzteYpcxnv7xmt7xnvrRmtrRlrrRkprXsxKRlr7xnvaxmtaxkp7xnvKRmtKVLO71KM71LOrVKMreZSteYIcxnO7xmM7xnOrRmMrRlK7xnOaxmMaxkI7xnOKRmMKVLvzlKtzlLvjFKtjOYxlOYIMeZzlOYpUhnvzhmtzhnvjBmtjBlKrRkIrXsxCBlrzhnvShmtShkpzhnvCBmtCFLOzlKMzlLOjFKMjOZSlOYIUhnOzhmMzhnOjBmMjBlKzhnOShmMShkIzhnOCBmMCOb3lOb3QvcQ5vdaEPfOEClKWveUEIwQWoxjEOb3a7Xv77XvrbXF77XFlLWUvbXvzrXvjK1r763va0pr70rva0prrUqta0IIOq1K763vSkprzkrvSkpKrUqtSkpra3tahCkIEO/W9973///v/wAAAJDhcDoAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAPHUlEQVR4Xu1dW3KjvBK2boDFs1hEZy+UnhFoDTYbUZb4v84SXJOijsDYsScGhBDE8cmXmRg8Y4xo9VXdrd0vfvH/B9g3APv+5MWQIiQOCinSn78SoMgYU1qwWvbvvBRowmG306xu+jdeCQWL7G9yrOn5/KWgknZCyvcan89fCThL7HxsBFP9G68EmXMMktfaMt7LQTOOsoS/pKwEkcdGicy8IuFkktnfwJk5n78U4ly3L3ZyvqCayzpFsDOs1eQvBlyfKYYY6s5fChET7YvJk7Q7fyF8SM4qwKVKWPxys9KIYyKsyyOq9PXECTGpTI0pyld0CH7xi1/84hcjAFxEClWoErxFhip7rIvyh8cZoDQaZVZpI1Wp9o/ieX9YIXHKhIqKHxknAmIUaiEqnZYYALdxZiOwpaQ9oakd9wm1BNXFj6Ih0MKOTHAUS3pvjVTHuwDDBymsW36qtJE/xNjEMkYZF9GjiLnOvr4LqeJcqII+/fgwLapaaAKP7UcyQCFI20/Z2dufPyEakJYIgyMbBWCDamGednhQcK5S/9vDJLJ8+pTrP2A4WioXGitgMlT2Z08D0AJpOTkdh3juE2DlZ1X0J08BrJHbeuIjafkvwFSiepqQdCOVcFwqVfd6bgCNQSJ6DtOFmMx5FfhQO/5PI9QT6HWQKHNnkcJ5kQArHn8z8QBrbj76ExfM0IDyJAoPhRkO0uql1WYPNln1fcSz8n9Vi74pFfousYkVmhsVxzPtFxyJNj9gexSochWSVxg0k9L7P296e3fPqlqPbz3nMsxCidTW9hi27NYfzoHi82/Uzv5tR4fjk5ccK3zmmJ0kxYYK3T7MLRnBmmPpZqPDutqYyVO0VYYArtSGs6RDI6ttRkfRwZtu4BOB6JCiLg9iZRC1QPEY/yxSqaLVE2wxOiyYkx567gqC1l5Jtz73km9Qtb/KaqSYjmMsAcSnRXLSLApumVXNaIjFMh2w8MnrNS2x+PRdHkiPg1rNwSu+PeYGaC0VSyv9rW5/C4zWyR8O8dTMYudMenkjkzBiiaQ7Y4me6xGJ8GwHZRZAmCzRcz2wqoKzHUbRnBDeACKHcPoUcBbau1us4c7AOIBIkgGe0C0aycNecAlAz49MjYGg74mwPQbmf0I6CDpbSXf6oXgLaIYFUy5F9BHimTfiEIx0oFAg0ySAKugQUJUbEcpeVqEqHqtTAMXUAkQwey6EnusQTMLpcOkTJNiClw6id3fAn7GqCKNDf7QEEKNvXr59DMMDkA5q8+1e3CMQsbwIb1+EtOSmk2yc0UTLDYuPoFWKOoBPeAHlS1dHQPKQHBfAWb1iuaOCw4Z5dUjngvKFZkoR1tWRf4JopzNAqUVXg2XR85WxkHRSPHOJIvBFNpipn5hwloWX9FXBKnDhLA7KwdYlX2AZylPgWWlOYUcnlL/1