Chemistry-
General
Easy
Question
Density ratio of O2 and H2 is16:1.The ratio of their rms velocities will be-
- 4 :1
- 1 :16
- 1 :4
- 16:1
The correct answer is: 1 :4
Related Questions to study
physics-
In the figure, an air lens of radii of curvature 10 cm (
=
= 10 cm) is cut in a cylinder of glass
. The focal length and the nature of the lens is
![](data:image/png;base64,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)
In the figure, an air lens of radii of curvature 10 cm (
=
= 10 cm) is cut in a cylinder of glass
. The focal length and the nature of the lens is
![](data:image/png;base64,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)
physics-General
physics-
If the central portion of a convex lens is wrapped in black paper as shown in the figure
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF4AAADlCAYAAADa30DYAAAd0klEQVR4nO2daVdb1/X/P1cSQghNgASIUcw2k8HGEOyfk9Rt4jhukybNWm0f9kkf9TX0lfRBV9vVlaw2zdSuZrDdxBlsHIzN5IEZLEYhBAiB0HT/D/y/CiaABVzde238Xesug4Slcz7a2mefffY5VxBFUeS5FJdO7QYcVT0Hr5Keg1dJz8GrpOfgVdJz8CrpOXiV9By8SnoOXiVpBvzq6ioffvgh5eXlFBYW8oc//IG1tTW1m5U2aQZ8V1cXH330EfX19RiNRr777jvu379PPB5Xu2lpkSbAx+Nxrly5wkcffcTLL7/Mr3/9a9xuN3/5y1/o7u5Wu3lpkUHtBsTjcT788EPGxsY4fvw41dXVNDY2YjKZeP/99yktLaW5uRmTyYQgCGo3VzapbvGzs7O8//77RCIR3njjDZxOJx6Ph6amJhKJBLdv3+a7774jkUio3VRZpSp4n8/Hd999R19fHy6Xi5/97GeYTCY2NzfJzc3lnXfeYWFhgb/+9a9Eo1E1myq7VAXf29vL3//+d6qqqmhsbMRoNCIIArFYDIvFwv/93/+Rn5/P2NgYX331Faurq2o2V1apBn5zc5Nbt25x9+5dOjo6OH78OJubmwCIoojBYKC0tJSmpiYsFgvvvfcevb29ajVXdqkCPhKJ8I9//IP+/n7q6upobm6moKAg6ccFQUAURTY2Njh9+jRtbW3885//fKZ8vSrgl5aW+NOf/sTU1BQXL14kNzcXeARcuiQ5nU6OHTtGY2MjDx484LPPPuNZWK1UHPzq6io9PT1MTk6Sk5PDqVOnyMzMJBaLodPpHrsADAYDJSUlXLp0ibm5OT744INnwtcrDr6/v59//etftLe38/LLL2M2m9Hr9Y9Zu3TpdDqi0ShWq5Xz588TiUT4+uuvGRkZIRKJKN10WaUo+Hg8zvfff88XX3xBa2srbW1tiKKIKIo7gpdcjk6nw2KxcOrUKYqLi/nggw8YHx9XsumyS7GZqyiKySjGaDRSXV1NYWEhoVAo5RlpZ2cniUSCy5cv09LSQl1dXZpbnT4pZvGRSIQPPvgAn8/H22+/jdPpJB6P72rp260+kUjQ1NREa2srXq+Xnp4exsfHn9qBVhHwsViM4eFhvv32WwAuXbpEbm4usVjsMX++27X1A3C5XLz88ss8ePCAf//7309t/kYR8NPT03zxxRfE43HKy8spKyvDaDQ+5tv3kvQ3kUgEh8PBxYsXCYVCfP3118zNzSnRBdmlCPj79+/z8ccfc+LECdrb21lfXz9Qnj0Wi2G1Wmlra8PlcjE9Pc0333zD4uJiGlqdXqUVvCiKzMzM0NPTw+zsLCdPnqS5uTnpl1Px7zv5e0EQ6OjooKysjHfffZfJycl0diMtSit4QRC4du0a9+/fp7q6mvLychwOx2PP7/dKJBLE43FaW1upr6+nv7+f+/fvP3WDbFrBRyIRrly5wsLCAhcvXsRms7GxsXEg4FstXhRFysvLqaurw2QyMTg4SH9/fzq7IrvSBn5zc5PBwUFGRkbIysrizJkzOBwO4vH4nhHMky7pA4jH47hcLl588UWGh4e5evVqurqSFqUN/NzcHFevXiUzM5Pq6mry8vIwGA4/X5PAR6NRcnNzOX/+PMvLy3R1dREIBGRouTJKG/iJiQk+//xzampqaGtrY3Nzk0QicSg3s/WKx+PYbDZaWlqwWCxMT09z584dgsFgurokq9ICfn19ncHBQQYGBmhsbKStre2HNzyEm9nucuCRvz99+jRut5tPPvmE2dnZdHRJdqUF/K1btxgaGqKsrIySkhJsNlvyObksXqfTkUgkSCQSdHZ2UlFRweXLlxkdHU1Hl2SX7OATiQRXrlxhcnKS119/ndzc3MciGTklhZD19fVUVlYyPT3NvXv3nooJlezgFxcX+fLLL5mdneWnP/0pLpfrsZxMOq5EIkFJSQmvvPIKQ0NDXLt2Te5uyS5Zwfv9fr755hsAKisrKSoqIjMzM+3rpLFYjPz8fM6cOUN/f/9TEVrKCn56epqPP/6YyspKXnrpJYA9FznktHi73U5jYyNLS0vcvXtX86GlrODn5+f59NNPKS4upr29HXgEXq5IZrdLFEWysrIoLS3l7NmzOBwOLl++zNLSkpzdk1WygQ8EAslZanl5OW63+7GkVjov6T1MJhOnT5/G4XDw2Wef4ff75eqe7JIN/I0bN3jw4AFtbW2UlJSQkZEh10s/UZK7kVapCgoK+P777zWdq5cNfFdXFyMjI3R2duJyuYhGo2m39K2XNJbU1NRQXl5OMBhkZGSE5eVlubooq2QBv7y8zODgIGtra3R0dJCXl5fyeqrc7sZoNOJ2u6mtrWVoaIiBgQE5uii7Dg0+FArR19fHysoKubm5VFVVkZ2drXipnQR/c3OTgoICzp07x/3797l586ai7UhVh04X+nw+Ll++TGFhIfX19cRiMeAHEEorFotRWFhIZ2cnf/vb38jMzFSlHU/SoS1+aWmJ//znP+Tl5dHR0fGYv1XjAjCbzZSWllJWVsbm5ia9vb3JSmSt6NDgvV4vk5OTuN1u6urqFAsh9wKv1+sxm82cPn0ai8XC1atXNTehOhT4/v5+BgcHaWpqorKyEovFojp4QRCSFQzNzc3YbDZu3LihuULXQ4EfGBhgbGwsWd8O6gKXLmm23NLSgt1u59tvv9XcZOpQ4Pv6+hgbG+PkyZM4nU7N7FOSxpji4mLy8vJYW1vD6/VqqsL4wOATiQR9fX1MTk7S0tKyr1pIJV2OlDcaHh