Physics-
General
Easy
Question
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. If he continuous to walk along the same line how many more maxima can he hear
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)
- one
- two
- 5
- 10
The correct answer is: 10
Related Questions to study
physics-
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y - axis. The speed of sound in air is 330 m/s. The angle q at which he will hear maximum intensity for first time?
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)
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y - axis. The speed of sound in air is 330 m/s. The angle q at which he will hear maximum intensity for first time?
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)
physics-General
physics-
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. The angle q at which intensity of sound drop to a minimum for the first time
![](data:image/png;base64,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)
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. The angle q at which intensity of sound drop to a minimum for the first time
![](data:image/png;base64,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)
physics-General
physics-
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is an antinode is
![](data:image/png;base64,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)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is an antinode is
![](data:image/png;base64,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)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
physics-General
physics-
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is a node is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAAA9CAYAAABcDdA7AAAMlElEQVR4nO2cWVMbx9eHn5nRhmRkISSQ2KHEZsXgykZuErsqucs3TK5T8SdIOVWpVOxcmMQxCWYxAgESWIAFZhFikWb7X7i6X2H7BdkRiMA8VSq7jOjp6f71OadPn7Zi27aNg8MFo9a7Aw7XE0d4DnXBEZ5DXXCE51AXHOE51AVHeA51wRGeQ11whOdQFxzhOdQFR3gOdcERnkNdcITnUBcc4TnUBddpP7Rtm3K5jKIoqKpKuVxGVVXcbjeqqqIoykX106HO6LqOZVm4XC5M08QwDFRVxbZtbNvGsiwaGhqwbRuX61RZAWdYPMuyADBNU4rOtm0Mw6DW1VROdda7EZNqWVbdxsi2bRRFQdM0Of+ANDyWZaFpGpZloarVOdFTv2XbNru7u+zu7mJZFoVCgb29PSm8Wg2EGFxHfCcRY2yapvzUY4yEx7MsC8MwKBQKrK2tAbC3t0cmk3lvD3iqTTRNk+XlZbxeLy6Xi+npaTweD0NDQxQKBVpaWk48UKyM98GyLMrlMsVikcbGRrxerxzc6+7KTdOUix0gEAjQ1NSEpmkoiiLH+7zHqfI55XKZ+fl5Njc3iUajZDIZstksvb29UpzVWL1Tv6FpGt3d3YRCIdLpNLlcjtbWViYnJ/nhhx/Qdf1fr8BSqcTc3Bw//fQT29vbWJZVt5V9GRDvb1kWW1tbPHr0iPv37/Pjjz/y66+/ks/n0XUdwzBq7nlOwzRNdF1nc3OTR48e0dHRwfLyMqlUiuHhYfL5PMViser2ThWeqqo0NjZydHTE1NQUiUSCcrnMgwcPmJyc/Ncvbts229vbPHz4kL/++otCoYBhGDUR9H8V8f6maZLJZCgUCgwODpJMJtnZ2WFhYUGOu7Aw541w97ZtUywWyefzAExNTdHZ2UkgEGBiYoJcLodpmlW1eaarffXqFVNTUwwODtLU1MTs7CzhcJitra1/beIVRWFlZQVN0/D5fPIFr7OLFW5K13Wam5v57LPPCAaD6LrOq1ev2NvbwzRNPB4PiqLI3eVFuFtVVVFVlb29PdLpNIFAgHg8TjqdxjAMwuFw1f041eLpus7q6iqaptHT08OLFy8olUr09/fjdrtr8rKtra0kEgkaGhpkECtW8nW0emJMVVWlra2Nnp4ewuEwN2/elPGvsHgXYe0EmqbJ/m1sbLC+vs7Q0BD5fJ6lpSVu375NU1NT1XN2ZowXiUQYGBhgbW2NtbU1ent7OTw8rJk7bG9vJxaL4XK55Mq9yAG9jNi2jaZpuN1uGe8dHh5yfHyM3+/H5XLJYF9sNM4TYRDEfAeDQRKJBKVSiWw2Kw3RwcFB1W2eKjyXy0V7ezsAs7OzxONx3G43qVSKUqlUM4vk8XjkihIx43VNUIsJFqkLkUbJZDLYtk1bW5sUnvj+RQivMnMRiUSIxWI8f/6ccDhMb28vs7OzvHz5suo2z8zj7e3tsbi4SCgUor29XcZktVxplUlSQKYKriMidSHGRMTBKysr9Pb20t7eLmPh80jkn4boV7FYJJPJANDX10cmk+Hw8BCv11t1W2eeXOTzeQzDYGRkhPX1dcrlMslkUj6kciV8CJUCFimCynYvI8Iqn1cqQ1gYRVHY29tjYmICv9/P8PAwPp9PhiOGYVxYWFL5vjs7O6yvrzM8PMzOzg7ZbJbBwUHa2tqk5zqLMzN9Xq+XRCLB7u4uGxsbdHV1yZcVG4DKjcD7ToSmaaiqisfjqeqMr55Uvmvl3yv/rRYf4WIPDg548uQJi4uLBINB9vf3KRaLJ4RZ62e/6/Pm/GqaRmtrK16vl+XlZVpaWohEIpTL5arH8tSZ1jSNjo4OMpkM6XSaWCyG3+9nfn5eWibDME6c472vpbJtG7fbTTQaxe/3yzSB+NllQohCTLphGLjdbukSa2GlxTsbhsHm5iZPnjzh+PiYiYkJ5ufnGRsbI5FIyEKNyoP686JSfIqi0NraSnd3N9PT0wQCAZLJJDMzMyQSCQKBQFVtnmnxDg4OWF5e5saNG3R3d5PNZjk6OpKdeNP6fQjBYJDh4WEaGhqqNtX14F0TXOtJfzPOHRwcpLu7+0RIUpl2En04T95ccKZpsra2RrFY5NatW+RyOXK53HuNxakWzzAMmY0eHR0lm81yfHzMJ598ws8//yzNrqqqGIbxQRsOy7JobGxkYGBAltXA5Y7xhJUR6Q6gJhavcmOhaRpdXV3E43HK5bJckD6fT3oXVVVlwv28zmwrhSQ8Wz6fZ2Vlhbt371IoFJiZmeHOnTsyA1INZ9bjBQIBGUSm02k+/vhjcrkcHo9HbvUrV977rj4xgA0NDSdivMvmZuF1n0qlEoVCQbofIcJaWmrTNCmVSng8HlkH6fV6UVWVw8NDjo6O5LiLZ5+n8Gzblsd4Ozs7WJZFX18f0WiUX375hVgsRl9fX+2qU0QeL5fLMT4+Tn9/P4qi8PjxYxlIilMGl8slO/k+HRC/X+liLms6RVEUpqenuX//Pi6Xi1KphNfrlQuwVqiqSqlUkkl1XddPxHNizC7KK4jnlMtlDg4OcLvd9PT08PTpU0KhELdv3+aff/6hra2NRCJRVZunCk9VVY6OjhgfHycej9Pf38/Dhw9PrK7KQRIu4H0QQhVJZLFp+ZC2LoJUKsX333+PpmmyOrvWwvN4PG/F0OKQvjJhLP4872oeVVWlYXG5XNy9e5eFhQVevnzJt99+y9bWFs+fP6ezs7PqxXCq8CzLYnFxkUAgwMjICNlsFkVRSCaT/P3333z33XdSLB+6sxUDJtyFKAu6iDqzD2F6eprOzk6ZxBXxba02GaqqympeOBlyvBn/CgtYS9H/f4j5Ee52aWmJb775hmKxyOPHjxkbGyMej9dGeABtbW1Eo1EZRN67d4/V1VU8Hg99fX01i21EnChe7kNSMxdBR0cHX3/9tRSaEEkthQe8lRiuTJtUWrzzTqXA/wle1OP9/vvvjI6OEo1GefDgAcPDw3JzWG3p+6nCUxSFpqYm8vk84+Pj3Lp1C1VV+e233wgEAnz66acy71YZl11GwZwXlzUerRVvJrWXlpZIpVK0tLTw7NkzWlpa6OnpYXp6mlgsRk9PT1XG6EzhHR8f88cff5BIJOjq6uLPP/+UlRPhcFjutip/x+HqIHbv5XIZ2359du/1ellZWWF3d5cvvviC7e1t5ubm6Orqqo3FEwp3u9309fWxvr5OqVSSZVKapp0oZ7qs7tHh3yF20KZp4na72draYnFxkbGxMUqlEpOTkwwPDxMMBjFNs6qjzzO/EY1GCQaDFAoFUqkUIyMjrK6u1uSFHP4biJMSXdcB8Pv9JBIJwuEwT58+paOjg46ODnmMVw1n3rmIRqN4vV4mJiZobW3F7/czMzNzpeMah7epLErw+Xy0tbWxurpKQ0MD3d3dbGxssLm5WbUuzpTn0dERz549IxgM0tPTw9zcHKVS6S2X6gjx+qDrOuvr62xvb5NIJNjf35desCZ3LizLIpfLUSwWSSaT7O/vs729TVdX14kHOKK72rw514VCgaWlJWKxGIqisLCwQHNzM8FgsOo2q6rHSyaT6LpOOp0mkUgQCoVO1KKVy+VreznnOlCZKxS5y0gkQnNzM+l0msbGRllBU20y+1ThKYpCZ2cnkUiE6elpfD4fnZ2d5HK5twoir/tF7KuOqHjWNI1QKMTg4CD5fJ5yuczAwAA7OzvyfzyohjOrU46Pj0mlUliWxdDQEMvLy2xsbJxIEoqzRYerizAw8DrG297eZnd3l/7+fnZ3d3nx4gXBYLA2MR7AxsYGmUyGzz//nMPDQxYXFxkYGMDtdssOiR1PtVtph/8elVcpDw4OSKVSxONxvF4vi4uLNDY2EolEqm7vzFtmuq4zOjqK1+slm80yMDBAR0fHibud7zrIdrh6iOINVVXx+/309vaytraG3+/nzp07+Hy+qu/NnJnHGxoaYmhoCF3X8Xq9jI6O0tjYiM/nk5eNRWecGO/qommaPJePRqN89dVXuFwujo6O+PLLL7l58yZut7s2pe+KouByuXC5XLS0tBAKhfD5fITDYT766COAE0cklfcAHK4Wotr6xo0bjI6OEg6HaWho4N69e8BrHYgSuWqsnmKfIlGRKhEZa13XCQQCHB8fc3BwQCgUksWBwgyL2M/h6iCqU4RUisUiPp/vxJ0TwzDkXetqNHCmNCutmcfjAV7n9jwej1wFl/U6okNtEGkzoQW/3y8LViuP0qotEIAzLJ6Dw3nhBGQOdcERnkNdcITnUBcc4TnUBUd4DnXBEZ5DXXCE51AXHOE51AVHeA514X8YVPQIpqCn3wAAAABJRU5ErkJggg==)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is a node is
![](data:image/png;base64,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)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
physics-General
physics-
Figure shows the shape of a string, the pairs of points which are in opposite phase is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVEAAACmCAYAAABjlrxXAAAgAElEQVR4nO3dd2BN5x/H8ffNkIQk5k+WXas1atRWIwhitkaK1h6xR2KrvQmKSGyiRlAjQa3airaiRhG0Nq2RkD3knt8f0bQqSNzce25yv6+/6txxPq3bz33uOc95jkZRFAUhhBDvxUztAEIIkZlJiQohhA6kRIUQQgdSokIIoQMpUSGE0IGUqBBC6EBKVAghdCAlKoQQOpASFUIIHUiJCiGEDqREhRBCB1KiQgihAylRIYTQgZSoEELoQEpUCCF0ICUqhBA6kBIVQggdSIkKIYQOpESFEEIHUqJCCKEDKVEhhNCBhUH2kpREkrk55gbZmRD68IKYiGgS33RvXI05VjlssZYPuckxQIlGsG9kf652X83gjwzT2UJkuKQ/uXJ0P4ELJ7M5ND91OrnxgWXyQ9r4J/x2OITis44zs76VujmFwem91bQPd7Jp12F+tzpNn2m1sdb3DoXQB/MCVG7RGYtLa9l2wwX3kVP5Itc/D8f/7MOSJ0nq5ROq0fMx0Rdc3xzEH3bZuR/8LT+E63dvQuibpaVlqtutKn1Jh8oyCjVF+i3RuJ/Y/OMHjJv2GU7PDrAp6B5ave5QCBXEnuHHkFw45pcDoqZIryX67MBGQqt0oL5rR1qXjOf0pkCuvdDnHoUwACWGR9d/4/Jvv3H54s/s813EjtvywTZV+itR7R2Ctj+nQfuyWFiUpV27Kpj9toVNP8fpbZdCGIQSxvWTRzh+9AjHjx7m2JkbRLzprL3I8vR2YunF5U3sTqrJWO097twGqrpSyWoGu9YfZGiN5uTU146F0DezAtTq2j/lxJK2jTMBP2Xc22u1Ws6FhPDTmVNcCw3lWmgojx79lfK4ra0tJUqUpGSpUpSvUJE6depibWOTcQFEuuipRKM5tfEEVgVrc3Br4MttCkXK5uHMgfXsuu9OJxeZ5y+yBjOH1nzeQLcS02q1nDt7lt27gtizexd/Pnz4xuc+fvSIm3/8wf59ewGwsclOg0aNaNaiJfXru0qhGpheSlT7ZC9bb7kyZu0QSv9rD/F1YznTZhWBW67hMaR0hu08NjaG32/c4Mb160RHR6dsz5/fgRIlS1KwUCHMzeWgv9ATM1vsbbXc37OVP2q35VP7tL/0WuhVAjduYPeu4FeK08WlAA3dGvNRmTKUKl0aZ5cCmJlpAAgPC+NaaChXr17hxLGjnAsJYVfQTnYF7cTGJjsN3dxo0649devVR6PRZPS/rfgPjaIoGXw05wVXF7Rnds5FrOjm8upB1xeXmd/MjUXPO7D64Bzq2r7fHhRFIfTqVXYF72Tvnj3cuH7trc/Pli0bn1StSvMWrWjctCl58+Z7vx0LE/eC8zMa0maZA5N+CaRT3n89cjuQEQsTGTnnSxzS8CMr9OoVvpk/jz27glO2ubgUwL1FC5q3aEn5jyukuQDv37/Hnl272LMriHMhISnb69arz8Qp0yharFia/w1F+mVsiWofcWbtNCbP3E5s3WEMHdCFZuVzvyzSaEL3LGHWhPkcemBOgQZ98R7en9bl0nZ09O/i3L0riD3Bwfz++42UxywtLfmgeHFKlCxFrlzJB6q0Wi0P7t/nWmgo9+/fS3mumZkZdevVp+OXnanfoAEWFnIVlUiDpNucXB9IwPLF7LuZjeL13KnkkPzZUeIecfnET+QZdpS1XZzeerb2+bNnTJ08kS2BmwCwsrLCo0Mn2rRrl67ifJP79+8RtGM7fr6LiXj+HEtLSwYOHkrfAQPfOMdV6EYPI9GMpdVq2bMrmMULF3D1ypWU7Xnz5qNps2a4N29B1WrV31qGz58/54cD+9m9K5hjRw6TmJgIgKOTE337D8CjQyesreVaKqFfhw4eYNQIbx799RdWVlZ82bkLffr2J7+DQ4bvKyzsKbNnTGfThvUAlClbDp8FCyn94YcZvi9TZ7QlqigK+/ftxWf2LK6FXgVeLc5q1Wu813HOZ+HhbPtuKxvWBXDjxnUAHBwd6T9gEB4dO2FlJVediIyVkJDApPHjWL8uAIAqVasxZ94CihQtqvd9nzl9Cu+hg7l75w4WFhbMmD2Xdh5f6H2/JkUxQo8fP1L69OyuFHZ2UAo7Oyi1qn6ibNrwrZKQkJBh+9BqtcqBfXsVd7eGKfupWuljZe3qVUpcXFyG7UeYtvCwMMWjzWdKYWcHpWSxwsqqFcuUpKQkg2aIjo5Svh4zOuVzviVwk0H3n9UZpERjY2OVfXu/T1MJ7tkVrFQo86FS2NlBKVPyAyVgzWolPj5eb9m0Wq2yb+/3StNGrikfshqfVFLOhZzV2z5F5vfkyWPlyOFDilarfeNzbly/rtSpWU0p7OygVKlYXrl44bwBE75umb+fFKkeGKRE168LUAo7OyhLl/i+8TlJSUnKzGlTU/6Sv+rgody/d88Q8RRFSS7T/Xv3ppRpyaKFlOCdOwy2f5G5jBs9Uins7KAcP3o01cePHT2ilCtdQins7KA0a9xI+fPhQwMnTN1SvyUp/49t3RyodpwswSAz3sPCwgCIjIpM9fHo6Gj69OiGn+8izM3NmTx1OmvXb8TZxcUQ8QDQaDQ0atyYnbv38lWXrsTHxzOgbx++meeDYpyHjYWKnj59CkBkZMRrjwWsXkWXTh2IiIigabPmbNm+AwdHR0NHTFVvz76MGTceAK8hg9i6OfAdrxDvovr8nnv37tKza2euXrlCzly58F++kho1a6mWx9LSkinTZ1K8RAkmfj2O+T5ziIh4zrgJk2TisngrRVGYMW0Ky/yWADB4mBeDh3phZmZcV+f17tsPgOlTJ+M9dDAAbdt7qBkpU1P1b/fsL7/Qyr0pV69coXjxEgTt3qtqgf5bl249WLkmAEtLS1YuX8bUSRNkRCreavHCb1jmtwRLS0sW+vox1Gu40RXo33r37ZcyIh3hNZTjx46qnCjzUu1veOeO7XRo9zlPnz6hbr36bAveTeEiRdSKkyrXho1YtmpNSpFOnzpZilSkat3aNfjMnolGo2HhEn9atv5M7Ujv1LtvPwYNHYZWq6Vf7578fuPGu18kXqNKiQZu3MDg/n1JSEiga/eerFy7Dnv7dFxwbED1XRukFOlyfz/8lyxWO5IwMkE7tvP1mFEAzJzjQ1P3ZionSrshw7xxb96CyMhIenT9imfhcvuJ9DJ4iW7etJGR3sMAGDt+IhOnTDX6Sy/ruzbgm8XJx7lmTZ+WchWIEJcuXWTooAEAjBk3Ho8OHVVOlD5mZmb4LPiGsuXKc+vmTUaPHC6/ttLJoCV65bffGOE1FICvJ06mVx9PQ+5eJ+7NWzB91hwARo/w5vs9u1VOJIzBUr8lJCUl0bf/wJQTNpmNjU12lq5cha2tLd/v3sXOHdvVjpSpGLREDx7YDySPQHv06m3IXWeIjl9+hffI0SiKwqB+nvx48oTakYRKIiOSpza9SEzki46dGDF6jMqJdOPiUoAJk6cCMH7MqLeuZypeZZASff78Wco/Dxg8JFONQP+r/8BB9OjVm8TERHp27cyF87+qHUkY2IP79/npzGkAKlauzLSZs7PE9Le27T1o5NaYiIgIhg8bIj/r00jvJRobG8OObd8BUKRoUYZ5j9D3LvVKo9EwdvxEPm/bjpiYGLp06ihnNU1IXGwsvXt0Iz4+HoBu3XtmmQW/NRoNM+bMJXfuPBw/dpRvA9aqHSlT0GuJKorCqOHePH70CAC3Jk2Ndt5cepiZmTFr7jwaNHIjPDyMPj26ERMT/e4XikxNURRGDvfi0sULZM+eHXjzfegzq3z5/seMOXMBmDZ5Erdu3lQ5kfHTa6OtXL6Mndu3pXzQstIyc5aWliz286dkqdLcuHGdSeO/VjuS0LPlS/3ZuX0bOXLk4JMqVdWOozdNmrrzWZu2xMXFMmzwAJKSktSOZNT0VqI/njjO9CmTgOQz21mRjU12Fvv5Y2VtTeDGDQTv3KF2JKEnR48cZsbUyQAsWLQEWzs7lRPp18Qp03B0ciLk7FmW+vmqHceo6aVE7927S3/PPmi1WgYOGUqJkqX0sRujULJUaSa+PKs5eoQ3d+/cVjmRyGi3bt5kYN8+KIqC1/CRNGrcWO1IepczZ07mzvsGgAU+c7l3767KiYxXhpdoYmIinj17EB4ehmvDRgz1Gp7RuzA6X3TshHvzFkRFRTGgr2fK7UdE5hcVFUXPbl2IiIigiXszBgweonYkg6ldpw6tP29DQkICc2fNVDuO0crwEvVbvIhLFy9QsFAhFizyzRInkt5Fo9EwY/ZcChQoyPlfz8kHLovQarUMHdifG9evUap0aXwWLMwSU5nSY/io0VhZWbFj23dcvHBe7ThGKUMb7srlyyxcMA8AnwULjfZ6eH3ImTMnC5f4Y2ZmxlI/X44dPaJ2JKEjP99FHNi/j5y5crFi9Vpy5MihdiSDc3EpQI9efYDks/Uyd/R1GVaiiYmJeA8dzIsXL+javSdVq1XPqLfONCpVroz3yOSFKIYNGsDzZ8/e8QphrK5fC2WBT/JUH1+/ZRQsVFjlROrpO2AgefLk5fSpH/nh5VWH4h8ZVqL+S3z57dJFChYqxIjRo195rEbNWhQsVIhP69TNqN0ZLc9+A6heoyZPnjxhwby5ascR7yEpKYmR3sNITEzkqy5dqV2nzmvPqe/agKLFilH5kyoqJDQsOzs7hnh5A8kLOcsx///IiHuMXL1yWfmgkItS2NlBOfXjyYx4y0zt6pXLShEXR6VoASflWuhVteOIdFq1YplS2NlBqf5JRSUiIkLtOEYhISFBqf9pTaWws4MSsGa12nGMis4j0RcvXuA1JPlnfOeu3aleo2ZGdHumVqr0h3zZpStarZYpE2VF/Mzk7t07zJo+HYBpM2djl8Xng6aVpaUlo8cmr4Q/f+4cIiNTv1+aKdK5RJf6+XLp4gUKFCzEyDFjMyJTljDMazj2OXNy7OgRDv9wUO04Ig0URWH0cG/i4mJp/XkbXBs0VDuSUWno5ka16jUIC3uK3+JFascxGjqV6LXQqykH32f7zDPJs5dvkjtPHoZ5J8+RnTxxPAkJCSonEu+ydXMgJ44fI0+evIyfNFntOEYnefGdCQCsWrGc8Jd38TV1712iWq2WEV7/HHyvWat2RubKEjp91YXiJUpy6+ZN1qxaqXYc8RaPHj1iysTkn6uTpk4jT568KicyTuU/rkD9Bg2Ji4vl23UBascxCu9doju2fcev50JwdHJi1FhZfCM1lpaWTJg8BYCF83148uSxyonEm4wfO5qIiAgaurnRvGUrteMYtd6efQFYu2pFypKApuy9SjQmJpqZ019eLz5uvPyMf4tP69SlQSM3oqKi5EomI/X97l3s3bMbW1tbpk6fZXJXJaVX9Ro1KVuuPE+ePElZK9iUvVeJ+i/x5dFff1GxUiVatmqd0ZmynHHjJ2JhYcGmDeu5dPGi2nHEv0RGRjJ+bPK85jFfT8DRyUnlRMZPo9HQ6+VodPlSf5OffZLuEr1//x5LlyQvjTV+0hT51k6DosWK0f3lPaXm+8xROY34tyWLFvL48WOqVK3GFx07qR0n03Bv1hxnZxduXL/GkcOH1I6jqnSX6Ozp04iPj6f1522oWKmyPjJlSZ79+mNlbc0PB/bL7USMxN27d1i5fCkAEyZPMYnFcjKKpaVlysBgmb+fymnUla5PzdlffmHnju1YWVszcrTMCU2PPHny0t7jCwBWLPNXOY0AmD1jOgkJCbRp156y5cqrHSfT+aJjJ+zs7Dh18gSXLl5QO45q0lyiyVffJE8B8ezXHydnZ72Fyqr+Xg3nuy2b5Uy9ys7+8gvBO3dgbW3D8JGj3/0C8RpbW1s6fPkVAMtNeDSa5hIN2rGdX8+F4ODoSJ++/fSZKcsqUrQoTZq6k5CQQMCa1WrHMVmKorwyIJCTSe/v77udBgft5P79e2rHUUWaSjQmJpoZ05LnO44aM47s2WVK0/vq5Zn8BRSwZjWxsTEqpzFNwTt38Ou5EPI7ONC7b1+142RqTs7OtGz9GVqtltUrlqsdRxVpKtFlfn789eeffFyhIq0++1zfmbK0yp98QqVPPuFZeDhbN29WO47JiYuNZea05DnOI0aNkQFBBujVJ/mLKHDjBuJiY1VOY3jvLNGwsKcs9VsCwPiJk+UMZgbo/XI0umKZv9yO1sBWrljGgwf3KVO2HJ+3bad2nCzhozJlqFS5MpGRkez9fo/acQzunY243N+f2NgYGjRyo3KVrL8ArSE0cmtM4SJFuH3rFvv37U3ZbuqTlvXt8ePH+C5MvoPluAkTZUCQgdp/0RGAwE0bVU5ieG/9FIWFPU1ZOGPIMC+DBDIF5ubm9OztCcBy/+RR/qkfT1K6eNFXSlVkrHlzZhETE4Nb4ybUqFlL7ThZSrMWLbG2tuHUyRMmd9vwt5bov0eh5cp/bKhMJqFt+/bkzp2HkLNnOfvzz/x6LoT4uDh+DQlRO1qWdPXKFTZtWI+FhQWjx41XO06WY2dnR/OWLQHYHLhJ5TSG9cYSlVGoftnYZKdzt25A8sLWQr98Zs9EURQ6d+1G0WLF1I6TJbX/ogOQvC6rKR3rf2OJyihU/zp37YaVlRX79+0l7KkscKsvly5e5MD+fdjYZKf/oMFqx8myqlStRpGiRXn44AEnTxxXO47BpFqiMgo1jLx589G2vQcAP505rXKarOubl3dd7dKtO3nz5lM5Tdal0WhSRqOBGzeonMZwUi1RGYUazt8nmEz52mN9+vcotJenp9pxsrw2bduj0WjYv/d7k7l9yGslKqNQwyparBhNmrqb1DEkQ5JRqGE5ODpSz7UBiYmJ7Nhu3As2JyQk8OPJEzpfIPBaia5YulRGoQbWu2//lH9OTJQb2mWUv0eh1tY2Mgo1II8OL+eMbtxg1HOfs2XLxtmff6ZS+TIM7t+XfXu/Jy4uLt3v80qJJo9CVwAyCjWkSpUr41KgAABXrlxWOU3WIaNQdbg2aEiePHm5euWK0R+mqlq9OrGxsezcsZ0+PbpR+WWh7t+3N82FqlH+9VXhNXgg323dgqOTk9y908B+/ukn7t65jYWFBc1btpKraXT0LDycQz8cxNzcnCbuzbCyslI7kkm5cP48N65fo1ixD6hQqZLacd5q29YtqW7PkSMHDd0a06xFS+rUrYe1tXWqz3ulRJs0dOWqjISEEOIVDd3cmD5rLvnz53/tsVdK9ML5Xzl29CjOsuCywf1w8AC7g4MAKFCwIEO9hsv9q97TvXt3mTdnNpaWlnw9cRK2tnZqRzJJDx48wN7eHltbW7WjvJGiKHgNGZTqYy4uBWjr4UHbdu0pWKjwG9/D4t9/KP9xBcp/XCFjU4o0+euvP9kdHISNjQ337t7FycmJmrU/VTtWptSrWxcAuvfsTeeu3VVOI4zZzh3bX/mztbUN7s2b07a9B9Vr1EzTYTWLdz5DGFT5jytw5vQplvotkRJ9D/8+Iy8LLot3+fHllVVVqlajbXsPmrVome6Rs5SokSlbrhwXL5zn6JHDXLxwXqaZpdOcmdMBOSMv3i0qKopChQtz5MQpihQt+t7vI6eAjYyVlTVduvUAYME8H5XTZC4njx/n6JHD2Nvb07f/ALXjCCNna2tL/4GDdSpQkBI1Sr08PbGxyc4PB/Zz8cJ5teNkClqtlulTJwPQb+AgcuXOrXIiYSqkRI1Qnjx56dpdRqPpERy0k98uXcTRyYmuL0fyQhiClKiR+XtWk4xG0y4+Pp45M2cA4D1iFNY2NionEqZEStRING7iTr36rjRv2RqQ0Wh6fBuwlnt371CqdGk+a9NW7TjCxLwy2V4Yl7Cwp9SqWoXY2BiCv98nZ+pTERERQZ2a1XgWHs7qdeup79pA7UjCxMhI1GhoefFC+88fk15gL6PRd/L3Xcyz8HBq1KpNvfquascRJkhGoqpK4P7xtSxdc4C72ZxxzJ0DCxIxy1OSQn/dwHLIdJrbhMto9A0ePnhAvdo1iI+Pl/82QjUy2V410fy6pCt9VlnRZ9UKJpe3f7ldy9PTc/HsHULNblryuCSPRv18F7Fgng8r1wSomtqYzPeZQ3x8PC1btZYCFaqRkahKok6Mo+WX31F81mH8PRz/c1wliVurhrO1zEy8q2V75dho0J69sr4BEHr1Ck0aumJubs7h4yffukCEEPokx0TVoP2TYP9N3MpRl5bN/lugAOYUadudxnmTH/n3mfpJ479Gq9W+9oqsKDExkaioqNe2JyUlMWq4V8otkKVAhZqkRNUQe5rjZ6MwK/Ihpd80pdG+LOWK/3O0pd/AQfwvf37O/vIz323ZbJicKuvyZQca1vuU2NiYV7avXL6McyEhODk7M9R7hErphEgmJaoC7bNHhMWCxtYe+zQuGWpnZ8fXEyYBMH3KZJ6Fh+sxoXG4HhrKnw8fEh0dnbLt9xs38Jk9E4BZc+dhZydrhQp1SYmqwCyHHdnNQYmLJiYdR6RbtGpNzdq1CQ8PY/bL1YpMSVJSEsO9hhAfH49Hh47UqVtP7UhCSImqwq4iFUtZkvT7JS5Hv/vpf9NoNEyZNhMLCws2fLuOcyFn9ZfRCK1euYKQX37B0cmJseMnqh1HCEBKVB3mJWnTpSG5nx9i47bbpHbH+YSb+9j98/PXtn9QvDie/ZJvsTxu9EiTuV/9zT/+SFkrdOYcH+zt7d/xCiEMQ0pUFWY4t5vBzE5O/DKjO2M2nefpi78f0/L8QiCLdyZRvlLOVF9tnzMXkLyobGJiomEiqywqKpLExEQ0Gg329qn/dxFCDTJPVE3aZ1zauojF337Pb89y8D8nJ/Lny4NzxXZ4dqtFfvM3v/SHA/vp0bUztra2HDr+Y6p3IczsqlQox+PHjxnmPYJ5c2fj4OjI/kNHyZlTSlQYDynRTKxXty4c2L+Plq1as3CJv9pxMtzfJZrNyoqE+HhWBXyLa4OGascS4hXycz4TmzBlKtbWNgTt3EHQf+5amBVoX36/J8TH07a9hxSoMEpSoplYgQIFmTR1KgCjR3hz5/ZtlRNlHEVRiIyIBKDYB8WZNNX0pnSJzEFKNJNr/0VHmrdsRXR0NAP7eWaZE01+votISIgHwGfBN+TIkUPlREKkTko0k9NoNEyfNYcCBQtx/tdzzJ01U+1IOjty+BCzZ/wz8ixYqJCKaYR4OynRLMDe3p6Fvn6YmZmx1M+XY0ePqB3pvd2+dYtB/TwByC6jT5EJSIlmEZUqV8Z75CgAhg0awOPHj1VOlH7R0dH06t6ViIgImrg3I3v27GpHEuKdpESzEM