Maths-
General
Easy
Question
Let F be the focus of the parabola y2 = 4ax and M be the foot of perpendicular from point P(at2, 2at) on the tangent at the vertex. If N is a point on the tangent at P then
equals -
- 1
- none of these
Hint:
Find the co-ordinates of F ,M and assume the any point N on tangent and Find the length of MN and FN in terms of t to find the ratio in terms of t.
The correct answer is: ![fraction numerator t to the power of 2 end exponent over denominator t to the power of 2 end exponent plus 1 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADIAAAAqCAYAAADxughHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAQ5JREFUeNrtmCEKAlEQhh8Go90kyCLiBYxeQWxewCB2k3gFg9UgYjGLfYNVjF7AK4hY9H/wwgYV2d0Z5w3zwZcWlvezvJnld46PZ/ABjzBxkVOBY3hySrhrCNGDaewh6uGONKUfNAkHfUcL7kMY8Qzg9sOXOMBaDCHmmTHrnWae+RDtmO7ADva/7JGsornAhoZld9OwH7oa9oNnCNcagizgREOQJVxpCNKB1zBaq84wDIOjHIhNwzCIh4I1hlKxxlAKHI2hL/Rm8FzkJRIaww0cFd3gFI1h3gPlDkLVGLIH8VA0hn8JQtEYsgcpqzEs6zc8dxCqxpD9i1A1huxBqBpD9iBUjSF7ECmN4c/D4QVZsY2FR6YwgQAAALF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1zdXA+PG1pPnQ8L21pPjxtbj4yPC9tbj48L21zdXA+PG1yb3c+PG1zdXA+PG1pPnQ8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tZnJhYz48L21hdGg+g5zt7wAAAABJRU5ErkJggg==)
Let F be the focus of the parabola y2 = 4ax and M be the foot of perpendicular from point P(at2, 2at) on the tangent at the vertex. N is a point on the tangent at P.
F(a,0) and tangent at vertex is x = 0. and P(at2,2at) then foot of perpendicular M is (0,2at)
N is any point on tangent let N = P as Point P also lies on tangent.
Then, MN = at2 and
![Error converting from MathML to accessible text.](data:image/png;base64,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)
Then ![Error converting from MathML to accessible text.](data:image/png;base64,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)
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biology
Given below is the ECG of a normal human. Which one of its components is correctly interpreted below ?
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)
Given below is the ECG of a normal human. Which one of its components is correctly interpreted below ?
![](data:image/png;base64,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)
biologyGeneral
biology
Cords of bill roth are found in–
Cords of bill roth are found in–
biologyGeneral
Maths-
Find the area of shaded region in the figure.
![](data:image/png;base64,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)