5mcHBQTnaH0oHAh8Nhbt++jcFgoKamBofDkVzIVhu2dMGjsvD8/HyampoYGhri3r178pE7pA4EfmVlhW+++Qa73c7JkyfR6/WaLCiKxWIUFBTQ3NysOYs/0ARqZWWF69evk5OTQ0NDA8BjG8fUlmQEUu1NY2MjDx8+5P79+0SjUUUTeLvpQBbv9/u5evUq2dnZtLS0PBbCqe1itroaKbqxWq0cO3YMnU7HrVu32NjYkI/gAbVv8NFoFK/Xy+bmJi6Xi6KiomQIpwVt/8YlEolkaGk2m7lx44YmjmPZN/j+/n6Ghobo7OyktLT0R8kwLVj6VvgS+OPHj5OZmUlPTw+hUOiQ2A6vfYMfGhpKnrThcrl2rHPXAnxJUvXasWPHMBgMdHd3ayJvs2/wIyMjjI2NUVdXl8y7a1mSny8qKsJmsxEIBDRRd7Nv8FNTU8zOzlJTU0NOTo7mLH67pLHHbDbjcrlwOp2Mj4/j8/kOgEs+pRxOxuNx5ubmCIVCOBwOnE4nJpMpOVvdrp0eU0K7DfKJRIK8vDw8Hg/j4+NMTk7icrkUbt0PStniNzY2ksto5eXlyROTtBLNPEmxWIy8vDwqKyuT4NVUyuDX19fp7e3FaDRSW1sLsOfynhbczFbF43GcTidVVVWMj48zMTGRatfTon2Bv337NhkZGVRXVyerdZ8WSXmbmpoahoaGGBkZUbU9KYMPBoNJ8HV1dU8deFEUMZlMOJ1OzGYzwWCQQCCgmqtMGbzf72dqaors7GzKy8tT8u9acjXwyDUaDAYaGhowGo309fURDodTRSCrUgI/NzfH5OQktbW1FBYWJh/XCvhU2iL9jU6no7S0FEEQVD1+JSXwXq+Xhw8fUlFRQW5uruZcTKqhq5Q+KC4uRhRFhoeHVZvFpmzxMzMzFBUVYbfb9zVb1YKLkbTV4uFR+kPTFj8zM4PX602C36/FawW8ZPFlZWUIgsDw8LBq68QpgZ+enmZqaoqSkhIcDse+wO8HTLolWbzL5cJkMrGyssLKyooqbUkJvM/nY2lpCbfbjdVq1ZyPT1Vb8zZ2ux2j0cjc3JwqCyN7gk8kEiwsLBAOh8nJycFqtZKRkXGg2FdtN7O9X3a7HbfbzcOHD5mfnz/Q6xxGe4KPRCKMjIwgiiJFRUUHWqvcXkcplw7zWvF4nJycHAoLC1UDv2d2cnNzk+HhYQRBSA5Ih3UzcsM/yLdPsviCggK8Xq82LX54eBhRFCkpKUlu9DqItOJm4NG30Gaz4XK5mJubU6W874ngx8fHEQSBoqKipy4/s5sSiQRWq5W8vDwWFhZUqSTeE3wsFmNqagpBECgsLDzwV1trEkURi8VCbm4uS0tLquyTeiJ4r9cLQH5+/qFcDcjvbg6qRCJBdnY2eXl5rKysaA98MBgkHA6TmZmJzWZ7ZiweHh3fYjQasdvtxGIxgsGgon3bFXw0GsXv95OVlUV2drYmyt7klJRvcrvdwKNEoLR/SwntCn5paYmFhQVcLhc2m02WQVULbkaSKIro9fpkefn09LSipSq7xvGBQICFhQXy8vKwWCyyRjOHBSeHS9iat5HGMk1ZfE5ODtnZ2bL5P60kzSTwUlHW7OysdsDPz8/jcDhkt3gtSEpl2O12RFHE7/cr2sddwS8vL7O4uIjD4ZDV4rUkQRCwWCyIosjKyoo2wK+trbGysoLNZiMrK0sT4OVMtEmuxmw2k0gkWF1dVRT8roPrxsYGoVCIrKysx44cl0Na8PNSf6RzF5QGv6vF7wT+WZMEHh5NFjUHXqsHMRxGksWbzWZEUVR85rqrqwmHw6yvr2M2m9Ni8Qd1N3K2Y6vFr62tacPiI5EI8XiczMxMDAbDM+dqJIuXzl9QGvyOFp9IJIjFYphMJrKzs8nKykIQBAwGA3q9HoPBgE6nQ6/XJy/pRLytP+90FrDckg7yF0UxeS6Z9Jj0bywWS/4cj8cxGAzJx0wmEyaTCUDR4qYfgZdiWkEQsFqtRCIRwuFw8hug1+uTZ8DvBH07eEEQHvtZ+h1SDw+lb5t0sy4J8nbY0u8SYFEUdwS/9TF4dFu77OxsRU/i/hF4KbQymUysr6/zxz/+MZmZ3C1ZtdfPe/17EG11eds/kK2Pb31s6+/bn9PpdNy9e5fMzEyCwaBiG5B3BS+dTdDV1ZX2RmhB+fn5BINBNjc3FQH/o8FVAh+Px7FarbLc5eBpkBRSKuXndwUviiJms1kTs0wllEgkkituSmhX8NK65FEBL1m8JsAfRYtX1dVIKdLs7Oxk6PesK5FIsLy8rFgB6xPBHxWLl27OrlS9/J7gj5Kr2ToZU0I/Ai+KYvJYkaMEHn64VZIi77X9AemTlxpyVJSOUvK99COygiCg1+sBNH8kitxS0tB2fCcJvJR4OipS1eLhh0/+WSvpeJKkzKoS2tHVHEXwUr9VtXi9Xi/LtpunTaqDP4oWDxpxNVtXeY6CpGhONfBwdF2NJsDD0XI1ksWrOoEyGAzPLT7Neu5q/r8kg1N1cD2qM1fVw8mjnKtRPUl21FwNaMDilWyAVqTT6bBYLMlyvrS/3/YHBEEgMzMTQRCIRqNHxsfrdDpycnLIyspS5v22P7C1gnZ9ff1IgXc4HOqB1+v15OTkoNfrCYVCRwa8Xq8nNzcXs9msyPv9CLy091On0yUryo6CdDoddrtduffb/oBk8YDiWxDVlLQtRyntaPG5ublHzuJB2TXXH5UC6/V68vLyEARB1dOmlZbSs/QdP2Jp681RgQ7K773ds/jdarXy+9//nuLi4uSk6klbbbZvu9m6/WannSSpaq/dHZK1bv19p606Wy94tKV0dHSUgYEB7Ha7omfy7Ao+IyOD/Px8zp49S0NDAyaTCZ1Ol9yAtv3avvFMTUn7nLZuPtv+uyAIrKyscO3ateQmNE2At1gsWCwWZmZmyMvLIzc3N2nx22Hvtetv67dgJ6vfr3bbeLb9sa2gt17SjkadTsfy8jIzMzNEo1EKCwvVL2iCR3WTVquVtbU1wuHwM5m7kfYCCIKAw+HQBniLxYLdbtcUeLl3dUu7QKRJo5QOV0K7grfZbOTm5qYN/G5bIPe65JSU9l5bW8NgMOB0OrVh8dnZ2c+0q9lu8Q6HQxsWn52djd1uZ319nc3NzWcW/MLCAgCFhYXaAG+1WsnJyUmLxR/EzaTD1cRiMebn55P3DVFyT++u75Sbm4vL5cLv9xMMBjVh8XKeBBgOh5NJQIvFoviZPLtavNPpxO12Mzs7y8rKyjO1w1un07G2tsbi4iI2mw2Hw6F8G3Z7wmQyUVBQQCAQUPy8rnRLmrX6fD6KiopwOp2Kt2FPM7ZYLBQUFBCJRJibm8Nut2vilNTDSkp5+3w+3G63KuD3DFyNRiMlJSUkEglmZ2eT91E6qLQAHR6BDwaD+P1+1Sx+T4oZGRl4PB6AJHg5LF6O6zASBIHV1VUWFxcpLi5W5U7GT7T4yspKQD7wWpDkahYWFigoKCAvL0/5Nuz1pAReEATNuZrDvJaUmZydnaWoqEgVi99zcM3IyKCiogJ4dKNFOU5bVdPPS22PRCIEg0HW19dV8e/wBPBGoxGPx4MoikxPTyfP431aJSXGFhYWEEURj8ej2mGme1LU6XTk5+eTmZlJKBQiFAoRjUafWj8vgZ+dnUUURcrKylS7BUdK5iutRy4uLrKxsXEg8HJFM4eJbqRNdZLb1Dx4l8tFQUEBc3NzrK6u7svdSB+S2tCltiQSCebm5hAEgYqKCoxG475fRw6lRDA/P5/CwsIDgYf0WftBLD6RSDA1NUUikaCmpkbb4N1uN0VFRcmE2dM6wEqp4LGxMQDq6+u1ObhKKi4upqSkhKmpKZaXl59K8JKb2djYYHJyEr1eT01NjWo+PqVcr8fjoaKignv37uHz+cjIyEj5tDop9k9H/L6fQV6n07GysoLX603ey1VNpQTebDZTXFxMKBRiaWkpeXRWqh1P16RpP6+r0+lYXFxkdHSUyspKysrK0tKmlNuT6h/a7XYaGhrY2NhgaGgo5fRBOgfW/Qyyer2epaUlJiYmKCsro7S0NNWup0Upg8/OzqapqSl5O2ktgYcnf/u2gq+oqHh6LD4rK4vm5mZisRijo6NJ372X0uViDvpefr+fqakpKioqKC8vV6BVuytl8GazmebmZqLRaBL8kyxeKTezF3TJODY3N/H5fPh8PjweDxaLJdWup0Upr2CbzWZaW1sRRZGRkRHC4XBKVq+2pDDS6/USDofxeDzJG7KoqX0F5FKRUzQaZX5+fs+8jZJuZi9J+ZmRkRGi0SjNzc2KbSLes137/Q+VlZVUVFTw4MED/H7/ntVXSrqa3T5oKU0wOjpKNBqlqalJsb2se+lA4D0eD6OjoywtLWkK/E7wpXFobGyMaDRKY2Ojorv7dtOBwJeVlTE8PEwgENix0CnV2FoJiaJIOBxmcnISURRpaGh4Oi2+vLyc0tJSRkdHCQQCu0Y2alj79g9bp9MRDoeT0YzJZKK0tFTR4tTdtO+6vLy8PMrKygiFQszNzREIBDAajY8Nslqxdr1ez+LiInfv3qW0tJTq6mq1m5TUgdKMLpeLkpISAoFAypMpNWQwGPD5fAwMDFBbW8uxY8fUblJSBwJvtVp56aWXCIVC9Pb2Iopi8uurlovZyeXo9XoWFhYYHBykurr66Qdvt9vp7OxkdXWVvr6+5G4/0AZ4SfF4HK/XS39/P3V1dRw/flweajLoQOAtFgunTp0CYGJigpWVFUXv8P4kSfn/6elp/H4/FosFt9utdrMe04GK3vV6PaWlpeTl5TE5Ocn4+DhZWVlYrVZNHCAnzVb7+voIhUKcO3cOm82mdrMe06F2GzQ0NOD3+7l9+zb5+fk4HA5NWL4U4t69e5dQKMQLL7ygOfCHWjxtamqiqqqKW7dusbi4qNr65XZJibHbt2+zvLxMZ2fnswX++PHjj63FgvqDKzwaVFdXVxkeHiYajXLixAlNzFa36lCupqCggMrKSjY2NvB6vczPz6t+5IrBYGBxcZHe3l7cbjf19fWq1c7spUPXaeTn51NZWYnP52N4eBhQ/uyXrdLr9fj9fvr6+vB4PDQ0NKjWlr10aPB2u50XX3yRpaUl+vr6krNYtVyNTqdjYWGBO3fuUFFR8eyCz83N5cyZM/h8Pnp7e5PHpux2QE+6LlH84ciUiYkJ/ve//1FRUUFra6scnGTXoTevWq1WWlpayMrKYnZ2lqmpqeTZL0pu0ZS+ZePj48zOzuJyuVStBn6SDm3xgiCQn59PVVUVer2e7u5ulpaWFN+QLMXu33//PX6/n9dee42ioiJF27AfyVYE2dHRQXV1NdevX8fn82EwGBT37Tqdjjt37uD3+zl//rwqm8pSlWzgz5w5Q21tLd9++y1er1fR1IEgCEQiERYXFxkZGUEURc6ePZs8uFSLkg18YWEhVVVVyaKhxcXFZCyvhLUHg0EePHjA+vo6+fn5lJaWarqqWdaWFRcXc+HCBebm5ujp6Uke+pZu8Hq9Hp/PR1dXF1VVVbS1tcnZrbRIVvBut5tXX30Vr9fLrVu3kjc7STf4zMxM/H4/165do6Kigo6ODjm7lRbJCt7pdHLmzBk2NjYYHh4mGAwSi8XSDn5jY4O5uTkmJibweDzU19fL2a20SFbwGRkZ1NTUUFZWRiQSoaenh5WVFfR6fVqAS6mJwcFBJiYmksVWWo3dt0r2YNtgMHDq1CnC4TA3btygpKQEl8uVlru/S4Nnb28v09PTnDlzRnMrTbspLcP+2bNnqa6upru7m/n5+bSFlolEgnA4TH9/P8vLy7z66qsUFBSk5b3kVlrAnzhxgoaGBkZGRhgeHsbv9yefkzOEDIfDTExMMDw8jF6v5/z586occ3UQpS3QLSsro62tjYmJCQYGBpLnCssZQgYCAW7evInT6aS1tVW1rZMHUdrAl5aW8tZbbzE1NUVXV5fs0Y1Op2N+fp6rV69SXV3N+fPn09WVtCht4IuLi3n99ddZWFigu7sbv9+fPD78sNDh0dEnk5OTfPXVV3g8Hs6dO5eurqRFaZ1T5+fn097ejs1m4/r167KElpLu3bvH5OQkJ06coLa2VtPpgZ2U1tbq9XouXbqEx+Phs88+w+fzHXomK51H393dzcTEBG+88QZVVVXp7EZalHYz+clPfkJJSQnXrl1jZmYmWXdzGPCCINDf38/MzAwXLlyguLg43d2QXWldrRAEgezsbBoaGmhsbGRkZAS32011dfWPXEcq0uv1BINBxsbGWFtbo6SkhOPHj2tih8d+pcgyUX19PT//+c+5efMmmZmZ1NTUAPuvo8/IyGB5eZkrV65gtVrp7OzUdM59LykyInk8Hi5evMjY2Bjd3d1sbGw8lmtJVQaDgUAgwLVr16isrOTChQv7/vC0IkXAS1be3t6OTqfj2rVryTsVpBrJCILA2NgY9+7dQ6fT0djYSGNjoyY3RKQixWIwh8PBm2++idPp5KOPPmJhYSFZ4/ikCx75976+PgYGBjh58qSmat0PIkWD39dee43S0lK+/vprJicnWV9fB1KPcPr6+piamuKtt95Knof5tEox8NLdI9va2njxxRcZGBhgcHCQjIyMPWezOp2O9fV1+vr6mJ+fx+l08sILL6h2UKdcUny619rayq9+9SsGBwfp6uoiEokk/fhO4I1GI6FQiC+//BKj0UhHR4fqpyvJIcXBl5eXc+HCBXw+H/39/czOziYXSXaz+qWlJa5fv055eTmXLl16Jm4ioEqCo6CggF/+8pfYbDY+/fRT1tfXMRqNj9VBSuHm6Ogovb29CIJAU1MTra2tmtggfFipAt5sNvPb3/6WyspKrl+/zsOHD5MDLZA8Lt1oNNLf309PTw/t7e00Nzer0dy0SBXwOp2OlpYWmpubk1s2p6enH7NkURSJxWIMDg7y8OFD3n77bWpra9Voblqk6q1uWltbefPNN7lx4wbZ2dnU1dURCoXQ6/Wsra1x584dgsEgjY2NtLa2Knoz83RL1SR2XV0dly5dIhaLMTw8zMTEBLFYDKPRyMrKCp988gkmk4nXX3/9qQ8ft0tV8GazmZMnT3LixAkCgQBXrlwhFAqxvr7O+Pg43d3dlJWVcenSpaduoeNJUr03WVlZ/O53v8NqtfLee+8RCAT4/PPPeffdd+no6ODcuXPJm/g+S1IdvFQA1dbWhs1m48aNG/z3v//l4cOHvPPOO7S3t6vdxLRIE/eR0+v1vPLKK6yurnL58mUePHhAY2Mjv/jFL56JWepO0gR4gJaWFgwGA59//jnNzc385je/0dxubDkliBpYSZBmqdFolD//+c/YbDba2trweDzPxCx1J2kCPPwA/6hI9cFV0lGCDhoCf9T0HLxKeg5eJT0Hr5Keg1dJz8GrpOfgVdJz8CrpOXiV9P8AR3uxV4BqadgAAAAASUVORK5CYII=)