FDy6gJySSd1x8Ld796irfA4IFbjlBPFPDUtnJ65NQcYB9VyLN2+hoJYto24Bf0daPH+TAek7ubDYIvVjGbzX64rQisDaFMHnedU2WPGADp+9ZsJG+S105neTWfgVWpWETkeQfukbwMOznFtFyBzQystIkcHizJ8wwXMZQXsZGvEKpWwQ3skwPr3fAP2MxmOFV5Ane34t16IUxfzlLDiuEUUPH98lVXRzUeNW/oPrFbJZFiSTDgGrm9wfc3QLIcsQeSf/Iryeu4thRQlzW90sAgaHr/inwj8IikucB+uEufVzBb1GeVfoMEOL9HjWBVjVnLGjiz0MS/K0B4FXuGbZl4qWqKyS3Cna9/H2U9o0ltfQBT7WyslNw1m8eqZ7GJDsIv7Nu6aV0+CWrjJsBiJ6hYw5I24Tf53BySg809HLEivNXX07Wgd3wy2CLmH1oOhsogBirnqGrqCRgGRJ+PmAe7lO814nTIPmwW0JrGuWh0/ixVXnvkDs3huahjeUVM4sgjdchUO3Bomz3Pm5kSQ0d+BubCwPmitp0ZcXFUw4X/ii98OBnAfHchPWH4eoi9Kp3N1FC5/3exkcy+ugxg/E7eBkPmOTgPA8B9astUhiZG33gCEM6HLxNav6cwdYnnN/Em5I65Zs8Q5SOzwezC63qgCszZHMuB4OmA5zgTwcWec2NwXKWabDTHx8sNc05ybKjvBW4qPzDeX9gBqTMZaZEMOzFsp+J2Z1Y/e0LZtitJpJ5dergkhyVgcYXpvkRJNZC9yetmWZjFo26LP1Nn6LC9EOb2mRCDnFO8VmxSHxf16RPWMn2whnq/w6ONL2oCiznB0X9qCjogA+T0JYZ7U/mgNpxf37COlQfr2Jost0hVKw9zpaMjqSpWbmliOAfFwvzY4sH1nW+6TctYwSSsTy4wK9R7jM2DwB4ZUSJ0WdJeY4/E3oMn2a6DNZErd6r/bOwJNJmszMvGx8SrpNlWZHrIatqyvl7ks6rIy1osWzTloeRT4zG2WfZvO/i2DMjwDDPUYvPFd+qcNo1TrXHsODP0l+nOsk2qncH82B9arGZsiZco18VNsrUWJtztlVFRDVZ7NnDsBrNwjKk7EvankOiMn01fWCm5qc0uq9xMzsLYtRfjF73NHUPooOZ8lYBZFihhhxsx6NzeF2SlFLvUTP0ns4Y/PLJ0D4iGeaJWP+sGLJUZjPeykFV2+3twbUEsIOrz91gMw/TTp3VD7CeZLnFLlp7UyQxqT1WG7wQVT+nrj3YCjY6Fx5DDA+uYwkG+e5O/ZoTm30o+3KfQcsW8XgmvegvTZEIzP6Vl5heW6ccrfXPKeHP8jub7rhOek9UnuFDLySbCYpd6tfuhWZxjwMZUqr92oHvacZ74/mQcxWHw6Uu9EvxXljrHQgFCWrVu9NVTYpz236fBLbZlDOPgdkCorPkblHIMIqBlOOXVAmnmV00qNNmr3jsXupbiyDBimd1Sc1lszT6r18zGrRzDMl8cOjENfquXHKfQ6uLQoAHItRM6+h6m+rGAYuCnyeC34DceoP3DHFczeU6+Nr0cS82lNt9d6AixLn3rXZHhW9M3iOdjoPq8npAURbyflweIIJ3wiMNSD6I2fMkJZnyjnlpe2JTtjxa9oorZl3zTGot/7IGXOkJbcDpa4J2FIdrdVyP7x9xeYFhu4wv1x5jp5TKJUzukmW1ZElfdPx84eami0o7yOzlcEcC4VWQswyzimqrWJoh0dk+zmTL9n1s3GoVMKSECIv3D5BuervDeWsMzd3LQujY6f3SmHd3SZjixbuz8HFMYBJGMvzS+3IpJ5bcjctsErYX41PVgXQ/L0jfLeWCXj2gu01x2MYmCZMkMszmMNzfthjq/eOPBdUszZc2RRtQAZn8xUeaDE5cZrjzfLALK/AE3Z