Maths-
General
Easy
Question
Six faces of a unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is
- 5/18
- 5/36
- 13/18
- 25/36
Hint:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Probability is a way to gauge how likely something is to happen. Here we have given six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then what is the probability that the sum on the uppermost faces of the dice is an odd number.
The correct answer is: 5/18
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes
Students can conflate "favourable outcome" and "preferred outcome." The basic formula is as follows. There are, however, additional formulas for various circumstances or events.
Here we have given six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. The total on the dice's topmost faces is an odd number. Therefore, one of the two numerals on the top face is exactly 2. So the different possible combinations are:
(2,3),(2,5),(2,7),(2,11),(2,13),(3,2),(5,2),(7,2),(11,2) and (13,2)
Total combinations are: 10
So the probability that the sum on the uppermost faces of the dice is an odd number is 10/36=5/18.
Here we used the concept of probability to find the answer. Probability theory is an area of mathematics that examines random events. A random event's outcome cannot be predicted before it happens, although it could take any of several different forms. So the probability that the sum on the uppermost faces of the dice is an odd number is 5/18.
Related Questions to study
Maths-
The adjoining figure gives the road plan of lanes connecting two parallel roads AB and FJ. A man walking on the road AB takes a turn at random to reach the road FJ. It is known that he reaches the road FJ from O by taking a straight line. The chance that he moves on a straight line from the road AB to the road FJ is.
![](data:image/png;base64,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)
The adjoining figure gives the road plan of lanes connecting two parallel roads AB and FJ. A man walking on the road AB takes a turn at random to reach the road FJ. It is known that he reaches the road FJ from O by taking a straight line. The chance that he moves on a straight line from the road AB to the road FJ is.
![](data:image/png;base64,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)
Maths-General
maths-
Nine points lie in a plane forming a square as shown
![](data:image/png;base64,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)
If N is the number of triangles with positive area, having three of these points as vertices, then the last digit of N is
Nine points lie in a plane forming a square as shown
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFcAAABfCAYAAACdm1sBAAAK90lEQVR4nO2cy4sdxfvGn+rruWY0cdSJzgiRGIILg/4BghLIIqILxTsIQYkgKgriJqCrSLLISoLibRMxoO5EZiMaIYK4E8EMmIPOnIUTM5czZ7qruy7vdzGp+k1C5sTT6eIXpD6bLM6kLk9XV79Vz1vFiIjgcULw/92A/zJeXId4cR3ixXWIF9chXlyHeHEd4sV1iBfXIV5ch3hxHeLFdYgX1yFeXId4cR3ixXWIF9chXlyHeHEd4sV1SDTqRyEEOOfodDpQSoExBgBgjEFrDa01gmDj+SilkCSJ/ZvrgYggpUQQBLb84XCIVqsFxhgYYyjLEkEQgIgQRZH9u3+L1hpKKRARiAhJkoCIwBjD2toaut2ubYtSClEUjd23kS3K89x2RGuNLMuglLLCMsawvr6OsiytIHWxWUSlFNrtNoQQtrOccwRBAMYYqhjYRsggCMA5t0KXZYlOpwMpJYQQti1VGDlym80mpJSIogicc0gpEccxgI0nv3l0hWGIKBpZ3L+GiKC1tg9sfn4eYRhiamoKWZYhiiK0Wi07cqtg3j5TllIKRVGg0Whgfn4eUkpMTk6i2WyCiOyDHIeRI7coCgRBgCzLEIYh+v0+Tpw4gePHj9sGmhEgpYTWulJHr8QIJqXEW2+9hXvuuQd79+7Fxx9/jCAIkKYpGGMQQtjRNS7m/5dlCcYYoihCHMf4+uuvsW/fPuzevRsvv/wylpeXAaBa32gEw+GQVldXKc9z+vXXX2nXrl2Upikxxuipp56iv/76i4qioLIsSQhBWutRxf1rpJS0tLREL7zwAm3fvp2iKKI0TWnHjh109OhRWllZISklKaVISkllWY5dR1mWtgytNa2srNBHH31EU1NTlKYpJUlCExMTdODAAfrnn39ISjl2HSNHbpIkSJIEYRji2WefRb/ft0/w9OnTeP/99y8bsUqp8Z/uVWCMYdu2bfjjjz8wGAxsucvLy5ifn7evsZn7q4wqujT1aK0hhEC73cbi4iIWFxcBbLw1w+EQv//+O26++eZK/RgprplHtda4++67obVGs9lEFEWYmZnB5OQk4ji2nQvDsFIjrgYR4cMPP8Rdd92FIAgQRREeeughvPbaa9BaY319HWEY2i/5uMRxDCklwjBElmWQUuLpp5/G448/bqedO++8E59++qmd+saFEW39RSAicM7tV/rw4cP48ssvwRjDBx98gCeffBJBECCOYzvpjxsSXQ2lFIQQSJIEvV4PX3zxBYgIb7zxhhXatI8qhmJEBCGEjUpMWUEQ4MSJExBC4MCBA9i3bx+EEJU+2CPFHQ6HtvIoirC+vo5+vw8hBPbu3QsACILAjoA4jmsR10QiRVGg1WpBa40wDFGWpa3DhErNZtM+iHEwZRVFAcYYkiSx9cZxbOP6PM+RpinCMBz7zRwprnn9kiSBEMKGYaYBnHM0Gg07CprNZi1TgwnwlVIIgsAuGNI0taKY6UophTAMKy8iTBiplEJZlkiSBJxzGwMDsOXXKq75yUz6aZraVynPc0RRZF+XsizRaDRqWaGZGDfLMnQ6HTunm9cWADjndm4korE7bkYmEaEoCluWWRwBsIukVqsFYPxvykhxPdeH37hxiBfXIV5ch3hxHeLFdYgX1yFeXId4cR3ixXVIPb5MzZhFo9k32LyIrGNjaBTGujJOhdnDqLLjd0Muf4UQ0FrbrUyzwaK1Hnv3qwrG/DT7uHEcV9ozuSGnhSiKEEWR3fI0wta5Gb8VeZ5b98W42WaHblxuyJFrmlSWJQDYvVzGGJrNptO6zZ7u5o30NE0BjD8l3ZAjF9gQ1iRiXLx4EQsLC7h48aLzeo2wf//9N/r9/vUVNsq9NO6qcXY55/T999/TsWPH6PPPP7fOr9aalFJju6OjGA6HVJYl9Xo9OnjwIMVxTHfccQfNzs4S0YZ7q5QiIUTtdb/55pvU6XSIMUbHjh0jIUSlckaKa8RTStFgMKDTp0/Trl27KI5j6na79O6779LS0lLtnSzLkrIsIykl7dmzh5IkoSAIqNFo0MzMDH377bfWXhdCVLK9t+LVV1+lOI6tvd5qtejIkSOVBL6m+1sUBcqyhJQShw8fttZzFEU4evQoZmdnrd9VVzqTcTeKosDc3Jx1BzjnWFhYwNLS0mX5alUTQ65Gr9dDEAT2I6a1Rq/Xq1TWSHGNlW78o263a3OqpJTodruYmpqq7MCOwvhmp06dws6dO9HtdtFqtfD666/jwQcftL5WXY6z4fjx49izZw+01mi1Wrj//vvx9ttvV6pjZLRgnFETc54/fx6HDh3C2bNnMT09jZMnT+Lhhx+2I8vEhNeLlPKyzMIzZ87gzJkzuP322/HMM8/Y+owzXMU8HMWff/6Jzz77DEmS4KWXXsJNN90EoGYPjS55+aYDSimsrKzgwoUL6Ha72LlzJ4CN2NCYeHWMIvNmmFjTGKAmJCqK4jLHt0qS3FaYN0YIYXMyNhuW43BDxrn/FW7YOPe/gBfXIV5ch3hxHeLFdYgX1yFeXId4cR3ixXWIF9chXlyHeHEd4sV1iBfXIdd0Ioy9TZfOpBlLB9jw86WUds+3TswpeVN2URTW9uacX3Z6ss7T8gDsuTtz8KXqKc1rjlxzcodzbnfizTF9s5mulEKWZbV5WaZDYRhCa421tTVIKZHnuT25I4TAcDi0QtSJqQf4v5NFVeoYuVluduM3H1Uydo7JQDGpP8ZDM27B9bB5pJjyv/nmG5w7dw733Xcf9u/fjyzLMDExYR9yHfUCsIf6fv75Z/zwww/odDp48cUXq3mEo6xhKaW116WUNBgM6Pz58/TEE0/QAw88QEeOHKELFy4Q55w457WdWhdCUJZlVBQFra2t0XvvvUeTk5MURRHddttt9Mknn1CWZbS4uEhSSsqyrJZ6Td3fffcdzczMUBAE1Gw26ZVXXqHl5eWxy7pm3oJJBpFS0tzcHD3yyCOUpim1221K05Sef/55WlpaIs45FUVRuVNXMhgMiHNOs7Oz1Gw2aWJigqIoIgDEGKO5uTnK85yyLCPOeW31EhHdcsst1Gg07PUHSZLQyZMnxy5n5Dg3U4I5b3vu3Dn8+OOP9lYNrTVOnTqFoihsumUd0KY7Z3bs2IFbb73VXpWSJAmmp6ft6fnNB63rQAiB3bt32491u91Gq9Wqdi3AKOWllKS1pqIoaDAY0C+//EIHDx6kJEkoDENKkoSee+45Wl1drTXjxqRHDYdDyvOczp49S/feey8lSUL79++nn376iVZXV+1UVGfGjVKKer0ePfbYY8QYo6mpKfrqq68qlXXNvIUkSex1LESEhYUFvPPOO/jtt9/w6KOP4tChQ9i+fbvNm61jFJkLMkzughAC/X4fw+EQnU4H09PT9jC0OWxd1wdNa408z5FlGRYXF9FoNGx9teYtmIy/JEkgpbSdJiI0Gg1kWWb/7XQ6lRqwFcPh0ObpCiGQ57m90MhMBeY3cx1BHXDOEUURsiyzlxSZQTZu364ZW6RpakOjRqOBOI7RbDbBObfpTRMTE7UuIsw8v7kz27Zts7cpNRoNO7LrzjQ3+XHmu1L1ygHgGuJuvvPAXPBg4ltzkZvpHGOs1pQiMxJNXM05tx9RpZT9yFZdPW2FWby02217l0QURfUvIq78aasL0upKJRrVBrq0gKFLdy5crW1113llf3060w2E3xVziBfXIV5ch3hxHeLFdYgX1yFeXId4cR3ixXWIF9chXlyHeHEd4sV1iBfXIf8DdWq0BMezbNUAAAAASUVORK5CYII=)
