Physics-
General
Easy
Question
A source S emitting sound of frequency 300Hz is fixed on block A which is attached to the free end of a spring SA as shown in figure. The dectector D fixed on block B attached to free end of spring SB detects this sound. The blocks A and B are simultaneously displaced towards each other through a distance of 1.0m and then left to vibrate. The maximum and minimum frequencies of sound detected by D, if the vibrational frequency of each block is 2Hz are Velocity of sound v =340m/s)
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LIkSMRHx+PmzdvwsnJCWlpaS9UD16KMAwjts2ePXuQn58PT09PpKam9rVp3aJfhCvZ2dnQaDSYN28eWJaFQqGAr6+v0bFuT6FfbmrKCQ/973bqab+c2dTvTebk5KCyshILFy4UQzxfX1+Tld8T9AuRh4WFQRAEpKWlgeM4REdHY8aMGX26roQQgt9++w0FBQWIiIgwWbk8z+PixYu4evUqAGD48OGoqqqCnZ0dFi9eDIVCYdJh1VmzZoEQgtTUVBBCsGTJEoSGhpqs/B6BdIFarRZff2t/qFQq8fWqnjp4nu/xPI21IyQkhIwaNYpoNBqi0+lMVq5OpyNeXl5ky5YtRKvVkvz8fOLv709CQkLEV8ikdujv29vb26De1Gp1V3LtlH4Rk7emv8ThOTk58PLywr///otDhw6Z7KmiXxRlZmYGa2trEELg5eWF0NBQ5OXlDYhVkz1NvwhX+hOCIECr1eLAgQP49NNPUVNTg6SkJERERJh8v8GsrCzY2NiIk0XffPPNC7Egqr/RZY3pXzJuz4u2fuFZ0e9HXlFRgZMnT8LFxQWVlZVISUkRf9rEVISGhmLNmjVIT0+HWq3GihUroNFoTFa+qelqua6xeuvSk0+ePFl8ta19r1+lUvX5CEhPw/M8Dh48iPT0dDg5OYEQgrKyMiQmJmLp0qUmm84mhEAul0Mmk8HJyQnTpk3DiRMn8Pjx4w6vmEkBhmEgCAJmzJhhcHIsICDAqLy7FLmxm2G+aAiCgObmZsTHx+PGjRuimPT7k58+fRoffPABdu3aBTc3t16zg+d5nD9/HtXV1fjhhx8gk8mg0WiQkZGBtWvXYvTo0b1Wdl9jbm6OL7/80mC6sf2RLn+sdqB0dIT/f/Wq9VJSuVwOQkib7S1Ylu3VITytVgug7ZYfrdtAv4fNQMWYqIGKnPJCYYzIB65LoAwYuozJpdSppAxMqCenSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcorkoSKnSB4qcork+T8YL3PE1Z7EFQAAAABJRU5ErkJggg==)
- 378.6Hz, 223 Hz
- 323Hz, 278.6 Hz
- 178 Hz, 276 Hz
- 420Hz, 220 Hz
The correct answer is: 323Hz, 278.6 Hz
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physics-
A sound wave of wavelength 32cm enters the tube as shown in the figure. Then the smallest radius ‘r’ so that a maximum of sound is heard at detector is
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)
A sound wave of wavelength 32cm enters the tube as shown in the figure. Then the smallest radius ‘r’ so that a maximum of sound is heard at detector is
![](data:image/png;base64,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)
physics-General
physics-
Two stereo speakers are separated by a distance of 2.4 m. A person stands at a distance of 3.2 m as shown directly in front of one of the speakers. The frequencies in audible range for which the listener will hear a minimum sound intensity are (Speed of the sound in air is 320 ms-1 and n is order of minimum)
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)
Two stereo speakers are separated by a distance of 2.4 m. A person stands at a distance of 3.2 m as shown directly in front of one of the speakers. The frequencies in audible range for which the listener will hear a minimum sound intensity are (Speed of the sound in air is 320 ms-1 and n is order of minimum)
![](data:image/png;base64,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)
physics-General
physics-
In the given arrangement, if hanging mass will be changed by 4%, then percentage change in the wave speed in string will be
![](data:image/png;base64,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)
In the given arrangement, if hanging mass will be changed by 4%, then percentage change in the wave speed in string will be