47WzhSV7TXRO9swSDYO/z2Y/wUbu1BclvRNYMC8UfWPeLtK1VSkzGCqOKdIqBvsKhljq6FVmTlAswONBvGec1v+wmL1nmuUxLjhMOI2S3N7w+z1mQ1IrnMkV9JKLhvpMdo88Y40OQv7cW6OrS8hPkkoQNaIoAg5hqIFi8H25sVzu4Mcrd67lFaK6yrqm8dTlko60noLrLldtCWp5xLTVqiG+owSIeLeKix7tViE14roM+J5E11s7BNceeZYcwmjYs723XzSjXx0BIZKzph3JDPS9coOEAZqN75YnPpsyUbRlEz7XQZy+V8EQ2uzLnvv1/mmq4Fyit+0RAOId5tpKWRc9xUPyx3wd//Pt5lpcU6a8oWJdP1pSGdBpjI54DNCPTawJaPF5rkKp1sHSk0SXJZYrnAk1LHXDbEDKgyXVtzaC6Ptb1JfS+DeXCVrA7xxs2kZaNClr62mXGuWAb29Jn/WkErnsFbCEt8Sn0rgzGraRwSs8FsC3h8ZrXEsDBac1nA55bo+syFi7pZ+vzHBVrbBXiVPG/OuWwfvNdHRiFS9eYKZ5brMRD9N5/BJcNC9aWlnK1VuB0uqPByjyH0XqbXUg15c+va1viytvldoD1NMaf3LqUC2t2/Ytmip/XlJaw7tjs6OLxMvYVKddEKzRouQeMbxq4nrSEZVtNuWGvxjpATek5b9sSzDbbcKuRvh9r8Ry2dFtNCdzBmipDIfa1eE6v0O3pMUZ2IFmHcrCov+pMWOYeCNBM8ZyXEt90bPbr4oFo36S09BgcRpuOrdXm6GGWxQo8J0+HbcdmIatHjDdpW87lOTBija4zU8AKfQ1ih6Yc1cPR7lXR6NOXVuhhpSUQtIFZMgCZHf7JYg1KOSznpU+FxR6ju/3S9iGlJZAq+54peQEUt5U5lFrKAdDBxz3DtgTDDxtZXMMo9WeKvjlEWY31sHhz57lCbLiH+DCaAl0yxPBbnSXR0Qwmd7jyHK2ET6HgGrDyGp2HZ/KEjRWQulFOqtPISvXmkEiotnLsQzA2lhTiYltKjYQOtI1XIJQoOxR4Jxkbyz+dpBxIg4JulhMIBP2HyqIeNbDGeQ6wNIJ/GdqeYgtoX+myZgBLQDTnmRjrtTBiWzZgvW2eFc2Xj1tlyq21sAP7z99hZ/YAnFZHHg0/3iHKNW2hf20l5KMnA5KzzFpCe51n4bab8gEu2+c/UFuEOePxg9un9jNcp7cfAvJpVDYoaYUUyb7P0LygoYWVd1zEX54yETljt3m1LXCheIbUl0K5lH+GYLsttOys/PaxdSBGVwiJSht5Y4uhLnn3OjMxkfa/VUpr82AdGOL62qeIt2vWxRodfD3REFMJJBCqlDKmKC2SbnCM6xYHdeJ1l4iNCmOhY226n0jH9o89qBkTZ7O85rAr+YKdXNZAQ0ujLTtlQlRItQr+Hnme/7V/z8f2p/3dv7wza+z0nWNwUrUi87nGdsGe0jSOTdS2xrKohaWnUgdLPjsldfvavhzaE/vuwb7R/qPilqqdtUMTtco24gHR7OKORn1O+RRwlNR9W74iL0jwjWZCo4mOluPc7nL/h1/bHJhc6TVXHcMAMBl2ZP/B57ZZjbJy81+18iqAE5tfX/pTAEn4RqJPA1BP5LmOwWsDuh/Cb6DD5SY/G0AnIfN3nwuyXqGP85OA6nqi6ukHQxUieI/hJwHoqEHOHcB/FhqCZJP5bH/0A1CKTKvcszXLkwNrpA5vs3r2/hiAUdY3I8n89jFPjwZMlw73ijocS96OCjBngg4ub/1QpIgniO7Kqq7rb4yHrwMqS0LBegQlkSNtrn7xi1/84sdgt/sfXs4lrd3iWYgAAAAASUVORK5CYII=)
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