If N is the number of triangles with positive area, having three of these points as vertices, then the last digit of N is
maths-General
maths-
The number of different triangles formed by joining the points A, B, C, D, E, F and G as shown in the figure given below is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANEAAAB0CAYAAAAb69eyAAAP4ElEQVR4nO2dW4hV1R/Hv2vfz23ONDSOg4jQJEGIZUSZBqXdTKkQYQjxqbyMD1EvRaQWmBYRZdEFukAP1pMPkZVREfhgFyuxVAZCqxkndUx0zplz23vtvdf+P/hfq3P+6hn//93p7DP/3wdEZ5yjv33O+q71u621WBRFEQiC+J/R2m0AQXQ6JCKCiAmJiCBiQiIiiJiQiAgiJiQigogJiYggYkIiIoiYkIgIIiYkIoKICYmIIGJCIiKImJCICCImJCKCiAmJiCBiQiIiiJiQiAgiJiQigogJiYggYkIiIoiYkIgIIiZG/RdhGCKKIjDGIIRAFEXwfR+MMdi2DcYYqtUqHMeB7/vqe4yxdtmv7OacQwgBwzDAGINhGPA8D1EUqe8JIaDrOgBACAHLstpq93QkDEMwxlCr1ZBOpxFFESqVChzHgWma7TavKbVaTdmoaRqCIAAAmKbZdIw3rERRFMF1XdRqNciTtDzPg2Gc15oQQr1Juq4jKadtBUEAy7LAGEMQBNA0Da7rwnEc2LYNTdPAOYfruuCcwzAMElALiaII6XQaQRDA8zxks1loWrKdHjmp6roOXdfh+74a91ON84YnE0LA8zyYpgnTNKHrOrq6uuC6LiYnJxEEAdLptPqPkiIiXdfBOYemabBtG4ZhIAgCCCHg+74Sla7rsCwLYRiqWYb4+6nVavA8D7quQ9M0lMvlxIyVZjDGlDcmhIAQ4vJeV394o3ThoiiCpmkYGRmBrutwXRdXXXUVNE1r+E8Mw0jEEi1XSCls6cYxxpBKpdTfe56nZkjGGK1GLUB6AqVSCdlsFgDgui4sy0rEWLkUIyMjOHr0KDKZDKrVKkqlEvr6+jBnzhz09/c3XUkbYiL5BnieB03T0Nvbi1dffRW1Wg3Lli3DDTfcgFQqpX4WgBqs7UYKXC7L77//PsbHx9WqyTnH2rVrYRiGcjeI1lAul5WAZEwaBEGiRbR371588MEHWLBgAfL5PAqFAgBgxYoV6OvrayqihpVI+rCGYUDXdZTLZSxbtgzr169HqVTC0NAQTNOEEELFH/Jn2w3nHLquK9tuueUWbNq0CY7jKNdu9+7deOmll2BZlnL9iL8XIQQeffRRjIyMIAxDGIaBjRs34s4770y0iN59911MTk5i/fr1Ko6uH+OXvRIBUKLwfR/Hjh3D3Llz0d3djZMnT6JUKuGKK65QKxWARASMUjjyd8YYNE3DXXfd1ZBY2Lp1q3LvkvyBAkChUEA2m8X4+DhGR0dhmiauv/76KT/QduP7Pr777jt8/vnnAM7Hq9u3b4emabjnnnvabN2lYYxhbGwMw8PDYIwhiiLouo7Zs2ejt7e36WsbRCRjHfmPrFu3Dt9++y2EENi3bx9++ukn3HrrrQiCANlsVsVP7XbnwjCE67oq6yYzcG+99VZDkuGOO+6ApmkqfZnkmMhxHBw/fhw7d+7E5OQkoijCgQMH8PDDDyfabtu2VfnDsiwEQYDt27djwYIFiRaRrus4cuQIdu3aBd/3oes6GGN44IEHcOWVVzYd4w0ikvUVAHjhhRcwOjqK1atXQ9d1DA8PY//+/di9ezccx0EURQjDMBGzIuccvu8jiiLYtg3btpHP55FKpZDL5eA4DjRNw9jYmPLX2y38qajVanjuueewdu1a3HjjjahUKvj444/x4osvYtOmTe0275IEQYBMJqMST52QlQPO271ixQo89thjqowjJ+OpxvgFiQXgfKbi5MmT+OSTT3DNNdeAMYbJyUls3boVBw4cwNKlSxGG4ZRFqH8Kx3HgOA6A865dpVLB6dOnsWbNGqRSKTDGUCgUsGXLFuzYsQNhGLbZ4qkpFAr47bffMH/+fHDOkcvl8OCDD6JSqbTbtKbIzO7lpoeTgizpyAk5lUrBtm3lxVx2TCRn8/feew/Lly/HzTffjFqtBsuykMvlsGPHDixduhQ//PCDSkLIroV2Uu9WCiGQzWZVutt1XVX3kulLy7IS7RIBQHd3N1zXBWMMjuOouoX0FJKKaZoolUqqHjfVAEwSe/fuVbXEUqkEwzBw2223Yd68eU1f1/CJZDIZeJ6H1atXo6enR2WwpH/oOA62b9+ufEbOeSKWazn7yVhO1rKGhoZUkVUIgfXr13dMt0IYhsotkvU7xhh832+3aU2RLhDwV8nklVdeweOPP95my5qzePFi2Lat3vdcLgdN01To0owLiq31M55MNEgRNbzw3wNW/rmdXOwhJyYm1Ewon6OnpwdRFME0TfV7UpmYmMC6devw2muvobe3F0II/Pjjj9izZw+2bdvWbvMuiRACq1atwtmzZ1USZ926dVi5cqVyuZNIEATKzZe9lrILZqqwpUFEsuFUBuie56kXd8LsfTE8z0MQBEilUqqlSc7qSXaNXNfF77//jl27dqGnpweMMZw4cQLPPPNMoutbMoYwTVN5KjJjl/QxVKlUYFmWWjhklnEqd7Thb+XAMk0TQRCoRtRyudxS41uF7J2T8ZF0L6T7l2Rs28acOXNw//33o7u7G7quY/PmzeCct9u0KXFdV2W4ZD9akld9AMoz0TQNExMTqtMlCIL/vgFVCKF6y3K5HA4ePIg33nijpQ/QSmRSIQxD1bJ0Mfc0aZw8eRK2bWPevHkYHBzEQw89BNM0E+0SAVCr/pEjR7B582b4vg/OeUc0/MpxMTQ0BN/3lecyFReISLo4YRiqps2xsbHWWP0PMDo6ioMHD6qUq3TlkpAQaUZ/fz+q1apqyY+iCLVard1mTYksbluWhdHRUZUJrVar7TatKfXx87Fjx1SW7nJS9Rf4NPUFpjAME+1/Xw6HDh3Cnj17VKAIJKdpthmcc9WnKANe2dSZZOp3AgDnZ/cwDBPf8FvfwCypf45mNETWcjmTMYNt26jVaiiXyxgdHf37LW8xURRhYmICxWIRp0+fhuu6qncu6UKSe7ukC3ru3Dn09PSohsikIutCIyMjqFarGBsbU31oSV79pW2yfQz4a3erLJ9cigu2h8tqc6VSQSaTQSaTwaFDh7Bly5YWPkJrEEJgbGwMtVoNZ86cUSus53kA2p+abwbnXHVb/Pzzz5gxYwZmzpyputWTikzgcM5x9OhRbN26Ve3jku97EpFlkO7ublQqFVWTkxsLm3FB75w8Q0Euv5xzLFy4EG+//XbrnqBFRFGEjz76CAcOHMDTTz8NIQRKpRJ6enoSX/2X+29c18WTTz6JwcFBLFy4EECyxc8YQ7lcxh9//IFnn30Wr7/+OgzDUDsAkor0ToIgwKJFi8A5V20/csPnpbhgFMlmTTlrmKapDpzoRCzLQjabVf5uPp9v6G5IKtKds21bHcIiP+gkr0TAX2NIdlyUSqXEjyGZldY0Db7vqwLr5UxYFzSgGoah+uUMw0C1Wm04JaeTEELg7rvvxpIlS8AYU+lKud0jyc8kJzIZu8kNbklehSTFYhEDAwN4+eWXYVkW0uk0yuWyiu+SiqwhAn81HlxOk3WDsyfjIbmprVAoYO7cuVi1alXrLG8xslIuZ3IppKQPxv+0Wxb9kt47FwQBurq6VLe53B2a9PoWAOW21W/slH2YzWhYiWSMIGe8bDaLfD6P/v7+1lneQmTTrAwOZYDYCcVW+RlI22XLTNI7LaSrnMlkVH0r6ZlQAA0JhA8//FA9x3/tzv3nC5LeqjEV9S5bkl23iyFdC/lB1v9KMnIgygm5E2yWSDuvvvrqhq+nItnTGkF0ACQigogJiYggYkIiIoiYkIgIIiYkIoKICYmIIGJCIiKImJCICCImJCKCiAmJKKHIxke5UTKKInDOwTlXzZ2u6zY0RxaLRQRBgGq1qs7IANCxpzV1CsndlfZ/DmMM586dQ1dXlxIGYwyVSkXtjzIMA8ViEV9//bU6sbNUKmHmzJmYP38+giBouHCLaA0kooQSBAHy+bw6UFCKqaurC57nQQiBdDqNEydO4KmnnsK9996rOpH7+vpw7bXXqis1k9753emQiBLKxMQE+vr6kMvl1HYC2VUvb/8DznenDwwMYNu2bTAMA3/++Sd6enpQq9USvwluukAiSihnzpzB8PAwoihCoVDAL7/8og78AIC+vj7MmjULQghUq1Xs27cPuq7DcRzYto10Og3f99W1OPl8vs1PNH0hESWUr776CqdOnYJpmhgeHoYQAjNmzFBnQ69cuRKzZs2C7/s4e/Ys9uzZgyiKkEqlsGnTJnX0k7x0i2gdJKKE8sgjjwA4fx5EoVDA4OAgFi1adMEWfs45Zs+ejeeff17FPvXnSXTihVudBokooci0trxbqf57Qgh1Qqq8OrNeQPJn6/8tonWQiDoMuWVcJg3kWRhTnY1GtA4SUYchVxpZSO3t7cWaNWtotWkjJKIORN4jFUURcrkclixZor5P/POQiDoM2Q4kYyXZ9lN/qRbxz0Ii6jBk3CNjI8uyOuJct+kMiajDuNhqQwJqLxSNEkRMSEQEERMSEUHEhEREEDGhxMI0IggClfqWl5jJu6WoGNs66J2dRshmU3mXkczkyb1HRGsgEU0jwjCE7/uwbRtCCHUGA61CrYXcuWmEaZrqulDpwlENqfXQFDWNkHe81m+ZKBaLib5weDpAK9E0Yv/+/RgfH0cYhujr68Ptt9+uXDuidZCIEorv++rKxvqVRGbb5FaIMAxhWRY+/fRTHDlyRN36/uuvvyIMQyxevJj2GbUYElFCYYyhWCwil8vBNE1wziGEgO/7qnvbMAxomobPPvsM33//PYaGhtDd3Q3XdcE5xzvvvIOuri7cdNNN7X6caQ2JKKFEUQTbttXXQRCoi5w553BdF7Ztw3EcVCoVaJqG3t5eAOc7vbu6uvDEE0+gUqmogx6J1kDvbEKpVqvI5/OIogjpdBqWZTXUfTKZDBhjqNVqYIxBCKH2Gm3evBmmaaJSqWDjxo102k+LIREllA0bNmB8fByWZeH48eP44osvkM/nIYTAfffdhw0bNiCVSoExBtd1wRhDoVBAd3c3BgcHIYTAm2++icOHD2Pu3LntfpxpDYkooezcuRNBEMCyLABQbpyu6yrRINt7BgYGcPToUXDOEQQBrrvuOpw6dQoDAwPo7++n7FyLYREVERKJ53mwbVtl4XRdb8jYydN9hBDQNA3ffPMNvvzyS7iuCyEEbNvG8uXLsXDhQnUIPtEaSETTiMOHD6NYLEIIgUwmgwULFqhzvCmx0DpIRNMIzjkMwwDnHJqmIQgCuK6r0uREa6C2n2mEzODVk8vl2mTN/w+0xk8jOOcIwxCpVErVlegYrdZD7hxBxITcOYKICYmIIGJCIiKImJCICCImJCKCiAmJiCBiQiIiiJiQiAgiJiQigogJiYggYkIiIoiYkIgIIiYkIoKICYmIIGJCIiKImJCICCImJCKCiAmJiCBiQiIiiJiQiAgiJiQigogJiYggYvIvgHMjlZozswUAAAAASUVORK5CYII=)
The number of different triangles formed by joining the points A, B, C, D, E, F and G as shown in the figure given below is
![](data:image/png;base64,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)
maths-General
maths-
A rectangle with sides 2m -1, 2n - 1 is divided into squares of unit length by drawing parallel lines as shown in the diagram.