If the central portion of a convex lens is wrapped in black paper as shown in the figure
![](data:image/png;base64,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)
physics-General
chemistry-
At a given temperature ρ(X) = 2ρ(Y) and M(X), where ρ and M stand M(Y) = 3 respectively for density and molar mass of the gases X and Y, then the ratio of their pressures will be -
At a given temperature ρ(X) = 2ρ(Y) and M(X), where ρ and M stand M(Y) = 3 respectively for density and molar mass of the gases X and Y, then the ratio of their pressures will be -
chemistry-General
chemistry-
The density of a gas at 27°Cand1atm pressure is ρ. Pressure remaining constant, the temperature at which its density is 0.5 ρis-
The density of a gas at 27°Cand1atm pressure is ρ. Pressure remaining constant, the temperature at which its density is 0.5 ρis-
chemistry-General
physics-
An object is placed at a distance of
from a convex lens. The image will be
An object is placed at a distance of
from a convex lens. The image will be
physics-General
physics-
The ray diagram could be correct
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)
The ray diagram could be correct
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANIAAAB6CAYAAADK1g3BAAAbRUlEQVR4nO2dfVTUVRrHP7+ZYRhgeAcDFYU0BOMkYuFLvuZqZe9ZgpWlmRUtpq1busVW7p7t7KbptliGulYqdbLS1aOZrhWWxgE0XcBSRFDxBXmH4W3efrN/eJgjOiDIMAPO/ZzzOx6Y4d7nIt957n3uc58rWSwWCwLBDcT+/fv5+uuvmTFjBqNHj3ZInyqH9CIQOIDa2lpWrFhBXl4eiYmJxMTEOKxvSXgkQW/HZDKxdetWvv76a6Kjo5k1axY333yzQ20QQhL0an755RdWrlyJh4cHSUlJxMbGIkmSw+0QUztBr6SkpIRt27bx3XffMW3aNObOnYtCoXCaPcIjCXoVsiyzceNG9uzZQ0xMDImJiURERDjbLOGRBL2HwsJCVq5cSXl5Oa+//jqxsbHONsmKEJKgx3PmzBl27NjBgQMHuPfee5k5cyZKpdLZZrVCTO0EPYqysjLKy8u5cOECFouF6upqPv/8c0aMGMGzzz5L3759nW2iTYSQBB1m79695Obm8sorr9gtMlZTU8PmzZvZv38/JSUl6HQ6dDodlZWVeHl5cf/995OQkMD48ePt0l93IYQk6BAmk4lnn32Wbdu28cMPPxAXF2eXds1mMzU1NdTU1JCZmcmBAwdYt24dbm5u/POf/+Spp57C09PTLn11J86LFwp6FXv27EGWZV599VVSU1PR6/V2aVepVBIYGMigQYPo168fOp0OSZL44x//yPPPP98rRARCSIIO0NDQwNatW7ntttuYNm0adXV17N69227tZ2Vl8dprr7F//37CwsKIj4/nxRdftFv7jkAISXBN9u7dS1VVFZMnT0aSJO655x6+/vprqqqqutRuQ0MD77//PikpKURFRbFo0SJCQkKYO3dujw0qtIUIfwvaxWg0kp6ezoMPPoibmxtms5nbbruNH3/8kX379vHII490uk2DwUBOTg6bNm3C3d2djz/+mP79+2OxWBg8eDDDhg3rhpF0L0JIgnbZvXs3siwzYsQITCYTkiTh6+vL6NGj+eabb7jnnnvw8PDocHv5+fmsX7+eqqoqkpKSGDlypPU1g8HA+PHj8fb27o6hdCtiaidoE71ez8aNG3n00UcBUCgUKBQKjEYjY8aMobKykqysrA61ZTabWb16Na+99hrR0dGsXLmylYgA3N3de6WIQAhJ0A7fffcdarWa6OhoFAoFSqUSpVKJQqFAq9UyZcoUNmzY0G4bJpOJjIwMnn76aRoaGkhNTWXevHn4+/s7aBSOQUztBDYxGAx8++23xMXF4ePjg16vb7UJazAYmDRpElu2bOHXX39l6NChV7VRUFBAWloap06dYv78+UycONGRQ3AowiMJbFJYWEh1dTUjRowAsHqjyx+VSsWkSZP44osvWv2sTqdjzZo1fPjhh4SHh7N27dobWkQghCRog6ysLPz8/AgPD0eWZev66PJHkiRGjhxJbm4u1dXVAPz3v/9l9uzZnDlzhgULFjB//nwCAgKcPJruR0ztbNDU1IRSqUStVjvbFKfQ2NjId999xyOPPIIkSW0emJMkiYEDBzJo0CA2bdqEwWDgp59+IikpicmTJ6NSuc6fl/BINrh48SLp6ekdjkjdaBw/fpyKigpGjBiB2Wy26Y0UCgUajYbm5mbKy8tZunQpbm5ubN68mbvvvtulRATCI9kkPDyciIgI3njjDYYOHUpycjKRkZHONsshWCwWNm/ezL333ou7uztGo/Gq1yVJQqlUkpmZycaNG9FoNEyZMoUHHnjAZb24VFZWJrK/baBUKq1hW39/f6ZPn05ycjK+vr7ONq1bqaur4+mnn+bvf/+7zT0dHx8f6urqWLduHcXFxTzzzDOMHTuW5cuXc9tttzF79mwnWO18pAkTJggh2UCSJNzc3MjMzKS+vh43NzeGDRuGl5eXs03rNiRJ4uTJk6hUKvr27Yssy1e9Z+HChRQWFmIymZg5cyY+Pj6oVCr279/Ptm3b+PDDD9FoNE6w3rmI80jt8NVXX/HCCy8QHx9PQkICjz/++A0tJIvFwvz585k6dSp33XUXJpPpqvcYDAbgUqaCJEnWqZ4sy8yZM4ePPvqoRxQjcTRijdQG6enpfPHFF7z//vvcd999N9xOvC1OnDhBc3MzAwYMoLm5GbPZ3OZ7WyJ5LZu0np6eDB06lKysLCEkwSVOnjxJUFAQn376