![](data:image/png;base64,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)
physics-General
physics-
The vibrating of four air columns are represented in the figure. The ratio of frequencies ![n subscript p end subscript colon n subscript q end subscript colon n subscript r end subscript colon n subscript s end subscript text is end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG4AAAATCAYAAABx5zjkAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAihJREFUeNrtWM9HRFEUHskYI5GMJIkk8x+kRdq0GCNJJCNpMWS0aDUkSas2rTK7tMhsR1q0aJsWI5GkRTIkaTlkjGQkpu9whnG9Oz9e585783ofH9Np3vnOvefcM+e+QMCHm1D1t8BPnA+3Yx9Mg0PgKfgFfoBbwtXTTTqdWoNObxy8Yv9VXTw5FqZAZsEecASsgGHBDe0mnU6tQad3By40e6gAbljYqZIGBU+2F3RM+VYTRydtoNEDVDGfFvZeflgKXtAx6VtN3CKYBxO6B6a4l6qY1tjtwgs6Jn1bteY+8AR8AifVfya4X7dqtwsv6Jj03eg6sAPeq8YMmLT4ss5uF17QMem72qRFf6vGczBu8WWd/Rlc4Qoogbc8VTULol0dwjb4Dpa56mgwGBXWofXMc6ur1K1Fwvcc+Aj+sL8Rm4lLWrVimoZCmikpZJF5CuKgLghqE8ctBNGODmEX3OTPNGbv8cZK6tTWQ78jEwZ8F8Exmyeudnej+C7B4b/+OF8rthhXnCQifLpMDjG19eQNvdQIcqEtueENC7XIrOHhopFOVljHROz1WOfTeAP2O5m4I/BQsWV5oyWR4lapDgApYZ2M5jItCRrpH8BlJxNHLfEFnOG/o+ArtwXpE3fGn6lS0zykxA2sJ254zyJ8D4s6mbgiB1DgFnBhdTEUevuR47cUVBhrrBcW1tENGxIo8XDxBq46mbQgB+OUdjngwxZifAr+m7br8At7Xrpgt5UQUQAAAPh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+bjwvbWk+PG1pPnA8L21pPjwvbXN1Yj48bW8+OjwvbW8+PG1zdWI+PG1pPm48L21pPjxtaT5xPC9taT48L21zdWI+PG1vPjo8L21vPjxtc3ViPjxtaT5uPC9taT48bWk+cjwvbWk+PC9tc3ViPjxtbz46PC9tbz48bXN1Yj48bWk+bjwvbWk+PG1pPnM8L21pPjwvbXN1Yj48bXRleHQ+JiN4QTA7aXM8L210ZXh0PjwvbWF0aD4nmC6MAAAAAElFTkSuQmCC)
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)
The vibrating of four air columns are represented in the figure. The ratio of frequencies ![n subscript p end subscript colon n subscript q end subscript colon n subscript r end subscript colon n subscript s end subscript text is end text](data:image/png;base64,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)
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)
physics-General
physics-
A ‘pop’ gun consists a tube 25cm long closed at one end by a cork and the other end by a tightly fitted piston as shown. The piston is pushed slowly in. When the pressure rises to one and half times the atmospheric pressure, the cork is violently blow out. The frequency of the ‘pop’ caused by its ejection is (V = 340m/s)
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)
A ‘pop’ gun consists a tube 25cm long closed at one end by a cork and the other end by a tightly fitted piston as shown. The piston is pushed slowly in. When the pressure rises to one and half times the atmospheric pressure, the cork is violently blow out. The frequency of the ‘pop’ caused by its ejection is (V = 340m/s)
![](data:image/png;base64,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)
physics-General
physics-
A source of sound is travelling at
along a road, towards a point A. When the source is 3m away from A, a person standing at a point O on a road perpendicular to the track hears a sound of frequency ‘n ’. The distance of O from A at that time is 4m. If the original frequency is 640 Hz, then the value of n is (given velocity of ![text sound end text equals 340 m s to the power of negative 1 end exponent text ) end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJcAAAASCAYAAABW4kwSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA15JREFUeNrtWV9kW1EYj4mImRF5iJgYUzVVUaYqZiZMzURNmaqZqtKHqdlbVc1epw8zfRhV04e9TVQfpsZUVO0h1MzMVKjZw0xeYvYQV4TsO/wyZ9/OOTc3N7m50vPjp73fvefec7/zO9+fm0jEwsKMUeIT4ifrCote4zVxmdiyrrDoF9zE9Yz40LrJoh/iEvhAzJ6FF/WLPHGfWCc6xArxBTHpMq5gmN9F4ktiGdyCbRD+09GPz68Rj6y43FEizhJjkm2C+M4w5gLxq2F+B8QZJsSDIfP5EURmxdUFfhvOiUi0pJnfPeKmwi6i4fwQ+fwR6q+/uIKdWjeExwJ2ZQN/ZzxMoKU5Fg4/Rdo5JGYUY2+iDW7g2sUBikv46URz7roUhVTzKxKnNem3yGxPiavEFARZJf4k3sH5BPE5sQaxr7Hx68TvxCbmshqguHI8Gh9rxNLGFBZ2HMfjOM75EJcQ1gbxMmyLEJiMqxBy+7ljWIiWR6e40Q0pzK8iLbAMkTo/S++iumeNpVh5bJXZ3kBgx4hqUdz7GzENP83BnsHmTEnC2tY8q1f1mQkxHt3r2A06FBG5eCTb8yGuPLOdQ3SS8UqTMoKKXNypjw1t+IrL/JqG5/D3rmD38zX5AeGo7GmpY7s14BT6z/vcxaTmDXVGzE2hXaRFt+tEKoiHoOZKwEdlpGkZWfgu4kNcDttkYrOfV2w+k12u7T66ZKJAxdXudLaRhkY7XMxGn8XV7EFB34u0KPuozGzieKSD+VU1qSrO0uIU6l9VadKpPY2urYQ5B4mYqelZg/LDELkc7MwwdYuOR/HKpcVtxf2mWUEvsseO4jqv9jjqwAcB+ydn+ryiqn2KijAr0sSuItJwMWz6EFcJXZiM5ADFlUU91E1nNYvMwLHDyhHhr2XFdV7t7Zr1fsA+WkGjpsSSIsxOojsck5x8qlh40cUs4P8RdD1zPsQlQv574iWItoD6JghxHaJ+ieLZeXRrCz7a9hKagigi/7qiQ97VdKRe7ZMocZIBi+u/j6jtEC4iz77UefDu8ARR7QsiF0cGzmogNOZ8psUI6r89pCMhrImAxHWD+BbPdSCMgs9vQglEEwdF+JaiJqppmphO7L+kdSzhU06QGIqffyzCiaH44doifNjgtd8fCVshMO2rGo4AAADUdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG10ZXh0PnNvdW5kJiN4QTA7PC9tdGV4dD48bW8+PTwvbW8+PG1uPjM0MDwvbW4+PG1zdXA+PG1yb3c+PG1pPm08L21pPjxtaT5zPC9taT48L21yb3c+PG1yb3c+PG1vPi08L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtdGV4dD4mI3hBMDspPC9tdGV4dD48L21hdGg+1tZL/AAAAABJRU5ErkJggg==)
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)
A source of sound is travelling at
along a road, towards a point A. When the source is 3m away from A, a person standing at a point O on a road perpendicular to the track hears a sound of frequency ‘n ’. The distance of O from A at that time is 4m. If the original frequency is 640 Hz, then the value of n is (given velocity of ![text sound end text equals 340 m s to the power of negative 1 end exponent text ) end text](data:image/png;base64,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)
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)
physics-General
chemistry-
Faraday is equal to :
Faraday is equal to :
chemistry-General
chemistry-
0.1 ampere current is passed for 10 seconds through copper and silver voltameters. The metal that is deposited more is..
0.1 ampere current is passed for 10 seconds through copper and silver voltameters. The metal that is deposited more is..
chemistry-General
chemistry-
1 Faraday of electricity will liberate 1g atom of the metal from the solution of :
1 Faraday of electricity will liberate 1g atom of the metal from the solution of :
chemistry-General
chemistry-
During electrolysis process of fused CaH2, H2 is liberated at :
During electrolysis process of fused CaH2, H2 is liberated at :
chemistry-General
chemistry-
Assertion (A): Carbon exhibits catenation to maximum extent.
Reason (R): Valency of carbon is 4.
Assertion (A): Carbon exhibits catenation to maximum extent.
Reason (R): Valency of carbon is 4.
chemistry-General
chemistry-
Statement - A :Carbon has two unpaired electrons in its ground state.
Statement - B :Carbon forms 4 covalent bonds in all its compounds.
Statement - C :Carbon exists in ground state in all its compounds.
Statement - A :Carbon has two unpaired electrons in its ground state.
Statement - B :Carbon forms 4 covalent bonds in all its compounds.