![](data:image/png;base64,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)
The number of rectangles with odd side length is
A rectangle with sides 2m -1, 2n - 1 is divided into squares of unit length by drawing parallel lines as shown in the diagram.
![](data:image/png;base64,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)
The number of rectangles with odd side length is
maths-General
maths-
The number of ways that the letters of the word "PERSON" can be placed in the squares of the adjoining figure so that no row remains empty
![](data:image/png;base64,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)
The number of ways that the letters of the word "PERSON" can be placed in the squares of the adjoining figure so that no row remains empty
![](data:image/png;base64,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)
maths-General
physics-
If ' P ' is in equilibrium then
is
![](data:image/png;base64,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)
If ' P ' is in equilibrium then
is
![](data:image/png;base64,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)
physics-General
Maths-
In the given figure, if POQ is a diameter of the circle and PR = QR, then RPQ is
![](data:image/png;base64,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)
In the given figure, if POQ is a diameter of the circle and PR = QR, then RPQ is
![](data:image/png;base64,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)
Maths-General
Maths-
In the given figure, find the values of ‘x’ and ‘y’
![](data:image/png;base64,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)
In the given figure, find the values of ‘x’ and ‘y’
![](data:image/png;base64,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)
Maths-General
Maths-
PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If QPR= 35° , then the value of PSR is
![](data:image/png;base64,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)
PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If QPR= 35° , then the value of PSR is
![](data:image/png;base64,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)
Maths-General
Maths-
Find the value of ‘x’ in the given figure
![](data:image/png;base64,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)
Find the value of ‘x’ in the given figure
![](data:image/png;base64,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)
Maths-General
maths-
In the given figure, find PR
![](data:image/png;base64,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)
In the given figure, find PR
![](data:image/png;base64,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)
maths-General
maths-
In the given figure PA, PB, EC, FB, FD and ED are tangents to the circle. If PA=13cm,CE = 4.5cm and EF = 9cm then PF is
![](data:image/png;base64,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)
In the given figure PA, PB, EC, FB, FD and ED are tangents to the circle. If PA=13cm,CE = 4.5cm and EF = 9cm then PF is
![](data:image/png;base64,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)
maths-General
Maths-