qUsIqIWjR4+i1WoJDg4G6NRxcrPZzMiRI/nhhx9ITEzsLhN7LCL8bYNBgwZx9913u5SILBYLv/32GyEhIfj4+FinbB19ZFkmJiaG48eP09TU5OzhOBwhJAEA1dXVlJaWEhUV1e7eUVsPgFarZeDAgeTk5Dh5NI5HCEkAYC2BFRkZaT131JkHwM3NjSFDhvDzzz87eTSORwhJAFzKZtBqtYSEhCDLsjU1qCNPS/ROpVIRFRVFXl5eu4GKGxEhJAGyLJOTk8Pw4cOtIe/r8UiyLBMcHIy7uzvFxcXOHJLDEUISYDabycnJITY2tlVKUGc8ElwSkr+/P+7u7hQVFTlrOE5BhL8FVFRU0NjYSP/+/VtlM1xPNVWtVotarebChQv2NLHHI4QkoKCggAEDBtgUTmfEZLFYUKvV+Pv7U1ZWZk8Tezxiaifg+PHj9OvXjyuzxToScLgSs9lMnz59qK6utls11t6AEJKL07IRGxYWdpWQ4NpBhyuRZZk+ffpQVVVFXV2dI4bQIxBCEnDy5EnCwsKu+n6LsK5XSPX19d1ue09BCMnFqa+vt0bbOostDybLMkFBQTQ0NFBbW2sPE3sFQkguTlFREf7+/qjVapvCgM55pMsDDmfPnu1u83sMImrn4pw+fRpvb2/c3NzafE9bkbv2jrIFBQVRUVHRZft6C0JILk5VVRUajabdO1k7u59ksVjQarUuFWwQQnJx6urqcHd3v+blxleKqT1vJMsyXl5e1NTU2MXG3oBYI7k4LUJSqVTtiqOzaLVaampq7NpmT0YIyYWxWCzodDo0Gk2bRSBbuFaQ4cp2tVottbW1QkiuTHV1tcuEbg0Gg92r/lgsFry9ve0qJFmWe3T+nhCSDfR6PRs2bOCrr75ytindisViwWKxWIV0rSyGKzO+23q6K9hQWlrKO++8w5EjR+zarj1QudLuc0fx9/fnzjvvZNGiRaxbt46UlBRGjhyJxWLBaDTeMNOVhoYGaz5cQ0MDSqUSk8mE0WhErVajUqlQqVTWO5Eun9KZzWbrYzKZ0Ov1GAwG9Hq99QoYnU6HTqezS/liSZIYMmQIR48eZcaMGUybNo0//OEPhIaGWm3oCh4eHtcMuLRr35gxY26Mvwo7UlRUxMWLF62CUavV1k/bW2+9FXd3dydbaB9MJhNnzpzB29sbLy+vVl7H1pqo5d+W30uLR2t5ZFm2/msymTh9+jS33nrrNddfHUGv13P8+PFWaUcajQaz2YyPjw+RkZHXdeyjZVwffPBBl+6uFQUibbBlyxb27NmDLMts2bKFyspKAgMDSUhIYNmyZXh6ejrbRLvQ1NTEkiVLGDVqFPHx8ahUKjQaDRqNppVHau8P1GQyWT2SXq+nubkZvV7PxYsXSUlJISMjwy62NjY28sEHH1BUVERFRYV12n3rrbeyYMEC5s2bZ5d+rhexj2SDRx99lEcffZQPPviALVu2kJSUREJCAuPGjbPLp2tPwWg0IssyBoMBg8FgvQepZZ3TMnVTqVStjk1c/trlQmppx2Aw0NzcDFwSmj2mdp6enrz66qvo9XpmzZrFwIEDefHFF3nkkUcYMmRIl9vvKkJINjAajaxdu5bs7Gx27txJXFxcuyk0vZXLgwPXOy1qC1mWu7TmuBKLxUJFRQUpKSlERUXx7rvvEh4ebrf2u4oQkg3Onj1LfHw8SUlJdv8D60lcuea5HKVSiVarbffn2mvXYrHY1XubzWbOnDnDkiVLemRJZCEkG0RERPTI/yx70+Ixrrx1QqVScfLkST755BM8PT2ZNWsWZWVl7Ny5E61Wy8KFC695mYC9PZJKpbLeZ9sTuXEm/IJOc/nU7nIsFgu+vr5ERUWxfv16HnroITIyMoiOjmb58uWkp6dfM8m1urq6W6aMPRUhJBdGqVRa63Zfjtls5qabbuKhhx4iNDSUpKQkFi9ezJNPPsmAAQOsxR+VSiVeXl54eXnh4eHRSjQWi8WlaqeLqZ0L0xLabm5uvspzSJJEXl4eZ8+eZcqUKWg0Gn777TcaGhqIjo4GLt21u337dmu296hRo6x7bjqdjqCgIJfxSEJILo5araaxsfGq6Z1areZ///sfkiQREhICwC+//IKfnx9xcXGYTCbeeecdlEolOTk53H777YwdOxa4VFiytraWwMDAG2q7oD1cY5QCm0iShL+/P42Nja1qdbd4qaKiIuLj49FqtciyzO7du7njjjvw9/envr6e3Nxcpk+fTmxsLCNHjiQgIMBaN7ympoagoCAnjs6xCCG5OAEBAVYhtUzDFAoF58+f5+eff2bMmDFoNBr0ej3l5eUUFRWRkZGBm5sbs2bN4u2338bDw4N7773XugkrSRJ1dXUEBAQ4c2gORQjJxQkMDESv1191e4Qsy0ydOpX77rsPWZbRaDTMmzePoUOHsnv3bvR6PefOnSMuLg4/Pz/27t1r9UYtHikwMNBJo3I8XV4j7du3j/feew93d3eWLFnCoUOH2LFjBwEBAaSmptq8Yl7QcwgMDKS5ublV9rTZbCY0NJRly5ZhMpmsUb2W1CmAwsJCNBoNISEhGAwGfvzxR8LDw7npppswm81UVVW5lJC67JGGDx/OokWL+P7775kxYwZubm4sWrSIrVu3snXrVnvYKOhGgoKCbF68LMsy9fX1mEwma3a30Wi05ud5enpy+PBhPvvsM7788ksGDhxIeHg4FouF6upq1Gq1S32Idtkj+fj40K9fP/z9/VmzZg133XUXZWVlBAQE4Ovraw8bBd3IgAEDqKysbHWdy5VcGdEzmUwEBweTnp6OwWDAZDJZk1UlSaK8vBxfX1+XEpJd1kg5OTnU1NQQGxsLwLFjx5BluVVWbm5uLsePH7dHdwI74u3tjUqlorq6ut36dbbOHl3uxVq+r1AoKCsrIzAwUAips2RmZhISEoKfnx8ABw4cYOjQodxyyy0AvPDCCyQmJnL69Gl7dCewM4MHD+b06dOd3jy19X6lUklFRQX+/v5tJr3eiHRZSLIsU1JSwuTJk1EoFOj1er799lvGjh1rzcf661//yuDBg11ml7s3IUkS0dHRlJSU2HwNbHuklscWZWVl+Pn5ucxmLNhBSMeOHSMzM5MJEyYAl+bPzc3N7Nmzhw0bNlBXV0efPn3w9vbGw8OjywYL7E9kZCTnzp1rs5Z3R4UkSRJNTU00NDRw0003Ocr8HkGXgw0BAQEsX76cyZMnA+Dl5cWyZcsoKCiw5l2lpKTw/fffU11dzYoVK4iKiuqy4QL7ERUVZfPO15a1UEdpSQ0yGAwMGDDAnib2eLospJCQEJ566qlW3xs/fjzjx4+3fj1r1iyeeOIJLBYL/fv372qXAjsTEBBAYGAgp06duurYdmdKerQcnzAYDAwePNjeZvZoHJK02hPO1AvaRqlUMnz4cPLz8xk6dKj1+9dTF6eiogJJkggODraniT0e11kNdoILFy5w7tw5Z5vhMBQKBcOGDSM/P79VbYprrY+uXCeZzWaKiopaidFVEEKygUajYdOmTbz33nsYDAZnm+MQbrnlFioqKqirq7OempVlucOPJEkYjUZOnTrF8OHDnT0chyOEZAN/f39eeuklcnNziY2NJT09naqqKmeb1a1EREQQGhrK