Statement - C :Carbon exists in ground state in all its compounds.
chemistry-General
chemistry-
The end product ‘Z’ in the following reaction,
is
The end product ‘Z’ in the following reaction,
is
chemistry-General
chemistry-
Identify Z in ![](data:image/png;base64,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)
Identify Z in ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATMAAAAfCAYAAACLQSqnAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAqDSURBVHhe7Z1Ji9VOF4fLdy+On8BhIQqKOIDDQsEBV+5UdCEoigOCirMuBFEUdSE4gYILZxE3tiiCLnThCAq6csCFuHL+Av3mqc6v/8d0cm/SN0l3364HiuRWkhpPnZycSuoO6YxwgUCgm8WLF7sHDx64J0+euDlz5sSxA5enT5+6uXPnukWLFrn79+/Hsc358eOHmzlzpvv48WMc07/5X7wNtCH37t1zQ4YMcW/fvo1jisP1hGPHjsUxXYM9GZcFA2Ljxo1u5MiR/prp06f7wSWUFkHoN8eqhLKRz/nz5+OYLq5cuRLvNadZ/eqEfl6+fHl3+40bN87HoZD37t0bn5Wfhw8fumXLlvl9pak+oY6KK0MOSgHLLNCeRHfizrFjx3ZGghzHFKejo8OnMWLEiM5Pnz75uO/fv3dOmzbN7zeDMkQDwl9D2LBhA08C/6TFb/IR7BPHsSo5evSor1taXcg/ssziX9k0q19dkDd9RP4qC+VSHagrZS0C7aJ6pPUJclWWHJRBUGZtCkKM8Jw7d84LuUWCjjBxDIFE2NMgHQmiHQx23won6UkxvXnzJlVgOcfmxzlWcbBPXJVQZhSZysjWkixTGnnrVwf0M/XJoqgyo05WUaX1Sd4062qn8JjZply9etUtXbrULViwwP369cs/copNmzb5bTSg3YcPH/zxZpw+fdq9ePGixyMZrFy50k2ePBlJdwsXLnSnTp3y8c+ePfPbMWPG+K2YMWOGe/ToUfyrC3w6emxhv2p4hKKslDtSAu7mzZvxkfwUqV/VPH782D9WlgXts3bt2vjXf6iPCLt27YpjG1NXOwVl1oZ8/vzZXb9+3ftPEKDoDuvu3r0bH3Xuxo0bbvPmzW7UqFE+2EHAtQhqEs47cuSI27Nnjz/HglN5/fr1fn/q1Kl+C3/+/In3ejJ8+PB4r4vozu+VIYH9qtm/f393mSOr07dJFihw2oh2Yav656kfNxH8Q7q2Ff9lI37//h3vNYfyW99ams/rwoUL/kaYRH1EiKyqOLaLVtqpDIIya0OOHz/urS0J66tXr9zZs2e9E7YZKD8ENQ0GP3dT0rcwYHEM49y1d+tZs2b5bVL5MTs2b968+Ff9oOijRx43ZcoU3z6HDx/2v631arlz5447dOiQb5fo0ch9+/bNx+ep37t377wFyLVsmSWtgvnz5+eedaT81BfLvKOjo4d1hMLl5pW0pJrRSjuVQpRxoI3AP4Evwvp75O/ArwL4QvCBAcca+S7wf1nfCX4Pzre+EtKWnwzfmT1fDnb5S3Aacz0+K2Brrwf2idM5ZUKalMfWlzjKpDZJKxMQzzm2XM3qJzhOmyV9c2VB+pRZ9VJZJQdZznpk4tq1a/GvLjg3GZfWJ1lpttJOrRCUWZuBwCkIBpHiEG4GFMLFb4SK41nKTNfZ4wwAq8yUPluO2fMRXgRb6bBvB7Qtm9Bvm0dZ2Pw00Cmr4thPKxP10EyhpVn9QOmTblXKDFA46lcCyoP8dDMjJPsxqbSANJL11PXqk6w0W2mnVgnKLOCFHqUWSIeBqQHKoLSDtxmcK4uYNBjE/QGUmBQZ5RIomN6WsZV2KoOgzAY5CJzulrJUAv/CAFUbEYoMUhQGj1Nch8VTpWWWFxSNrQ9BUNc0ay0PrbRTGYTPmQKBQDfMQg6Uz5eSBGUWCATagqavZqR978U3VprmZ1/H2BdMfyue64uQ/I6LLWnoHR2bNuURHLfXFIX3bfSeDIHXDTRdn0xbZQF7jY1vhK2DDaS1b9++XK9RDGZsm9OWYPvIysVAwY4zZEBYWbFjrN1hPKreyZDav1hmWfB8z/O+nHogH4v1r+BATpt54jquLwL5kJ6dxtXMiX0Gx2GdVnye94kv6ptQWVUv8sbHYeul6emkb0k+CDl685KsA3VXXN3+hoEGbUX/ECz0I2GgoplUjTdBPYvK10CHMUC9bVtoDCZfm4GGyixNWIA4O6DpgDRlRmHS4huBIFJYKTJBvB3g7FtFIKT4iiAFmHR88tuWX2knlRlkxTciqw7EFW23wYj6Q4OcG1hS+AcayD03VSvr1G8wygNtYMekbmBZbZE56hEMKyiNIPG0DChM0U6gI/NMDZepzMgvjwVZhzKjw4jTqxKyjonjmCy3/ijcCF7yhlA16jvaBmu+aB+URZl1l1yg2DSAkzf3voby1G0B23ZJI9Nnps8uJk6c6Ld1wPpGfIZjv++rA77L4zOdvobPPfgIPBqUbtu2bT6OD6EvX77s9w8cOOBmz57dq7Wp6oBv+U6cONHtw6oDPoCH8ePH+8+F+moxxTLrvnPnTv/xO/2MPPCJUNFPi6pG5anLh8fY4FO5SKFlt0Ws1HogLZjnToeVwLlpoYgFIcuHvJuh8mWFInB+nnKqfFmht5aZDWl3YeWb5ifob8iSrNNCk7VatP3Lpsy6q8/7y0u2acgarsNCY3w2cyGU9qF5lBka5J+AFq2aZJ6REMRHqoM8kvm2gtKIlJhbt26dvyunffS8ZMmSeK9a0maP8gY+3sa6XrFiRZxatTDri2WNNbt69eqWZ4HT6pQ3lFl3WZhVP6XYlX6LhtGjR3cvYlDl6rqMBZ4UWVqKD+CzyFRmkyZN8tuvX7/6bVlglmpana19lWHChAl+++XLF78ti+SrHnbaGxgIVbwoaF/1QGiaDTTMZz1iaE2wvsAq6aIhsk78igmRdRKnVi08hu3YscMrtJ8/f7qTJ0/GR3pHWp3yhrrrXgYs35RWlzwhspL82Ikss8oe7xkzW7Zs8cZSs5t5pjLjjwzg0qVLfmthgPZWE+NTuH37dndDsEaWQOsSxznJgY8yyrPWeBoXL170W4Q9elTzS77Y8uNrwSpK1olyaM3zopDWrVu33PPnz33aLGyocrQr9BkL+p05c6bwu4W9gTs2bcvSRNwIdu/e3aNv66LuuvcH8OGyVht1rgrGDH1s86CtMRCSZCozFAsOSMw7rS5KIlg1JG5JKh7BomwMYgsKBac26WOBYC1ZDh486E11GkrpolQwZS1ZC779/fvXb63Fh7WjxpB2Hzp0qN/CmjVr/B1169at3WsuMSBYwM+itJOonO/fv/db4E718uXL7nWhmGAYNmxYfLSLZB1IB4VN+7I+lZB1nPeF3L6C1Um3b99ey2CmLVatWuXlRdDP6scsmayKsusuOWy0sGFfovJVqciynP6NjILIYswGJzWON84jRJaTd7jKEaf3wgjWEYgTVPFpTkyO49RLc+jh6CYfXU/+pI2DFWzaHBNywBLPNg3STnNYci3lVLpcz2853ZNpqyxg28fGi0g59airrYMN1Js2F43yHazQBmqvLJmjrQYqts8J1GswYsdjWkjSJ99mykSMCuuXYcZSqwPu5mj6Iv8d2CpYCKyRzx0sc0o5EAi0TGmzmUVAf+Iz4xEz758itIoUWZH/RGwVKbKkmRwIBMqndmXG5AHPwviSIlM6jq0WlArOWRQZ+eKDq8NJLEWG5UmdezuBEQgEmlO7MuM9KmYsedR8/fp1Le+iMZnA+zC8F0O+dbwDhcJk8kR/msFkRyAQqI6wnlkgEGgL+sRnFggEAmUTlFkgEGgDnPs/glYXmZarZCMAAAAASUVORK5CYII=)
chemistry-General
chemistry-
Westrosol is
Westrosol is
chemistry-General