If TP and TQ are the two tangents to a circle with centre ‘O’ such that then
,is
![](data:image/png;base64,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)
If TP and TQ are the two tangents to a circle with centre ‘O’ such that then
,is
![](data:image/png;base64,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)
Maths-General
Maths-
In the following circle, ‘O’ is the centre .If ![C A B equals 35 to the power of ring operator end exponent text then end text left floor A B C equals](data:image/png;base64,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)
![](data:image/png;base64,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)
In the following circle, ‘O’ is the centre .If ![C A B equals 35 to the power of ring operator end exponent text then end text left floor A B C equals](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
maths-
The length of AC in the figure
![](data:image/png;base64,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)
The length of AC in the figure
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAACSCAYAAABfcMgDAAAX8ElEQVR4nO2deVxTV/rGH0IIyo7KogG1oFCtC2CBurSVqhQRKkVRKTojtODS2oqMdUN+Wq0L046jU1sUqnW6qCBSxCIo+BMLWhCwCLggCAYjkrAKxQSSnPmDQpmpC0vIuTH3+/nkD+ByzpObJ2e573nP0Wp6JCVgYVEhHNoCWDQPbtcfDAbwaOlgeU5olrQ+8xq2pWNROazpWFQOazoWlcOajkXlsKZjUTms6VhUDms6FpXDmo5F5XCffQnLn1Ggrvg4dq6LgnDiIrgNb0W1oAFWc1fhLy6D2G/yM2BN1ys4GDRqCJpuyDD+8xAE22tDIUrGSg8vlH+Vhq2uerQFMhr2S9lLWn9Nx2VjN7jbagMAOObueG92M6L2nKasjPmwpusVctw+ewHSV2dhfGdfoQVTEyP8JhTQFKYWsKbrDXIBUs9XY5q7M/5YIiGDQFAFw5G2FIWpB6zpeoFCfA7ppS6YNa3L2K35Z5w4y4HP4ln0hKkJ7ESiFzSmn0XBRA9MN/z9F/IqnN6wDTf9DuDYLAOq2tQB1nQ9QoHa66fxjwPpkGqPQNzBL9D2sB61omYYu3+NJO9RYOetz0ar63J1dhEnS19hF3GyMBLWdCwqhzUdi8phJxI9QCKRQCgUorq6GlKpFGKxGAqFAhYWFuDxeDA3Nwefz4eeHjudeBqs6R6DWCxGTk4OcnJykJeXB4FAAKFQiLq6um79v4mJCfh8PqytreHo6AhXV1e4uLhg6NCh/axcPWBnrwB+++03pKSk4Mcff0RmZiYqKioAADweDxMmTICNjQ2GDRsGPp8PPp8PS0tLDBgwAOnp6di8eTNiY2NhZmaG6upqCIVCCIVC3L9/H+Xl5SgoKIBEIgEAWFlZYcqUKfDx8cGcOXNgZGRE8233C92ZvWpsS9fU1ITExETEx8cjJSUFEokEw4YNw4wZMxAWFgYXFxdMnDgRurq6TyxDKBQCABwcHDB69OjHXtPW1obCwsLOlvP8+fOIjY0Fj8fDzJkz4evrC19fX5iamvbL+2QkTY+kpOOlCdy5c4esWbOGGBkZEQDExsaGrF27lly+fJnI5fIelRUXF0cAkJKSkm7/j0KhIHl5eWTTpk1kzJgxBADR09MjK1asIDdu3Ojp22EcXf30pJfGmC4rK4v4+voSDodDeDweCQwMJLm5uUShUPS6zN6Y7n8pKioiK1euJHp6egQAmT17Njl37lyfdNGENR0h5Pbt2+Ttt98mAIiFhQXZunUrqa6uVkrZyjBdB3V1dSQyMpJYW1sTAMTd3Z1cu3ZNCSpVi0abrq6ujoSGhhIdHR1ibGxMPv/8cyKRSJRahzJN10FbWxuJiooiZmZmhMPhkJCQEPLgwQOlld/faKzp4uLiyODBgwmXyyWrVq0iYrG43+pRtuk6aGxsJOvXrye6urrE0NCQxMTEqEWXq3Gma2hoIEuWLCEAyLRp08jNmzf7tb7+NF0H5eXlxMPDgwAgPj4+RCQS9VtdyqA7pntuwmAXL17ExIkTcezYMezatQsXLlyAvb09bVl9ZuTIkUhOTsb+/fuRmpqK8ePHIzk5mbasPvFcmG7//v1wc3ODvr4+srOzsW7dOmhra9OWpTS0tLSwcuVKXL16FcOHD8ecOXPw6aefghD13ERVrU0nl8sRGhqKDz74APPmzcOVK1fg6OhIW1a/YW9vj6ysLAQHByM8PByBgYFobX12BIBpqG1Eorm5Gf7+/jh9+jQ2bNiA7du3g8NR6+9Qt9DR0cGBAwcwevRorFu3DhUVFYiPj8fgwYNpS+s2avkpNTU1wd3dHSkpKTh06BB27NihEYbrQEtLC2vXrsWJEyeQk5OD6dOno6amhrasbqN2n1RLSwu8vb2Rm5uLxMREBAYG0pZEDV9fX5w7dw7l5eVwd3dHQ0MDbUndQq1MJ5FI4OPjg8zMTMTGxsLT05O2JOpMnToVSUlJuHHjBjw8PNDU1ERb0jNRG9PJ5XIsWLAA6enp+P777+Hj40NbEmNwc3NDQkICrl69Ci8vL0ilUtqSnoramC48PBxJSUmIjo7GwoULacthHB4eHjh+/Dh+/vlnrFq1iracp6IWpouLi8OuXbuwevVqBAUF0ZbDWHx8fPDJJ58gOjoaBw8epC3niTDedEVFRQgMDMT06dMRGRlJWw7j2bhxI3x8fPDBBx/g8uXLtOU8FkabrqWlBb6+vhg0aBBiY2Oho6NDWxLj4XA4OHLkCGxtbTFv3rxu53WoEkabLiIiAqWlpTh+/DjMzMxoy1EbjIyMEB8fj9raWoSFhdGW8ycYa7rs7Gzs2bMHq1evxuTJk2nLUTvGjh2LiIgIfPPNN0hNTaUt579gZDaYVCqFk5MTJBIJCgsLGZtHeuLECfj5+aGkpOSJiTk0aWtrg4uLC2pra1FUVKSS7DO13cskMjIS169fR0xMDF3DSatR/PM55AjUL6gOtMdpDx06hPv372Pz5s205XTCONOJxWJERkYiICAAbm5ulFS0ouLHcAR++A1umzrBYTgzeoDe4OjoiPfffx9fffUVysvLacsBwEDT7dy5ExKJBFu3bqWkQIGqkysx/ysTrNm3Dj7jBkN9LdfOpk2bwOPxsGXLFtpSADDMdJWVlfjyyy8RHBwMW1tKe/c2piBi7S9w+7+VGC2XQkFHhVIxNzdHaGgovv32WxQXF9OWwyzTbdu2DRwOB+Hh4dQ0NKX+Gz82D4XWlS/wyXuvYbz7p8hspCZHaYSFhcHExAQRERG0pTDHdDU1NThy5AiWLVuGYcOGUVIhw92bpWh9ZTE2ffQxdnx7GAEP/46IbyrUvsUzMTFBWFgYEhISqI/tGGO6w4cPo7W1FStXrqSoQgv6+nrQ5uq0L6nWHoVprhYQ36+GjKIqZREcHAwul4sDBw5Q1cEI0ykUChw4cACzZs2i/LxLG9Yz3GB7Ow+/SgGAoFVmDCdXe7WfTADtY7t58+bh0KFDVJc/McJ0aWlpKCsrw/Lly2lLAdchFHsWlGPf7lPIPL0fSYZh2DLXhLYspbFixQqIxWKcPHmSmgZGRCQWLlyIzMxM3L17F1wuE3KFFGgW3kRF61C8+ILpE7OXmB6ReByEEIwbNw6WlpZIT09XevlqEZGQSqVITk7G/PnzGWI4AODAgD8W455iOHVFS0sLCxcuREZGBurr66looG66jIwMNDc3w9vbm7YUjcHb2xtyuRwpKSlU6qduuqSkJBgZGeG1116jLUVjcHBwgJWVFZKSkqjUT9V0hBCcOnUKb775Jni852F+qB5oaWnBy8sLZ86cQVtbm8rrp2q60tJSCAQCzJkzh6YMjcTT0xMNDQ3Iy8tTed1UTZebmwsAcHV1pSlDI+m45xpnuvz8fBgYGMDOzo6mDI3E3NwcVlZWyM/PV3ndVE2Xl5cHBwcHjdqHhEk4OTlpVktHCEF+fj4mTZpES4LGM2nSJBQXF3cerqIqqJnu/v37aGxsxIQJE2hJ0HgmTpwImUyGkpISldZL1XRA+9FFLHTg8/kAgKqqKpXWS9107CFt9Oi49x2fhaqgFlrs+HY9/6aTo+FOHvJLHkLfzhnONsb0w0C/Y2FhAS0tLc1p6aqqqqCjo6NW25b2lNbyRGxdGYboPBksRxqi5O++mPPpJTTTFvY7XC4X5ubmKjcdtZZOLBbDzMwMWlpatCT0K7KyI/jLwni8+t0JvP9ie4hv7Kd/RcLYjTi4KB1rbJmx+7u5uTnEYrFK66TW0rW1tT31WEvGI61A8YX28xzu/e8SMnkJvgxZj3t+u7H8xS4xZb3BGMS9jaIbqo93PgldXV2Vx1+pmU4mkzFo/VwPkZchev4r+GT/YQCA34exuCP/488taZ/jH7+6IjjQHl3bM4WoFGUNgzHUkjnvm8vlQiZTbQYI1YfD6oqi5hzizok6M8Rqfz6Dc507crUiP/UCxA4zMWtI19urgPCnZPzKnwXPCcwxHaD6z4Ka6XR0dFT+DVMWHJOXMG7EH8bhWtnhpc69aRRobGyGgZU1BnW9u5Ir+OrAVbh8tBKvMGgVl0wmU/m+f1RNx/QNmZ+I7qvYdvIb+Ex1AgDs/uIjTOscnvLg4DoRpPIuRJ3Jso24tD0UCaN2Y3+ILZgxhWintbVV5cMcau38kCFDUFNTA0KIWs5g9V96BwGrefgxyw/eo7vuLMUB/6+7sTX9I3y8axhCJnNRmpGGwoEbkfy9F15gVs8KkUiEV199VaV1UrsFQ4cORWtrK+rq6p6/Z3W647Hi+Fn4372FSokpnMN9EMIwswHtxySIRCKVP6Cnajqg/SHxc2c6AAAXJiNeApMzZkUiERQKhcpNR21M19V0LHSgFYqkZrqOTXKEQiEtCRpPx73XGNPx+XwYGhqisLCQlgSN59q1a+BwOCpPF6BmOg6HA0dHRyrLpVnaycvLw9ixY1W+rzPVVTaTJk1Cfn4+FAp13/1NPcnLy6OSLkDddE1NTSgrK6MpQyOpqamBQCDQTNMB7QeVsKiWK1euAGjPCFM1VE1nb28PPp+PM2fO0JShkSQnJ8PIyAjOzs4qr5uq6bruqaGuwX91hBCCpKQkanvIUF+u7+3tjfr6emRlZdGWojEUFRXh7t271LZno266N954A3p6ejh16hRtKRpDUlISOBwOPD09n3mtQpyMT/95Uan1Uw9DDxw4EG+++SaOHTuG2tpatdpioqKiAgCwfv16GBsbU1bTPQghuHTpEqZOnfrsmLeiCvFrViHB5iQ2KVEDddMBQFBQEBISEnD27Fno6+vTltNtmpvb87pyc3PVZn+9R48eQSgUYuPGjc+4Uo7K08eQXtWGwZMtlCui6ZGUdLxoIZPJyPDhw8mcOXOoaegNcXFxBAApKSmhLaXbLFmyhJiampKWlpanXicriyP/PJpPDr89jCyK/a3b5Xf105NejOjLtLW1ERISguTk5M4ui0X51NbWIjY2FoGBgRg4cOCTL2y9iWOJCnj5mqKu3gjm5srtEFVmOkXDLZze6ofXF6zDv/bvxvqwHUi680fu3rvvvgttbW1ERUX1m4bWwn8hKHg/LpVX4Je9SxGw91q/1dUTmi7vRfCSIAR5v4QhNktxorp/woKHDx+GVCrFsmXLnnKVFEXxJ3FXuxHnD0fjbKkxzM2UvMBedd1rG7my0ZG4bi0kbUROhF/MJIM9DhCh/I8rlixZQgwMDIhIJOqX+vPDXyaz9gqInBAiv7eXuL++q08lKqd7bSNlBUWkgRBCZDfJjikvkJAUSZ90PY6mpiZiZmZGPD09n3rdw+zvyL+z6tt/eBRPAoZ6koO1PaiHUd2rvAxpF+V4zd0OXChQI64Hz9AQul0UbNmyBRKJBDt37uwHAVyMmDAa1/eG4ZvrjbgZ/wsGL5rbD/X0FC5sJrwEYwAgLVDY+iNgqvKT0Pfu3QuxWIzt27c/4YpG3Dq9De98lAou3wBorULu0UTk1AtRkHFDuWJU1dLJ7+4jM8xfJ3+LPkD+vv49snhZJEmvkv/puhUrVhBdXV0iEAj6QcQDkrLWmQwaPILMjMgiTX0sTpkTiYdF8WTbQkfiuPAg+bW5z8X9F7W1tcTY2JgsWLBAuQU/Bga1dArUpKVB+FYYPn5rGkZLr+OKyBRWZn+ufvPmzeBwOP1zsnWrCJVkFjZ+6ICyfcH4WyJzlsrrjXCG1+IA2OavwdLdyl1juHv3bjQ3N2Pbtm1KLbfXqKalqydHF44i/scfEkIIkd3cSV7Rn0723P1zS0cIIRs2bCBaWlrk0qVLStQgIzd2u5HZ/7xL5ERKbsX4EOsX1/SpxP54ZFJ/dAEZ7ndUaeUVFxcTHo9HQkJClFbm02BOS/fbRaTmvog3XtcHoIDoSi4Ew53wssXjqw8PD4eNjQ3effddJSZky/DgnhgDTIzAAQ92iz/AXFOmbNr1B9wBg+A6WTnLjeRyOYKCgmBqatpP4+Te0e8RCUVjGf5//5dIadUGP24/Iu/l4+frZtj6/ZYuWfH/jZ6eHmJiYuDm5oZt27Y9ZfDbE3QxbcUqHNr0Cf49cgGGlaZhQOAqJZTbRxQCHP7LQsQavYW3xnFxv+ZVbPlYOTkL+/btQ3Z2Nk6ePIlBgwYppUylwISIxJNYvnw50dbWJvn5+corVFJNbl29Sm5V9/2xhLK617a6O+TX3F/JrepHfdbUQWlpKRk4cCDx8/NTWpndoTvdKyPOe30SDx8+xPjx46Grq4ucnByYmDArdZmp570+evQIU6dOhUAgQHFxMSwslBw7fQpqcd7r0zAyMsKJEycgEAiwePFiNoGnGxBCEBISgoKCAhw/flylhusujDYdADg7OyMqKgo//fQTtmzZQlsO49m3bx++++47REZGYsaMGbTlPB4mj+m68v777xMAJDY2lraUTpi2yuTs2bNEW1ub+Pv7E4VCQUVDd8Z0jFhP1x327NmDGzduICAgAPr6+t1a9apJZGZmwsfHBw4ODoiJiWH09muM71470NHRQWJiIpydneHr64u0tDTakhhDdnY2PD09YWtri9TUVJVn7PcUtTEdABgYGCA5ORkTJkzAW2+9hYyMDNqSqHP16lV4eHiAz+cjLS1NLbZdUyvTAYCxsTFSU1Nhb2+P2bNnIz4+nrYkapw7dw7Tp0/HkCFDkJ6eDnNzc9qSuoXamQ4ATE1Ncf78ebi6umL+/PmIjIxU693ae0N0dDRmz54NOzs7XLx4sXPrNXVALU0HtBsvNTUVS5cuxbp16xAcHKzyQzhooFAosHbtWoSEhGDu3LnIyMhQu/PV1NZ0AMDj8XDo0CHs2LEDX3/9NaZNm6bys0tVSWVlJWbOnInPPvsMH3/8MeLi4hg/aXgcam06oH1rig0bNiApKQkVFRVwdHREVFTUc9fd/vDDDxg/fjzy8/Pxww8/YPfu3WqVI9wV9VT9GLy8vFBYWIgZM2ZgxYoV8PLywr1792jL6jMikQj+/v4ICAiAk5MTrl27Bn9/f9qy+sRzYzqg/US/xMREREdHIyMjA3Z2doiIiOhMilYnJBIJdu3ahVGjRuHkyZP47LPPkJaWhuHDh9OW1nfUJQzWU+7du0eWLl1KtLS0iKWlJYmJiSEymUypdfRHGEyhUJCjR4+SESNGEADEz8+PlJWVKa38/oY5K4cpwOfzcfjwYeTl5WHMmDF47733YGdnh7179+Lhw4e05f2JlpYWHDx4EOPGjYO/vz8sLCyQmZmJ2NhY2NjY0JanVJ5b03Xg6OiI9PR0/PTTTxg5ciRWr14NKysrhIaGorS0lLY8VFZWYuPGjbC2tsayZctgbGyMuLg4XL58GVOnTqUtr394XrvXJ1FQUECCgoKIrq4uAUAcHR3J9u3byfXr13tcVm+719LSUhIZGUleeeUVAoBwuVzyzjvvkOzs7B5rYBpqv3K4PxGJRIiNjUV8fDwuXrwIhUKBMWPGYObMmXBxcYGLiwtGjRr11McS3Vk5TAhBeXk5cnJykJOTg/Pnz6OgoAAAMGXKFPj6+mLRokXg8/n98j5VTXdWDmus6boiFotx6tQpJCQkICsrCw0NDQAAExMTvPzyy3jhhRfA5/M7X5aWlhgwYADS0tLw4Ycf4syZMxg6dCgePHgAoVDY+aqoqEBubi5qa2sBAIaGhpg8eTJ8fHwwd+5ctQpddRfWdL2AEILS0tLOlikvLw8CgQBVVVXd3hdZW1sblpaWsLa2hqOjI1xdXeHi4gJ7e3u1faDbXVjTKRGFQgGxWAyhUIgHDx5AKpVCJpOBEAIdHR3weDxYWFiAz+fD3Nwc2tpMOkpYdbCmY1E53TGd2ixXZzStdSi7dg13GgfC9mVHGP5WC8NhQzGAti6G8nwPMPobRR2yo0Lx3tpo/NJkAr5ZC9LCpmBaxBWwyZJPhm3pek09LmzyxKrK1Ug+sgjWvw/h7DcuxYPzzmwr9xTYMV0vabkYhpf9buNv+T8iiN+lw2i9j8o6S1hbamYnovYZ/sylGanR30Psthjz+P9zC3nDNNZw3YW9O71BdhtXC5tg5+QEA9pa1BDWdL1CGxxtgKujA+amNDMX1nS9gfsiZr9pi1sX0lHVdZqqEOHmTRE7c30G7ESitzTn4Yvg1Thl4oflCxxg+qgO9a0mGDtjOl40pC2OHj2OSLCwqAK2e2VROazpWFQOazoWlcOajkXlsKZjUTms6VhUDms6FpXDmo5F5fwHYln+5z5ZlZEAAAAASUVORK5CYII=)
maths-General