+fPn8fHxwdPTEw8Pj6sehULR6mRtS1FIwCqkrhRa7K2oPvroI2fb0CNRKBQMGTKELVu28NRTTxEXF8cTTzxxzaIfvRWDwcDx48f55JNPyM7Ovir3roVx48bR1NRE//79CQ0NpampCbj0+yooKMDPz8/l1kcAKle5deF6MBqNeHl5UV9fT1VVFefPn6dPnz7ONqvbCAkJIS8vj+DgYJRKpc1gg9FoJDc3l7Vr1/LQQw/xu9/9zpoalJWVxaRJk5xgufNRLV682Nk29FiWLFmCSqXi3XffZfr06dx8883ONqlbycvLY+3atSQlJREcHGzTK+n1eiIiIujbty+bNm1i3759zJ07l8GDB3Pw4EGWL1/uBMudj6jZYIP6+nrWrl2LJEnk5OQQGhrqbJMcwqBBg6ipqeHYsWN4eHi0ecODm5sbEyZMYMyYMXzyySe8/PLLTJkyxVrM3hURRfRtcO7cOZqamlxuUxFg6dKl+Pr6MnPmzGtmNUiShEqlori4mDfffJOTJ0+yevVqa5aLKyGidjbo16+fS4oIYOLEiRw+fBiDwYDZbG435G02mzEYDERERDBo0CCeeeYZNm/eTFJSEqWlpc4eikMRQhK04s477+TChQucOXOmVYi7vf2j3377jaamJmbPns0//vEPYmJieOmll1i/fj0NDQ3dZmt5eTnFxcVUVFQAlzbST5065ZTb1MXUTnAVK1asoKamhpdeesl6o19bqNVqtm3bRnFxsbXOHUBBQQGpqakYDAYee+wxpkyZYnc7U1NT+fzzzyksLGThwoUUFxdz+PBhJEnim2++cWgYXngkwVVMmzaNQ4cOodPpgLZTheBSYObYsWMMHz68VT3wyMhIUlNTmTp1Khs2bODtt9+muLjYrnbOnz+fVatWYTQaqaqqYtmyZaxatYpz585x8uRJu/Z1LYSQBFcRHh5OaGgoBw8eRKlUtrov9vJHlmUqKys5e/Ys48aNs9nW9OnTWbFiBUFBQSQnJ5Oenn5NL9cZfvnlFwYMGMA777yDn58f5eXl+Pn5WavDwqXb/uzZpy2EkARXodFoGDt2LPv37283585isXDw4EH69u1Lv3792mwvODiY5ORk0tLS2LdvH3PmzOHQoUOdOutkC4vFwp49e/D19UWtVmOxWMjMzCQ8PJywsDCampqYN28ekydPJiYmhuzs7C711x5CSAKb3Hnnneh0OgoKClAqlW1G7Xbv3s3MmTM71Gb//v1Zs2YNiYmJrFy5kjfffJNTp07ZfG9bKUqXYzKZyM/PZ+LEiQA0Nzezf/9+7rvvPpRKJbW1tfTt25fMzExeeeUVPv30047/AjqJEJLAJhEREYSHh5OVlWUzDC5JEr/++isA8fHxnWr7wQcfZPny5YSEhLB48WLWrl3b6nVZltsU2OWcPn0avV5vnVaWlJRw4sQJ65WYISEhLF26lNzcXEpKSpg7d26n7OwMQkgCm6hUKiZNmsSvv/5KTU3NVVM8lUrFrl27eOyxx67rZr6QkBCSk5N5/fXXycvLY/bs2WRnZ1vz9n744QfOnj3bbhsHDhzAYrEwZswY4FKNPj8/PxYvXsxbb72FXq/n888/Z9GiRdx///3degujCH8L2sRkMjFjxgwefvhhRowYYV3TqFQqSkpKSE1NJS0tjb59+3a5r61bt7Jx40bi4+NJSEigoqKCNWvWsHr16jZvRW+x5/JqRRaLBZPJZC1U+cwzz2AwGFCr1dx8881012kHISRBu+zYsYOPP/6Yv/zlL9ZqrO7u7nz66adotVoWL15stxvfa2trSU1NpbCwkEGDBrFx40bS0tJ6RUa5mNoJ2qVlI/XIkSPWT/6LFy9y+vRpJk6caDcRAfj6+pKSksKiRYsoLS3l1KlTvPXWW/SGoz5CSIJ2cXd3JzExkW3btlmnUkeOHMHT05PRo0fbrR+z2UxlZSU//fQT27dvZ9++fRiNRn766SeSkpIoLy+3W1/dgRCS4JpMnToVjUZDZmYmsiyTkZHBzJkzryvI0BZNTU0cOXKErKwsamtrGTduHI8//jj3338/xcXF/P73vyc9Pb3dYv/ORKyRBB1i8+bN7Nq1i2HDhnHw4EE+/vhju07r2qO8vJz8/Hx27NhBXV0dzz33HCNHjnRI3x1FCEnQIRobG3nuuefYvXs3O3fuZNSoUQ63obm5me3bt/Pll18yfPhwnnvuuR5z9F8ISdBhMjIy+PLLL3n//ffbDEk7gtraWt577z2OHj3K7Nmzueuuu5xelEYIyQXZs2cPhw8fRqPR0NzczKhRo6yXIPQmDh06RGpqKr6+vjz55JOdzrCwJyLY4IJ4e3tz9OhRFi5cyOHDh3vthWAjRoxg9erVjB07lmXLlrF06VIaGxudYosQkgsyevRonn76adRqNYmJicTFxTnbpOvGw8ODxx9/nNTUVDw8PHjsscfYsWNHtx+buBJRRchFMRqNSJLUZqUggBMnTnDo0CEUCgWjR48mLCyM+vp6du3ahVarJTY2luzsbPR6PdHR0cTExFjvWDpz5gw///wzFosFrVbLuHHjrDc6dgchISG89tprTJw4kXXr1rFr1y7+/Oc/tzqX1J0IjySwSV5eHs8++ywZGRls376duXPncu7cOfR6PTt37mTatGkkJyeTn5/Pf/7zHx544AEKCwuBSyJasWIF2dnZHD58mOeff57MzEyH2B0fH8+HH37I7bff7lCvJDyS4Cr0ej0LFiwgMjKSjz76CJ1OR2RkJJ999hmvvvoqKSkpfPXVV4wfP54FCxZw4cIFxowZw8GDB7nlllvIzMzkyJEjfPPNN3h6ehIWFoa7u7vD7FepVMyZM8dh/YEQksAGOp2OAwcOMGHCBHJyctDpdGg0GvLz84FL+zlubm7ExMQAl7Kwg4KCuHjxInDpPqyamhr8/PxYtWoV06ZNY+DAgU4bjyMQQhK04tixY1RUVGA2m9m7dy8FBQVIksSkSZOsJ1Fbip+0pOtceUVmbGws69evJy0tzerFvvjiC+655x6njMkRCCG5KC1BgcvP8uh0Ov70pz+RlJRE//79SUhIIDk52fp6dnY2Op3O+jNXttHydXZ2NqGhoaSlpaHT6Zg5cyYbN25kypQpds3P60mIYIMLUldXR2VlJXq9nsLCQkpLSyktLWXTpk1s27aNsLAwXn75ZZYvX86PP/5IaWkpaWlpHDlyBLVazcWLF2lsbKS8vBy9Xk9ZWZn1xo6mpia+/fZbEhISOHHiBM3NzQwcOJA77rijlWhvNERmgwuyatUqtmzZYq290OJJZFnGy8uLf//734SEhPCvf/2LrVu3IkkSDz/8MPPnz+f8+fPMmTMHg8GAQqHgb3/7GytXrqSsrAxJkliyZAmenp688cYb1jSiBx98kIULFzpzyN2OEJJAYAduXF8rEDgQISSBwA4IIQkEdkAISSCwA0JIAoEdEEISCOyAEJJAYAeEkAQCOyCEJBDYASEkgcAOCCEJBHZACEkgsAP/Bxc3H61hA8K4AAAAAElFTkSuQmCC)
physics-General
chemistry-
Which of the following molecule has the lowest average speed at 273K?