9+A6j16ac8efKEYYMGZKol8xRFYYTXUK6FXqV4iZLMnf8NaVybRQhVSYlmIWZmZsxf6EvevPk4fuwoC+fPUztSmiiKwvSpk9kdHISdnR3LV63B1tZW7VhCpImUaBaTP39+vlm8BI1Gw4J5c9kdHKR2pLdSFIUZ06aw3N8PS0tLFvsvo2ixYmrHEiLNpESzoNp16jB+0mQAhg0ZxMUL51VOlDpFUZg5bSrL/JZgYWGB//KV1K1XX+1YQqSLlGgW1bV7Tzp0+pL4uDi+6vgFZ06fUjvSKxISEhjp7cVSP9+UAm3QyE3tWEKkm5RoFqXRaJg8bQaN3BrzLDycTh7tCNy4Qe1YADx9+oROHu3YvGkD1tY2LF2xioZujV97XuEiRcmXLx92drLsnTBesgBJFpeUlMTsGdNZ6ucLJJ/BHzlmLBqNOue+b/7xB1918ODevbs4OTuzYnUAZcqWTfW5UVFRaLVaWTtUGDUpUROxJXATo0d48+LFC3r27sPY8RMNXqS3bt7Eo+1n/PXnn1SsVImlK9dkySX8hGmREjUhh344SJ8e3UhMTKRXH0/GfD3BYEV65/Zt2rdpzZ8PH1KjZi1WBazDxubVyfQJMRHEJv7zcdRozDHPZk0Oa4v/vp0QRkNK1MQcOniAPj27k5iYSL36rsyc44Ojk5Pe9qcoCju2fceEr8cS8fw51WvUZFXAOrJn/+8lnXHcObWboBWzmL/3AY41PXCvnBezyAeEnrtMRKHG9Bo+mKYfWOstqxDvRREm5/ChH5SPy5RWCjs7KGVLFVc2bVivJCQkZPh+7ty5rfTo+pVS2NlBKezsoPTs2lmJiop662vijo9UahUsqvTZHv3PxqhzysJWxZUPqg1V9j9NyvCcQuhCzs6boHr1XTlw+BiNmzQlMjKSkd7DqPxxWYYPG8Kxo0dQdPhx8vjxY1YsW8rnLZvxafWqHNy/H/ucOZm/cDHLVq1555J2GisrLP+7MUcFOneqieW9IL47GvPe2YTQBznYZKL+97//4b9iFcE7d+Dnu4grly+zJXATWwI3UaNmLSZNnUbJUqXT/H6PHj1imZ8v6wLWEh8XB4CNTXaaNmvGqDHjyO/goENaLVERUSRhQTZLuaJeGBcpUROm0Who2fozWrb+jD9+/53du4JZs3IFp348SdNGDfi0Tl0+/KgMJUuVSvXmcBEREVwLDSU09Conjh9LKc9Gbo35vF176td3xdrGRseUCTw5u44py85gVWEQXVxleTxhXOTEknjF8+fPmTdnNgFrVqX7Z30T92YMHurFhx999N77T/h5Ao3brCDqo0bU/DAnSth1Qk6f5y/bTxn4zQL61XaUb35hVKRERaoe3L/PhQvnuR4ayvVrocTEvn4s0sYmO8WLl6BkqVKULV+eggV1X4E+uUTXUWrhJfxbJ0+B0ob/SsCwbkw5BI19drKobSHecjdpIQxKvtRFqpxdXHB2caFJU3e1o2CWuwJfTezFrsOT2b9qG398NoQS0qLCSMjZeZEpmNvlxM4c0GqR307CmEiJCqOixMWT8N+N2jBO+wVwOiEXNTxa8YH8fhJGRI6JCiMRw40j2whaPR/fgw/JWaomFUs4kNvmBWE3Q7kV70KtTsPw6lSZXPLVL4yIlKgQQuhAvtOFEEIHUqJCCKEDKVEhhNCBlKgQQuhASlQIIXQgJSqEEDqQEhVCCAXc+MMAAACOSURBVB1IiQohhA6kRIUQQgdSokIIoQMpUSGE0IGUqBBC6EBKVAghdCAlKoQQOpASFUIIHUiJCiGEDqREhRBCB1KiQgihAylRIYTQgZSoEELoQEpUCCF0ICUqhBA6kBIVQggdSIkKIYQOpESFEEIHUqJCCKEDKVEhhNCBlKgQQuhASlQIIXQgJSqEEDr4P8eOEu+d0KnqAAAAAElFTkSuQmCC)
Figure shows the shape of a string, the pairs of points which are in opposite phase is
![](data:image/png;base64,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)
physics-General
physics-
In the circuit shown L1, L2, L3, and L4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. Assume that the voltmeters are ideal. If L3 were to burn out, opening the circuit, which voltmeter(s) would read zero volts?
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)
In the circuit shown L1, L2, L3, and L4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. Assume that the voltmeters are ideal. If L3 were to burn out, opening the circuit, which voltmeter(s) would read zero volts?