Which of the following molecule has the lowest average speed at 273K?
chemistry-General
chemistry-
In the below experiment, the value of P is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATMAAABLCAYAAAAcXmBGAAAO00lEQVR4nO2dv27qyBfHv/5pi/sIuyuEIoy0b5AiAooU2OUWWyTZJlUkU0ekoaQx2mYbIqWiunaxDwAptghWijwDttDVVe6+xfwKcibjwQabYP445yNZ4H/D+HjmMHNm5hxDCCHAMAxz5Pxv3xlgGIbZBqzMGIYpBazMGIYpBazMGIYpBazMGIYpBazMGIYpBazMGIYpBazMGIYpBazMGIYpBazMGIYpBT8BwC+//IL//vtv33lhPhE///wzfvz4se9sHCRcHxfkLSOGEEIYhgFeorkZLLvNYLmlw7JZkFcO3M1kGKYUHJQyC4IA9Xp939k4aqIogmEY+84Gw+yczMpsMBgUqmiiKEKz2Sws/XXU63UMBoNC0u50OjAMA4ZhIAiCQn6DME2z0PSJIAjkM+kb/yEVB/1ZJW1RFO07e/vlzZ+ZWIXrugKAME1z5XUfZTqdFv4bSXiet/HzrZOd53nC8zwhxLsciyQMw8J/Q8WyLOG6buwYgLV52GUej40ssnEcRziOI/dN0xQARBiGRWZtp+QtI5laZt1uF57nFaFLD4LRaITpdIowDLfecqpUKri4uACwkCOAwltn+4bKStmf85AYjUYAgH/++WfPOdkfH7aZkZ2Luh3UxajX6zAMA77vx65Xm8lZuyO+76c2qQeDgTxm2/bS79TrdXQ6ndS0oyjC+fk5Go0GTNPE169f84pgJY1GY+0xyqsqGwCwbRuGYSR2f1VZZCGpW0jKRpWv/k7o+GAwyNyNGY1GME0z8dmZYvj1119j+1Tu9TKSVl/oWt/3Y/WF6nEUReh0OrGyAsTLFWEYhkyPypNe/goha3PO87ylbhh1aQAIy7Jk0xBvzV3XdeVxwjRN2RS2LCt2Pq2bSenR702n09RzlLbjOLHjabiuK+9xXTd3VzOL7IgwDGNdAzUNKN1c6jJMp9NEuVuWJWXgOE7sfNrzmqYp7wEgu75J5+i767qx40ldGMuyZP5pS3rGpGdmkskiG72bSe9hOp3K73q5cV03ZhIAIN8xpaWWJ9d1ZTkxTVNeQ2YZYjqdyn0qu3q9Vvf1ev8ROcSuz3pTUqUSYlkBmaYpBeB53sqH0hVQkjLTK6dlWbGKGHsYJS3XdTNVqqT8qMpyHXkETgpWJ+kZqdDpMgnDcElGap7TlJmu6HU7F6EqNv39JZFkM8tiv2Fllk5WZab/iajl1jTN1PeibvTHmPS+0v7cVykzyr9aR5PymuUZ85aRnU7N+P79e2y/VqutvadWq8E0Tdklms1mqFQqsWuoCavS7XZxf38vm7xJ+L6PyWQim740ErjtriblsdVqZXrmVby+vi4dyzKCaVkWXl5eACy6tdVqNXaeurhhGMpjFxcXmM1mS12SdcxmMwDAX3/9lfkeJj+O40AsGiQQQmTq1nueF7tnPB6j0WjAcRyYphkzDZGNdxujpXpeRQGTgnc+z4wKusq6Ct7v99FsNmEYBm5ubmIvrV6vo9/vJwqHhPb4+JhojH56eloSsOu6uL+/3+DJVtPv9+VAwEdRFQ6h20x0er0eLi8vYRgGarVaLC+2baPdbkMIsaQYZ7OZlK1u/1zHLqYKqDagTaeEdDqdxLzmUeDHwrdv32L79Ec/HA5l+b+8vIw1HoQQsCzrQ9N+dPmusmNvyk6V2cXFBcIwlAZt3/fhOM7a+0ajkVQ29G8BvI+Wjcdjeez19VUaK+l8u91eahX6vo9Wq7X0W5T+NoVt23Ysjx9JmwYqKA0agMnyh0AyHA6H8ngURZhMJkt/MkEQYDAYSAV2fn6+VBHSICVwfX2d+bk2pdvtwrIsCCFwc3OTWeGqAxrD4VDKT3036jsrAzc3N7i7u5P1IggCnJycIAgC+dwkTwCx96/KgnpGJL9+vw8AqYb9q6srTCaT2EBWIX90Wfqm1EeGZlTUBwBUY7DaT1ZtV+o9q9JSgdbX1m106nE65ziOzI+enpq3dXaFday7JslOodvk1Pzrcssik7S01uWDUN8bXSeEkAM4SemRnSRtS7NrZpVbHkg2NOgkxHuZpXPqs1DeaTAKb/YikjcZyule9XpCfVd5bKxZWCUbtZ7Qptu61Hetl++kMqUOGqj1VZWZ/k7V4+r8ybQyoOqQrO8+bxnJPACwT/QX4nnewUwOPHTZEboMp9Pp1ithHopQZuroG1VI9U9A/U11MEb9ro+6qZ+e58WUJRnP1ynuvBxLmSqavHI4qLWZSSR1yZ6enj5sSP9MDAYDzOfz2LGvX7+Wah6YYRh4eHiQtsBWqwXDMGLdZ+o+bcrp6Wlsn7rRWbvfTLH8tO8MrGM4HMIwDNzd3clj0+l0jzk6Prrdrpz8SJRtRYfQBoBocGdbRvwoivD6+ro0CswcEJs055h3WHabsS25kb0mzS5K8x51+xbNoSJ7GHVLaX6Wen2SzYz2VRvjtuAytSCvHNg54wdh2W3GZ5Zbp9NBq9VKnarzmWWjklcOrMw+CMtuMz673Or1OtrtdmyaDPHZZUPklcPB28wYpozMZjNpx2TFtR0OfjSTKT+qd4c8m23be7l31fbbb79lvpZWcqgeTJjN4W7mB2HZbQbLbdHVDMNwSQ4smwV55cAtM4bZA+p6WGY7cMvsg7DsNuMzy41HM7PBo5k7hmW3GSy3dFg2CwrtZq5ztUKjM0kGTTqe141MGVgXnUk9r7vIpnNldEfDFEvawENZBxsyKzPbtmNO1fQ1k77vx1z1qOv+bNuWTuF6vV5phZkEuRoSb76i9HB6URTh5OQk0cWR7/uIoghCCJyfnxfiA4opL1TmyEWSePNL1mw2y1kHsy4bUD0sJLnQTnPDrLt5pqUlZWGd7JLc/ajH0uQmRNzXf5bfOiaO8VloWVPR3ka2KRs9Dge5EDqGOphXDplbZrqHhXa7Lb9HUYS7u7vEJuzLy0usW1qpVPD4+LiUPs37UT2HAljaB97dZKvRjKh7ltZd2xfrojM9PDyk5ncymcQ8yKruwwmKlqPKglp0SV172qfIT9R91feZZci99CoOXX6l9jaziQZUo/YIIaQvKNL6amtDDyySFLQkyVkiLeBV9ymSEl1L+VYdv6n7uyDP7yRFZyLZmaaZ+A+qogYbESLuIFGNqKPv61Gf8Na6UGWp7u/Cz1ne90POP2nhuP7O6TyVJXoWtayp5YzuoTKmBvXQ01avdRxnKXgMpaGnvyvZrEJvmVEet+2DrQjyymEjZbYqYo9eCbMoM0pTD52Vtq9Hk1m3XyR5ZJcWnYlQlVUWZSbEsuJet68X5HX7RZG3zOmRvKgMkcNEOk/7qsIKwzAWTk0tk7q346S01RBtqrInJaimnTdUYRLrZJMU3k9X3ATJQt2OQZEJsQPnjJ1OZ6Vv9FqtBsdxpI/varW6k8AWh06W6Ez9fl/GKqDrWHbvWJaFWq2GKIoQhiEMw8Dl5aV0PGlZlpy75bpu7N7n52ecnJwAAM7OzqRc2+227JZT/Ag97fl8jrOzMwCIdTO73S6en5+XBnWKZjweLwXiEUIkBgsCEBsAEEJsLbDOoZFLmaUFAUmCKuPp6WlMyN+/f4/Z2z4LWaMzqWH0LMuKhZYLw7BU3mE3hcIPUuVM8jyhU61W8fDwAGBRBql8Xl1dYTQa4eXlBY1GIzXt5+dnAIjZe8k+tmtnoWTf1LdNo1OVhcxeM6IowtPTk3y5vu+jUqksVS7dQF2r1VCv1xEEARqNBnq9Hkaj0RayfjwkRWdKqoC9Xi+m+K+vr6V768FgkCmSVVlpt9sysle320W/35eDQo7j4PHxEWEYotPpyFCB8/kck8kE7XYbs9kMo9FI3iPephg1Gg3MZrOY62s9bdXbsWVZuL6+xmw2Q61Wi3lAvrq6knMtwzAszNhetqhRWyNL3zQpEo/aP1f75Wn2NKzor+uRYVbt//7770v9/1X7RdvN1sluVXQmXa5JkME2Sa7rnl3fz3Nt0XaVdXL7zGxLNmnl7ljIKwdezvRBWHabwXJLh2WzgL1mMAzzKWFlxjBMKWBlxjBMKWBlxnx6eAF/SRBCiC9fvqSOevHGWxHbly9fco1UqUvlaKSVRopplj/wPiprWZb8TrP39eVbQryPFuvL6NTr1SVAQPEj5FwfNysjhhA8bMIcPjSv8fn5Gd1uF0EQyO/1eh2z2QyDwQB3d3cQQshQbre3t3LVim3bcn6fupKF5gHSgnz1dzqdjlw5MJ/P0Wq1EudXMvuHu5nMUXB6eopmsyknqTYaDZydncW8qQCA53ny++3tbezcbDaDaZowTTN16c/l5SWazaZcIgUAf/zxB4DFpFgAcskZEHdIWnbnh4cOx81kjoJarQYhBKIokq2lf//9V7bCslCv1/H4+LhyZr7nebnWLqYpRWYPbL/HzzDbR12hoLsAgmLXUr+TyyC82cRUm5m6goXcS9F3up5WaNAKFPrchmcMZvuwzYxhmFLANjOGYUoBKzOGYUoBKzOG2YBOp4MgCGJhAmlT4yqwc83dwcqM+VQEQfDhYDcUkZzmmgkh4HkeXNeFEEKOlo7HY5im+eE8M9lgZcYcBbZty02dy6UHSTYMQx6LokheX6/XEUWRnKtGx33fl9cn3a+nH0URoiiS0zeSnGyqx6bT6cFECis7rMyYo2A4HGIymaDX68HzPPT7fanQqDUUBAE8z8Pj46P0g0Xz0+g7taDG47GMEzAcDmULSr2fXJar6b+8vOD8/DxzvhuNhnTXzRQLKzPmaLAsC41GA6enpwAWM/Hv7+9hGAbu7+/lzPybmxsAC+V1e3sr3Vhnhe5PSv/bt2+oVqu58p3nt5nNYWXGHA002/719RW1Wg2VSgWO46RGHfJ9H+12G0KItbarJIWTlH61Wo3FC8gC2812xD5m6jJMXsIwjMVTINSZ/3///XfMK4YeY4EC+Orf8Tar/88//0z1qoG3lQdhGC7FY1BXI6gBsIVYxHnQjzHFwCsAmKOAjPGHEJmI1oZ2u92117I//93B3UzmKGi325hMJgcxMjgcDjGfz9d6x7Btm+1lO4RbZgzDlAJumTEMUwpYmTEMUwpYmTEMUwpYmTEMUwpYmTEMUwr+D4Sd7oYrmICTAAAAAElFTkSuQmCC)
In the below experiment, the value of P is
![](data:image/png;base64,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)
chemistry-General
biology
Digestion of hormonal vesicle by lysosome is called -
Digestion of hormonal vesicle by lysosome is called -
biologyGeneral
chemistry-
Glycerol on oxidation with bismuth nitrate mainly gives:
Glycerol on oxidation with bismuth nitrate mainly gives:
chemistry-General
chemistry-
Anisole is the product obtained from phenol by the reaction known as
Anisole is the product obtained from phenol by the reaction known as
chemistry-General
chemistry-
Propan-2-ol on reacting with
produces:
Propan-2-ol on reacting with
produces:
chemistry-General
chemistry-
Proof spirit contains about:
Proof spirit contains about:
chemistry-General
physics-
A convex lens makes a real image 4 cm long on a screen. When the lens is shifted to a new position without disturbing the object, we again get a real image on the screen which is 16 cm tall. The length of the object must be
A convex lens makes a real image 4 cm long on a screen. When the lens is shifted to a new position without disturbing the object, we again get a real image on the screen which is 16 cm tall. The length of the object must be
physics-General
physics-
The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit S and the collimating lens L is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure
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)
The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit S and the collimating lens L is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure
![](data:image/png;base64,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)
physics-General