![](data:image/png;base64,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)
physics-General
physics-
The potentiometer circuit shown is used to find the internal resistance of the cell E. At balance, the galvanometer pointer does not deflect, and NO current flows through
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)
a) the potentiometer wire PQ
b) the resistor R
c) the galvanometer G
The potentiometer circuit shown is used to find the internal resistance of the cell E. At balance, the galvanometer pointer does not deflect, and NO current flows through
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Xodrslyx/sWDHadKHWT2UeaqJONIz5zBnqTmlV6/jx47h06dKglkAHWRRFVFVVBYVHZ7FYsG/fPkRHRwPwLszIQT1XTU2NZOmB4r0HC2O2dFrY0Ov1mDp1Kurr61FfX//YdfIBI4Sgvb0d6enpY5d4DFAoFHA4HKiqqpIoxHKq1EB5WZaFIAjIzMwMCHki2BjTmTOU9apQKJCTk4Pdu3f73OslZ4YwDIMff/wRtbW1I76fv/jm6enp+Pjjj5GYmCjF9sHW9ANjfnJyssT6DReM6fBAujmALndSUlKg0WgGLYHSRI72nqOjo71q50OB9tNpL3msiqcyT5s2DWazWVK4r4kqX57JWTThgjEfHghAOqdNp9P5JEbSySHfTTIUP15eGu3t7cXevXsRExODXbt2SUsmmmGPVBGUkBEREYHIyEivZdZwfIGRTtCJhCfK3kfi8uhgyZdsFL5+ps+UBTt16lRwHCc1RnieHxVvTc7gHargM1Dm4a6bqAjpQCWPrzQ3oKyaUDjFeaIipJUO/MdscTgcsNvtT/3Xa/kDQam9C4IAp9OJvr4+r1LnwFhKWaI8z6OsrAwOhwPr16+XDuwfaVynrdBJ9GPc+uny9Xp3dzeuXLmCuLg4r2IOXT/TQk5PTw8ePnwInU6Hmpoa3LlzB5GRkTAYDENm3gPR0NAgvaZZeTgdJzJaBFzpNBbTwY6Li0NUVBROnz79mJumpVE5SeLevXtIS0sDz/P4999/cfjwYURGRnod1i+vow+mdJvNhhkzZnj9/WkOE+NOl1qyZAlmz57tsxtHwfM8nE4n9u/fD5ZlodPpkJeXh61bt0Kn00lLQMpApaybwVYUhPSfUh0VFRV2JdWxIKBKl3e1aNk2NTXV58nM8t0zhBBYrVapDlBcXIyCggIUFhbCaDRK19GjOuTHaPuSg1KpaC/+aXXxAVX6YIUa+RHhg3XK5O6dFlEiIiKQn58v/Y/L5fLa2CDvqw+mdFoVpDI87Uu9gLt3OXlCHkN9JWF0Z6y8M0e/87yzsxN//fUXnE4n9Hq9tCVpxYoVMBqNQ3LgBpZew6mWPloE/JOzLCspeyBjZuCDJnLyY77kJdOuri4cPXoUJSUl4DgODQ0NuHPnjte3NA33/vSZnqjxNGJcErnBqFG+rqOb9Kli4uPjpa1LTU1N6O3txZo1a8AwDJYtW4aUlBSpRz4U4WLgyRlPM8Z1qg+nfErKoBaoVquxbt06rF69GoIgoLW1FQqFAq2trfj111+hVqthNpsltz0cI2dS4f0IKTasvHBCCIFOp8PKlSsBAC0tLbh48SIWLlyI3NxcdHZ2IjExEYIgQKVSDUlpmoQ3QmqU5A0WAFJXjZD+b3js7e1FfHw8iouLsXjxYvz999948OCBdGCPv48jCVeElKXTbH3gd6c9evQIFy5cgMFggMFgwN27d1FVVQWO4/Dss89KS8FJ9z0yhJTS5Rk28J/lW61WqUDT2dkJm80Gl8uFVatWSc2XYH9v6kQCQ0K8UkEP2pGzb+jpEXq9XtpESGP6RDqmNFgIeaXTgg0tm8r3jdMw4PF4pAx+ou02CQYmhFnQpRzwH2eN7j+j8XxS2SNHyFv6JPyPycznKcSk0p9CTCr9KcT/AQBNh7Ukq8wKAAAAAElFTkSuQmCC)
a) the potentiometer wire PQ
b) the resistor R
c) the galvanometer G
physics-General
physics-
In the above circuit, C denotes the balance position on the potentiometer wire AB. Which of the following procedures can shift C towards the end B?
![](data:image/png;base64,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)
a) replacing the driving cell X by one with a smaller EMF
b) adding a resistance in series with the galvanometer G
c) increasing the resistance of the rheostat R
In the above circuit, C denotes the balance position on the potentiometer wire AB. Which of the following procedures can shift C towards the end B?
![](data:image/png;base64,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)
a) replacing the driving cell X by one with a smaller EMF
b) adding a resistance in series with the galvanometer G
c) increasing the resistance of the rheostat R
physics-General
chemistry-
Identify Z in the following series ![](data:image/png;base64,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)
Identify Z in the following series ![](data:image/png;base64,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)
chemistry-General
chemistry-
Which does not give iodoform reaction?
Which does not give iodoform reaction?
chemistry-General
chemistry-
Which one of the following compounds when heated with KOH and a primary amine gives carbylamine test?
Which one of the following compounds when heated with KOH and a primary amine gives carbylamine test?
chemistry-General
chemistry-
The well known insecticide – gammexane is one of the steroisomers of hexachlorocyclohexane. The reagent useful for conversion of benzene into hexa chlorocyclohexane is
The well known insecticide – gammexane is one of the steroisomers of hexachlorocyclohexane. The reagent useful for conversion of benzene into hexa chlorocyclohexane is
chemistry-General
chemistry-
Ethylene dichloride and ethylidene dichloride are isomeric compounds. Identify the statement which is not applicable to both of them
Ethylene dichloride and ethylidene dichloride are isomeric compounds. Identify the statement which is not applicable to both of them
chemistry-General
physics-
The coordinates of the centre of the smallest circle passing through the origin and having
as a diameter are
The coordinates of the centre of the smallest circle passing through the origin and having
as a diameter are
physics-General
chemistry-
Which one of the following formulae does not correctly represent the bonding capacities of the two atoms involved?
Which one of the following formulae does not correctly represent the bonding capacities of the two atoms involved?
chemistry-General