Find the area of shaded region in the figure.
![](data:image/png;base64,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)
Maths-General
maths-
If
dx = Ax + B log sin (x – ) + c then value of (A, B) is
If
dx = Ax + B log sin (x – ) + c then value of (A, B) is
maths-General
Maths-
If
Ax + B log sin(x –
) + c, then value of (A, B) is –
If
Ax + B log sin(x –
) + c, then value of (A, B) is –
Maths-General
Maths-
If
x sin x dx = –
=
If
x sin x dx = –
=
Maths-General
Maths-
A Square of side 4 units is combined with two right angled triangles of bases each 3units to form a Trapezium (as shown in figure). Then perimeter of the Trapezium is
![](data:image/png;base64,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)
A Square of side 4 units is combined with two right angled triangles of bases each 3units to form a Trapezium (as shown in figure). Then perimeter of the Trapezium is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAV4AAAC/CAYAAAC2RLSJAAAgAElEQVR4nO3dZ3NUV7r//e/unLMyyhJCgJBEEDlKFjnYDD72qfrXeQfn5dx1Ht331L/OnLHB2CDAJIOwyRkRBCjnrO5Wq3Pa9wOMxp4Zn3FA3S1pfar8BAl8dffev157r2uvJcmyLCMIQmaRZZCkdFchzBNVugsQhA8i7iMSSTKbMKDVqDHrFnJoySTjUeKxOAmFGqVGg1qRhHiMaCxBPKlAqdWhE2fvgiU+uqVEDiJH/UzNqonIJhwWFQbtQg4oAJmkf5jpt8/omFIzba+lrDiHVTpYuK9MJhkPEZgeY3pqimlfBH9ChVKjx2DUotWoUUmgQEZWaFHprVjsNhwWNZp0ly78KiJ4l5JwH8G+F9x4aWBMsZo9DfmsKtSmu6o/aBbf4D3unTnJ1YEsQhuzOWDJpToHlOku7Q+QpBhhTx99ty/y/b03PHE70ZXUsK6+iNIsLZJ3BO9QH32TMgHLSqo2b2fn1hVUWkGX7uKFf0kE7xISn+pm4E4LV7/T0+2QcRZbKSvUok93Yb+bTGyii75717h9s5UbnjWYCv1sDqe7rj9KQqHSoNVr0YYGmX5zn7t9pVgoZ9VGE1arHhI+4kYldL+lv72XgekgswodBzfkU+PULODR/tIggnfJiOAbG+HVo5e8uRNhoKyA52MrWYeDChbi6FBGjkwy/rqL18/6GAuGiZnUKNVKlNJCvs0AICEpTVhyK6ksL6GyNBdHqAh7yUpqNjSwaZkBRbyOeGQLq0u+4tpfv+LMw0ucVy0j225iudMlRr0ZTpHuAoRUCEG8hwmvm1eTaoKTo6hGntLROcKLUYgk013f7xAaJDz0hPbRMG+jJVisLsqcKoyadw0BC56kRGW0YrPZcTmsmK12zDYXWdnZOCxWbI5sXHkrqKurYUOxAuNMF13P39Ax4sULLIa3YDETwbsUxGdIjrQxFkjizt9ESWUBVYp+xl6+5ckLP57oQjpNZSBKZLSTvvZOBqUc1FWbqCzIpVyXQCMlicuLJHgScRKJBImEjCyDLMvIyZ+/slgoRlxSo1Br0aokJEkmnqZyhV9PBO8SkPB4cb/oxu0zYqj/iA1NG6jNDRHses7LtrcMBWLpLvE3CEGsl+6eMR53aVDbllFfn0dhth5VMgnJRRG578jyu7D98SVJkoRC8ZObQnI/o32veN7pZVx24igppTDbjpWFfqtl8RP3eBe1d6PDgMdNR0ccvzGfmq0bqVoxzYDcxZ3v3jDy/DEvxyood2hwLYCzNRnxEux5Tf94HI+zjvrlJaxQuXlthFhSAoUalWoh3rP+ZySQFCiIIUWm8A538PqZHXu+Bjk4TWDgNrcvtnK5U0esZDPb92ygodKFOd1lC/+SCN5FLQEMMT0zzLMpExGVi21ZBqpLy5GeF7Hsu+c87Wrj8euPqC604rKku95/JYpvaICO+71MRrNxNSwnr8CAfjgG0TjxpIpEMk4iAUkWweWcJIFCiUKOoQgOM9HzlEc3g4SzJaJjXQy/esjDl9MMKFdTtaKG+hUuCuzpLlr4NUTwLmbJGEy3M933jJdTGuLJaZa/fYklx8tIVINaniY48pqnT7pZvzKXhpX6zD0gEiFwv2Co/QE3X7rx2u2sjEzgG5lm5nUvveN+PLMx/JP9DA2V0pNnY5lDj069kONXfne7AQWyyojO7MKVm0d+roq4VkKrVJJUd2MZixEfaKP9Xi4FpjWoK7NwSovgi2cRy9jzTPgA4kHCHT1MdPURVJYQk2YZ6Ooh5o4zETJhyzVg9k0w3NZGx7oyJqrKyFNm6P3BRBB57DnjfS9pdxsIBMYw3W8lYNXg63rGwMAMo1MS071ttL/K5rG9GkuNdmEHryxDMk5C0pA0FpJT1cCWj3awu8CAMpEgkZhhuu08d07+hf976TRnBmbwqAwY87JYZwJjRn6QAojgXcQSRCMe3nb6GZ4yU7yyAkfZckp0CSw6FTZlkpzIEN5AJ991P+X1qxra95RhskOm3nGIRyEZi6FIevG7w/S8UjCsV+Mf7WVqKoB7JsnseA8D/QN0lRewYXkW2YviEFeAUofGYMHmcGLWv09UM+b6tWh7b3Ln9nPudT3m6ctGNo1upqoMjIvhpS9S4qNZtDwkfP10zFiYMm2kfu0GqlcXYUskUaNCFXESzw3inQzQ+20no2/aud+znfJ6PZZMHCQqdMiOavKqEmxWeRn2JVGpFCiUSsIKP8pxLZNhiZgtl6xsF/kOPRrlAh/yKdWoVEqUSundVYgsIyeT/GzqUGvB6bLjsGpQyxHCoRjBCCQWUXPHYiSCd7Fyd+Drfc5Qwoo/bz3L8kopsxhRyjLIEgq5CKwNVK95xsrb1/ih5zmPH/SyObea0oIMDCylDlXuakpMxThWRwjF5B97dSX83U7aZp/iV2rRVG+jYeNG9qyx4DQv8MNbThCPJ4jFEyQScZKJOPF4nJ8Fr3eakeFJJn0qMBWQl2cn3wn6xdHWsWgt8CNT+AfJIOHpQQZuXeDeDw+57duIfu0WZhPvHiJVSO+fp9WQRIdSKaOODjH+8gqjxhKKtAcwN1ZQlm/FoZYy536vpESht2LSWzH93Y/iyj48xiQ6pQLJWkzuslyKXWmp8gNJkIzMMjPUTmf7W1686WGwV8brvMed6xIUmdEkIyTCPjyd93l1Z5RubQ0rdu2jaVMla5xgzMSrFmGOCN7FJhkiMt1Nz5s+nrz24NZ7KZI9zEYjBOIGbO8/cTlK1BsgmtCjzc7DNRTEM/6cjtdltFXlYM8yY1MrF0Q/bExWobLmYHcZCJgVLOileAFIkozO4B3ro38ihDthxGaIow700vlEiTRuRR/3EfOOMNQ/xpBvGbbN2/ioaS/NG4qp0IoTO9NJYgeKRSbhJzTZS8+Ll7zp8+I1LMNVWUNlSR7FTi3G90kqR4l5RxnteU1nRw/dw7P4NTlYi6tZvqqSqiIbLo1iQbQkRd39jL26R6dHzWzuRipKCliVnaHdGb9KgkTYi2e4l4HODnoGpxgPq8Fgx2E3YzFrUSfDJIJevL44AaULV/lKVlSXUWZDrMm7AIjgFQRBSLGFMKARBEFYVETwCoIgpJgIXkEQhBQTk59L0MzMDFNTU0QiEex2O9nZ2SiVC6F/QRAWBxG8S0w0GuXFixfcv3+fUChEbm4uxcXFmEwm4vE4Yq41M8iyjNlspri4GKfTme5yhA9MBO8SMzw8zLVr1/jmm2+IRqMYjUasVitqtZpkciHuAbQ4ybJMeXk5x48fp6mpKd3lCB+YCN4lZHR0lMuXL3P58mXa2trSXY7wL7x+/RpZlonH46xcuZK8vDzUanW6yxI+ANHHu0QEg0HOnj3Lf/3Xf/HgwQPC4QW/B/qiZzabMRqNrFy5koMHD7J//36qqqpQKMSc+EInRrxLQCAQ4Pvvv+f06dM/C12DwYAsy8RiMZxOJ1VVVZSVlWGz2ZBlmUQikebKFz9JklCpVEQiEcbGxujo6KCnp4d4PE40GmV2dpaxsTFmZ2dRKBRYLBYKCgrSXbbwB4ngXeRisRhPnz7lyy+/pLW1lXA4jEqlwuVyodfrcbvdxONxCgoK2L9/P/v376e0tJRkMvnjSljCfJIkCY1Gw+zsLI8fP+arr75ifHycqakpVKq/nZ6PHj3CaDTicrnYu3cvWVlZaaxa+KNE8C5yz54948yZM9y4cQO32w3Ahg0bWLFiBYODg0xPTyPLMjqdjqysLEpKSrBYMnUp9MXLbDYzPj6OxWKZa+0zGAwA+Hw+ZFnmyZMn6PV6DAYD+/btm/u5sPCI4F2kEokE/f39XLx4kW+//ZaBgQEkSaKwsJCjR49SWVnJ+fPnuXPnDolEgng8Tjgcxu/3Y7Va013+khOPxwkEAkSjUZLJJJIkYbfbKSkpIRwO097ejs/no7W1FavVisViYcuWLSJ8FygRvIvU8PAw3333HdeuXaOrqwuAvLw89u7dS3NzMzqdjtbWVhKJxFzvrizLoqUsTZLJJLIs/+w/g8FAY2MjZrOZL7/8krt37xIOh7l69Sp6vR6j0cjmzZvTXbrwO4jgXYR8Ph937tzh9OnTtLW1EYvFMJlMNDQ0cPz4caqrq5mamhJBm8FkWUalUrFixQrq6+uJRCJMTU3R2dnJ9PQ0ly9fxul0YjQaWb16teh0WGBE8C4yfr+fBw8e8O2333Lr1i2CwSA6nY7169dz4MABtmzZgk6nIxaLEYvF0l2u8L+QZRlJkigtLeXYsWNMTEzwl7/8hbGxMUZGRmhpaUGn06HX66moqECSFu4KxEuN+JpcZF6/fs3p06e5ceMGwWAQgKqqKo4dO0ZTUxNmsxl4dw9YjHYz2/vOEoVCQWVlJQcPHqS5uZn8/HwAOjo6uHjxIhcuXKCnpyfN1Qq/hRjxLhKyLNPR0cH58+e5dOkSg4ODAJSVlXHw4EH27dtHaWnpz/6OGCFlvve91JIkUVdXx4kTJwiFQnz77bcEAgFevXrF6dOnMRqN2Gw2HA6H+FwXABG8i8TIyAhnz57l1KlT9Pf3A5CVlcWhQ4c4ceIE5eXlaa5Q+KPsdjtbtmxhenoaj8fD3bt3CQQCPH36FJfLhdPpZMeOHbhcC3qnzyVBBO8iMD4+zuXLlzlz5gyvX78GwOVy0dzczMcff0xdXV2aKxQ+FIfDwY4dOwgGg/j9fh49ekQgEODevXtznQ7bt28XbWYZTgTvAhcOh7lx4wZffvnlzxa+2bZtG5999hlr165NY3XCfCgqKqK5uZnx8XFmZ2d59eoVY2NjXL9+nezsbKxWK3V1deh0unSXKvwCEbwL2OzsLA8ePKClpYW7d+8SDAbR6/WsX7+eY8eOsW3bNvEU2iKkVCopKyvj2LFjcw+99Pf3Mz4+zqVLl9DpdJhMJlavXp3uUoVfIIJ3gYrFYrx48YKvvvqKmzdvMjs7i1KpZNWqVZw4cYKdO3dis9nSXaYwT95PtoVCIdxuNy0tLYyPj/P27VvOnz+P0+nEYDBQVlaW7lKFf0K0ky1AyWSSjo6OuSfT3ncwLF++nObmZhobGyksLExzlUIq1NbW8vnnn9PY2IjRaATetZl98cUXXLp0icnJyTRXKPwzYsS7AA0PD3P58mUuXbpEZ2cnAPn5+TQ1NXHw4EHKy8vFHmpLhMFgYOvWrczMzOD1eueufp48eYLNZsNms7F3716xfVCGEcG7wExNTXHr1i3Onz/P06dPgXcz3Vu3buXAgQPU19ej1WrTXKWQShqNhp07dxIOhwmHw1y/fh2Ae/fuodVq0ev1HDx4EI1Gk+ZKhfdE8C4g4XCYO3fucPLkSR4/fkw4HEatVrNp0yZOnDjBhg0b0Ov16S5TSAO73c6ePXuYmprC5/Px9OlTgsEgt27dwm63Y7FY2Lx5s2gzyxAieBeIWCzGkydPOHPmDFevXiUQCCBJErW1tRw5coSmpibsdnu6yxTSKDs7m3379hEKhQiFQrS3tzM7O8v169cxGAwYDAbWr18v9m3LACJ4F4iXL1/yxRdfzIUuwKpVq/jss8/Yt2+fCF0BePeI+L59+5ieniaZTPL69WvGxsa4du0aDocDjUbDunXr0l3mkieCN8Mlk0n6+vo4d+4c586dY2hoCIDCwkIOHz7MkSNHKC4uTnOVQqZ4v6DOsWPHCAaDTE9PMzExQW9vLxcuXMBkMmGz2SguLv7Z1kJCaol3PsONjo5y9uxZWlpafrYGw7Fjx/j444//YeEbQdDpdKxZswa3283ExAStra1MTEzQ0dHBlStXyMrKYu/eveLYSSMRvBlsfHyc77//nrNnz/Ls2TNkWSY7O5vdu3dz7Ngx6urqxKhF+KcMBgMbNmwgFAoRDAa5fv06gUCAZ8+eodFoMBgMWK1WHA5HuktdksRZm6ECgQC3b9/mm2++oa2tjUQigUqlYsuWLZw4cYK6ujoxSSL8r7Kysti1axfT09N4vV4ePnyI3+/n9u3bOJ1OHA4H27ZtE084poEI3gwUCoV4/vw5Fy9e5ObNm3i9XnQ6HXV1dezfv5/t27eLkYrwqzidTj766CNCoRB+v5+nT58SiUS4desWer0es9nM1q1bxZVTiol3O8O8n4k+e/YsP/zwA+Pj40iSRHV1NceOHWPHjh1kZ2enu0xhASktLeXgwYO43W78fj+dnZ2Mjo5y9epVnE4nJpOJ2tpaEb4pJN7pDDM0NMS1a9c4c+YMvb29wLsOht27d3Po0CGx6Inwu5SWlnLixAmCwSD/8z//w8jICKOjo5w+fRqtVovZbGb58uXpLnPJEIvkZJCxsTEuXbrEuXPnePv2LbFYbG4G+vDhw1RXV4vHPoXfRalUsnr1aj755BMOHDhAbm4uAAMDA5w7d46Wlhb6+vrSXOXSIYI3Q4RCIe7cucOpU6d48OABAFqtli1btnD8+HE2btwotvAW/rC6ujr+/d//ncbGxrk1Pd68ecMXX3zBhQsXmJ6eTnOFS4O41ZABIpEIP/zwA1988QX3798nEomgVCrZsWMHn332GZs2bRJrMAgfhF6vZ+PGjXi93rnVzN6v7WC1WrFarTQ3N4t5hHkmgjfNotEobW1tnDp1iitXrjA7O4tKpaK2tpYTJ07Q3NyM1WpNd5nCImIwGNi2bRuBQIBgMMidO3eIRCLcv39/bt+2vXv3igV15pEI3jR7vz13a2srMzMzAKxcuZITJ07Q2Ngo2saEeZGVlcWOHTuYmpoiHA5z7949AoEAd+/eJSsra27TTHGlNT9E8KZJIpFgZGSEy5cvc+7cOXp6egAoKChg//79HDlyRDzSKcyrZcuWsXfvXoLBIB6Ph87OTtxuN9evX0ev12Oz2VizZo3YNHMeiOBNk5GRES5evMjly5d/tovE4cOHOXDgAOXl5UiSlOYqhcVMoVBQUVFBc3MzExMTxONxurq6GBwcpLW1lezsbDQaDbW1teJY/MBE8KaB1+vlwYMHfPPNNzx9+pR4PI7D4WDLli0cPXqU+vp60TYmpIRarWblypUcP36cYDCI1+tlamqKzs5OWlpaMBgM2O12sQLeByaCN8UCgQCPHj3i22+/5f79+8zMzKDVamloaODQoUOsW7cOs9mc7jKFJcRgMLBp0ybcbjdTU1PcuHEDj8fDs2fPsFqtOJ1O9u/fT35+frpLXTRE8KaQLMt0dHTM7SLh8XiAd5NpBw8epLGxkaysrDRXKSxFarWaLVu2EIlECAQCXL9+nXg8zpMnT1AqlZjNZvbv3y8GBR+ICN4Uevv2LefOnePq1atzW7JXV1dz+PBhGhsbWbZsWZorFJayrKwsGhsb8Xg8+P1+Hj58iM/n49atW2RlZWGxWNi+ffvcNvLC7yeCN0UmJia4ePEiJ0+enOtgyMrKorm5mT/96U+Ul5enuUJBeLea2aFDhwiHw/h8Pl6+fEkkEuHq1atoNBqsViubN29Od5kLngjeFHgful9//TWvXr0CwOVyceDAAT755BNqamrSXKEg/E1BQQEHDx7E4/EQjUbp6Ohgenqaq1ev4nA40Gq11NfXi06HP0AE7zyLxWLcunWLv/71rzx8+BB4t2DJ9u3b+fzzz2loaEhzhYLwj8rKyuY6Hf77v/+b0dFRRkdHOXPmzNw6vhUVFSJ8fyex6so8CoVC3Lp1izNnznDv3j0ikQhqtZpdu3Zx/PhxNm3aJJrThYykUChYuXIlR44c4dChQ3MdDX19fVy4cIEzZ87Q3d2d5ioXLjHinSfRaPQfHgfWaDTU1NTMPQ4s1mAQMplSqaS2tpZPP/2U2dlZLly4wOzsLK9eveKrr76a27HY6XSKke9vJIJ3nnR0dHDp0iVaW1vntmR/P4LYuXPn3HqogpDJzGYz69evZ3JyEr/fz40bN/D7/Tx//pzz589jtVppamoSq5n9RiJ458HIyAjfffcd58+fp6OjA4C8vDyampo4fPiwWINBWFBsNhs7duwgFArh9Xp5/PgxoVCIe/fuodPpsFgs7NixA4vFku5SFwwRvB/Y5OQkN2/e5NKlS3OPA+fm5tLU1ERzczOrVq0SjwMLC05eXh67du1ifHycUCjE48ePcbvd3L59m6ysLEwmExs3bhSrmf1KIng/oEgkwsOHD/nyyy95+PAh0WgUnU5HQ0MDJ06cYN26dSJ0hQVJoVBQUlLC4cOH50a+3d3djI+Pc/XqVQwGAzabjdWrV4tNM38F8Q59INFolCdPntDS0sK1a9fw+Xyo1WrWr1/PoUOH2LZtG3a7Pd1lCsLvplAoWL16NX6/H7fbzblz5xgYGKCnp4crV67M9fiuWLFCTLb9CyJ4P5DOzk5OnTrFxYsX8fl8AFRVVfHJJ5+wb98+EbrColFTU8O//du/MTs7y9mzZ5mZmZk7/s1mMzabjby8vHSXmdFE8H4AfX19nDt3jvPnzzMwMAC82077yJEjHDx4kMLCwjRXKAgfjtFonFvNzOfzce3aNWZnZ3n+/Dlnz57FarVy4MAB0enwvxDB+wdNTk7S0tLCV199NddQ7nQ6OXr0KJ9++illZWVprlAQPjy1Ws3u3buJRqP4/X6+++47AO7fvz+3mtmBAwfEZNsvEMH7B0xMTNDa2kpLSwtPnz4lmUySk5NDY2Mjx44do6amRmzJLixaFouF3bt34/V6CQQCPHjwgGAwyN27d7Hb7RiNRnbu3CnC958Qwfs7RaNR7t27x6lTp3jy5AnJZHJuTdPPPvuM+vp6EbrCoudyudi/fz+BQGDuqbZAIDDX6WCxWNiwYQNqtTrdpWYUEby/QygUoq2tjUuXLvHDDz/g8XjQ6XRs3ryZQ4cOsWXLFtFMLiwZ7zfN9Hg8yLLMq1ev8Hq9XL9+HZvNhlKpZOPGjekuM6OI4P2NEokEHR0dfPPNN7S2tjI5OYlKpWLVqlV8/PHH7Ny5E6fTme4yBSGlKioq+Pjjj/H7/UxNTTExMcHg4CDnz5/HZDLhcDgoKSkRI98fiWvh32hoaIgbN25w4cKFucm0srIyGhsb2bNnj9gUUFiS1Go11dXV7N+/nwMHDsy1k/X29nLlyhXOnTtHf39/mqvMHGLE+xtMTk5y5coVvvnmm7kFzXNycmhububo0aNUVlaKp3aEJUur1bJu3bq5ToerV6/i9Xp58eIFarUai8WC2WwmJycn3aWmnUiJXykQCHD37l2++eYb7ty5A7yb1d22bRuHDx9m/fr14nFgYcmz2+00NDQwMTGBz+fj5s2bBINBnjx5QnZ2NhaLhT179uByudJdalqJ4P0VEokE9+7d469//Sv3798nFouhUCjYvHkzn3/+ORs2bBChKwg/crlc7Nmzh1AohMfj4dGjR4TDYe7evYtOp8PhcLBlyxYMBkO6S00bEbz/QjQa5eXLl3z99ddcvnwZj8eDSqVi7dq1fPLJJzQ2NmKz2dJdpiBklKKiIj766CPcbjehUIgXL14wPj7O999/j8vlQq/XL+kBiwjef6Gjo4OTJ0/OhS6825L9s88+Y9++fSJ0BeEXlJSUcPz4cQKBAF6vl8HBQUZHRzl79iw6nQ673c7KlSvTXWZaiOD9BbIsMzg4yOXLl2lpaZnrYCgtLeXQoUMcOnSIoqKiNFcpCJlLpVKxYsUKjh49isfj4ezZs4yOjjI4OMi3336L3W5Ho9FQUVGR7lJTTrST/YLx8XEuXbrEhQsX5naRyM7O5vDhwxw9epSSkpI0VygIC0NdXR2ff/45jY2Nc48Pv337lpMnT3Lx4kUmJibSXGHqiRHvP+HxeLh//z7nzp3j0aNHJBIJsrOz2b17N4cPH6a2tlY0ggvCr6TVatmwYQM+nw+/3/+z1cxOnTqF0Wjk8OHDZGVlpbvUlBHB+3fC4TCPHz+mpaWFBw8eMDs7i0ajYdOmTRw/fpza2lqxJbsg/EZ6vZ7t27cTDAbx+XzcuXPnZ50ONpuNvXv3YjQa011qSojg/YlEIkFnZycXL17kypUrTExMoFKpqK2tZe/evezcuXNJfSsLwodktVrZtm0bbrebeDzODz/8QDwe58GDBzidTnQ6HY2NjWi12nSXOu9E8P5Ed3c3LS0tXL16dW5L9urqao4dO8auXbvEws6C8Afl5eWxb9++uTUdOjs7mZmZ4fr16xiNRhwOB2vWrFn0Pb4ieH80OTnJ1atXOXnyJG/evAGgoKCApqYmjh49uiRnXgXhQ5MkiaKiIpqamnC73Zw9e5b29nYmJib4/vvvcTgcKBQKGhoa0l3qvBLBC7jdbq5cucJXX33F8+fPgXe7SOzfv59PPvmE6upqsbauIHwgCoWCFStWcOzYMXw+H16vl5GREbq7uzl//jwWiwWn00lJSQlKpTLd5c6LJZ8mkUiEu3fv8sUXX3Dr1i0ANBoN27Zt409/+hObNm0SoSsIH5hOp2PNmjUcOHCAxsZGsrOzkWWZ169fc+XKFS5evMjg4GC6y5w3S3rEG4/HuXPnDqdOneLOnTvE43EAdu7cyeeff86mTZvEamOCME90Oh0bN24kHo/j8Xi4fv06wWCQZ8+eoVAosNlsmM3mRbm+9ZJNlUgkwtu3bzlz5gxXr17F7Xaj1WpZtWoVf/rTn2hqasJqtaa7TEFY1JxOJ9u2bWNqaopgMMitW7eYnZ3l/v37ZGVlYTKZ2L1796I7F5ds8HZ1dXHu3DlaW1sZGRkB3nUwfPrpp+zevXtRfssKQiZyOBwcPHiQUCjE9PQ0bW1thMNhrl+/jlarxW63s2XLlkX10NKSDN7x8XFaW1s5c+YMr1+/BqC4uJjm5mYOHz5MeXl5misUhKUlJyeHffv24fV6icVitLe343a7uX79OlarFa1WS0NDw6KZb1lywTs5OcmNGze4fPkyT58+JZFIkJeXx969e9m3bx8VFRWL5sMVhIWktLSU48eP4/f7mZmZYXh4mNHRUc6cOYPJZMJms1FVVYUkSeku9Q9bUgkTiUR49uwZp0+f5v79+0WT/7sAABd2SURBVCQSCcxmMxs3buTIkSPU19cv2fVBBSHdftpmduzYMQoKCgAYGRnh/PnznD59em6VwIVuyYx4Y7EYz549o6WlhRs3bjA5OYlaraahoYEjR47Q0NAg1tYVhAxQX19PNBplZmaGc+fOMTMzQ3t7O1999RVWq5VPP/2UrKysBT3yXTIj3p6eHr7++mvOnj3L5OQk8G4y7ciRI+zbt0+swSAIGUKj0VBXV8fx48dpamqaWzinvb2dr7/+mvPnz8+dwwvVkhjx9vf3c+7cOc6fPz/XlF1VVcXHH39Mc3Pz3FbUgiBkBrPZzLZt2wgEAng8Hh4+fDjXZqbX67HZbOzatQuHw5HuUn+XRR+8Xq+XixcvcvLkSd6+fQtAVlYWBw4c4MSJE1RWVqa5wvSQJOmfXqot5Mu3heyX3vel/Hm4XC62b9+Ox+OZW80sGAzy6NGjudXM9uzZsyCXaV3UwTs1NTXXNva+g6GwsJCDBw/y+eefs2rVqnSXmDZarfYfujcUCoXo6EiT9+/9T4NWoVAsqt7V36OoqIiPP/6YaDSKz+ebW1Dn+vXrmM1mXC4XdXV1C25SfFEGbyKRIBAIcPfuXb788ksePnxIPB7HYDBQV1fH/v37qaysJBqNIssysiynu+SUeT/SnZmZmXv97/9cSK+/vwqJx+MEAgEikQiSJJFMJtNYXeq9fz9cLhcNDQ309fXh9/vp7e1leHiYGzduzD3RVlNTM7et0EKwKIM3EAjw8OFDLly4wK1bt3C73Wg0GlasWDHXB9jV1UU0GiWRSKS73JRSKpWo1Wq6urqYnJycO5mTySThcBi/308sFkOW5bm1K4T5I0kSarUav99PIBD42ZdhKBSip6eHx48fo1QqiUajaa429RQKBRqNhmg0SmlpKRUVFXg8Hqanp+nq6uLrr78mEokQDodZu3YtJpMp3SX/KosyeGVZxuPxMDQ0NDf7KUkSCoWCkZERLl68iEKhIB6PL6nRLvwteMfHx+ns7JwLXrfbzZMnT5BlmZycHBG8KfI+eIPBID09PfT09BCJRACYmZnh9u3bTE5OolKp5v58KXk/6tVqtYRCIYLB4NzPotEob9++JZFIoFQqsdlsrFq16m9LScoycjJBEglJqfy7Fq4kyaSELEkokCEpIyOhUL6/4kggJyApKVBIEh/6glCSF2HyxGIxXr16xZ///Gf+/Oc/MzMzA4DJZJq7HEkmk0sudOFvB3IsFiMUCs2NojQaDSaTCaPRiEajWXK3YNLl/eeRSCSIRCLMzs4SCASQZRmFQoHBYECr1S7JWw0/pVKpkCSJUChEIBD42ZWqJEnU19fzn//5nxw9evRv/fjJOLHgLKFQiFAc4rIChQSSBAqlBqXOhN6gQSclkMMBgsEg4XiSWFIGSYlCY0RnNGBUK1F/4GWBF+WIV61WU15ezpo1a1i2bNlc8Pr9fvx+f5qry0zRaBS3243b7U53KcKPksmkOGZ/BVmWaW9v58WLFzQ0NGA2m38c9SaI+SeY6nlBx5tO2vumGI0YUdpLKamuoW51JStKNOilBHJyiqmuZ7x4+JpOt4JkUQ1lNWtYU6ZHZ4MPPcW5KIMX3vUBVldXs337dnQ6HaFQiGQyKWbtYW7E6/f7CYfDc6Pb91cBYqSbHu9vh70/RjUaDQaDYUFNGs0XWZbnrg4kSUKWZQKBAF6vl3g8TnZ2NiqV6sfzXEapBCRAjhLzjTHVdZ/HV29zs1vG7djO+iMmzMtKWaEECQXKxDgz/Q+4f/UuD6Yc2HfloC1JsCLJB7/NAIs4eOHdQxL/8R//QXNzM7FYDBCz9+9ffyQSYXp6Gp/PNxe2S/29ySSyLKPT6XA6nVgslrmwEf5menqagYEBvF4vdrudrVu3kp+f/7fBlaRCbc7FVbmRWpVEYHqYqaHHXB3sp294hhlZ4t0Rr4TAJIlIEJ+tGkd+DTs217K+1E6OUYFKBO9v43A42LRpU7rLyFjvZ9KX8r3DTKbRaLBarWIXlF8QDocZGRlhamoKo9FIUVERZrP5J7+hRG3KwmnKwlleSb5JwqbWEL7oY3iim+6BKYarjVjUHjz904wEcsnduo6G1Q3sW2cnax6fyxCf6BJmMpkWTPuNIPw9nU5HaWkpBQUFv+JhExvO2p1smRnnbf/XnOu8z73rtSx3hjHlDvG2K0T7TCllW6vYXD+/oQsieAVB+HvJIJHZCEH0aM06DBk8LfK+1exX0VdQsKGZ/U3tTM685OLdbzkd7ia8Vo2sLsZQWcPqymxKDPNbM4jgTbF3vYLiTqqQeWTkeIxocAL3yCBDQ24mIwa0OUUUlS0j36rBqFzoR64WhW0ldXv2Mjblo+PUPR63dDHr3UHTpzvZu3M5pc7URGIGBG+CeDxBIi6DUoVKrUT540EQiyaRVUpUGjUKQErEScbjxBVKUKhQynHkRIKYrEShVKFRffhG5w8m6sbnDuBLGNA5ndh18IFbAwXhDwjg7Wmj6+k92rpHeN0/zsRkiKBlBYUbmviosZatKxws+BWrFXbUKz+ibvsgW2628eqtm9d9m9mgsJHrUpGqG28ZELxJkmE33rERRsfcTPvjxCQtWrMDmzOL7FwHDo2ad7dcEsQDk0yODTM6OYM3pkNpycWVm0O+y4JdlWGjyWQMOexlZnKIof5+evvGmAzpILuC4uVVVJc4cBmVpGx5D1lGlpPIKEGxhBZjFv53yRhydArPaB89PaMMTYfwx8LEfW/ofN5NW3eUhNFMTrGDGj38ygv7zJU0oHPkUVRVTMnbAbr8o4x0D9EzWUmeS4ExBSGSAcErI0WnmOm9y4NLN2h9NMxANAtX3S627N/NLrsDK+9a8lAkSIZGGLh3hms32ngWLcW69gC7d1qwOaw4Mip1gaiXYM9t2h638f3zEQYH+pn2BBiN5pO3cT/7/nSQxvosylOVvMkYyWiIUFQmKitRqSSUyCSTCZJJCUmlQa3To1ORWV9gS4JMMpYggRK1OsXvfsxPcsZD1JCPpb6ErQYlRuUE8eEfuPCXW1x70UbPq/W0T6ynsBByFvI3diJCvP8FU2PT+Ipqya6Sifa/pO/eLS5VVpC7q4g1KQiSDAheBQq1Hp3JhE3rJTb0kMc9OlTBPOyb97BRpfvbiFACtTbMzOQ4/W/H8GSXkmU3YzFo0M5Hs93vJgMRouEZJid9ePwqNPYC8pUaTJoXTN+7S/v3CqRl1WRl2ygqUZOacy1JMjCFb7iXrr4RBibD+NFjsFmxmAwYVDIqKUEkHCUaU6Oy5pFTXEpZsRWHuC/ygYWJu4cY6B1l1BclqtCgUChRKxWoVBISCRKSkrjCgdmWTXGuCZtxvj4ECRQmLAW5VFbmkW8DAzHAQKh7goGOYaLhIJEkJDLpNPvNfMieHtqfv+HlmAlN9T4+MpgZvXKWb9+0cr2llNLcQ+RtdpA1z68zA4JXidJQQG5NI43qAIpYCM9fOnkV9+MPyISiP70XGkGSEiStlTjXlFC1ZStbDtaz3GTAqs2kUZoMhAknYdZQTUH9WlYvs6GTkvh7rnBb9f/Q0jHIaP8IvSM1xIpTFLySAjkeIDbxjK4bVzn9/Rg9UiElDWtZXZ5DvsqPPDvOyOAIwxMxQqZKSjfsYlfjejatdC3skU5GCSFPtNPx+B43H/TS6VGgtGdjtxmwamXkWIRocILZSJIJVlJQuZnD20vmL3jVJhQ2HVmSGlnFjwOdOMhKJEsBjmIr5pI8yh1gyJyT7Lfz9TDe/ZRHwyomDWvZXFPBqnUGejUDDP5/z/jh8WVu3CmhuHgHjQVgnMdSMiB4JVDq0JiW4aw/yM7ALGP9/0PkRS+9D5/SVp3L+txcsgDcU8y87mRWYceyvYF126vYmG3KwEkqCVCj1jlwFGahNVhxvZ+VsG4ktvwb3nr9hAxqZJUydROCCiVKow2zS4dV5cc7MMKINpdCZym51UWsVAZJBvPIyraT2/Wapy/u8vhsP/1jbsaONLK/NpuiBX3mZQIP4YFnPPz2Cq3PxhgwlOEoLWFFvg2HWYtRJZOIRYlN+Rjp7eDFgB6PtILNdQXM291VhQpJofr5egSRKfxdA/hVOTh376RmUy11VjD/0r+R8SYZ7erhyVM3Pt0KiutWUlVowanbgLlpgqb2MSauPeP19WtcKSqg/HA5q+bxSe0MCN6fUBZjX7GTXU2v6Bq/z7n7F7m5LIc1Kz9ijzNOYrSP9qdjeNQVFNQvJzc3E0MX3gWvAZ3BQL7+p50WMuGZEDOqIpxlWjatLWXVMi2alGWZEqUpB3tpBeXLKynJCxMwV7N68y62NBWxQSkDMnLSTbT/Lje+/H/56+nb/NASwytbsdu346yyYJAy6epiIUkQd7+k+/Y5vjnziEexVdT8n3007a1jq0tC+9M31W1j8LmGUVnNhCqKQk7REp3JCNHALNPtt3lxrZUHY1l4qjZTa7djkEGxkD74ZJRYOEhwto+ZvidcvtpN24iTyqZlrKmx4NQAONEU1LOmtoxnj9p58vAcVwxmCuyHkOsKKDTpMWpVqD7w1V5mBS+gclVR0fgRW7uGeP11G11373Glpoji2hm0EwM88xcgF6+gvthMYUavHfJjh8VPD9TwW6ZGu3kTL0cqqmBnTQF12SluK5NUSDotGr0OrVqLVqtDbzRh1Cp/cjDkoK7cypZdb/H299Nx8Slvb5fyw7pKygosrDGTuk6MxSThYeLZbe5fv83dMRuJ+g2sW1PJujz1P17WZq8if5VE/cwkY0EJuy4VwZskER5j/OV9Hl78mstX7nJjzIFUa8bkMlOSv5JqG6Tg+YIPQEaOTePtaeP57cvcuXmXS6/1BIoOkCUZ0Srfh58MCdBqNejUfmJTT+m8ouAvuhj+iT00baiittiG4wNfbGRc8KK0oivfzvo93Yz0nOIvnQ/5/qQee0+CslwL3sLNrFxeQZVpAbW1RH0E3L2MvfyW1tantLTZ0a4ooSwQR0r5MgkJiMeJxxMk5STJRJx4JEwkwd99A2RhX7ONHc1vufPsIiO9j3n27CNe1JWxwqhCI+73/kZRkqFeep485P6jUcaNG6lfv4X6IjPOf/r7DlTZdaypHac8ECPHlqq915LIiTgYnFjKSnBMdDP86Aw3s1w4C5bhWGemVL8Qhr3vV9xLEI8qiCmzya3Ix1JbSWmuGW0UZD1IxJETajT59VTtmuWIa4qBoB2dUUKKJUgkZeZjaaLMC14UQCGFNVtpbO7gzfRLzt/+llMjxWw//BEb9xaxerkF7QI68eXQJDNd93l86z43rj/leUeS2GQCKT8HraGB5uXazPwSseRhqSynOFePrWeSiZ4hhodDxIvFkPe385LwdTLQP0D3hIRUk09+QT5W3S9f7yiVJgqKNCQTCZQp2fRSQqHNJXvVbrYuq6Nm3xs2fP3fXLr4jLtdr3j4dIBdJVWULlsIG3AqUGic2EsbWGeroHx3iCB6NFYXdqsF29xkvBLJXETuho9pXr6HjYEIoZgCWWPCaLFjtxmxzMPLzcDgBVCiyl3D8h272fi0m+eveumcqcStraR8mYPiVHQ4f0hKHRprPlmVW1nr06NT3ObB+CPuX6sgvyCHlaWVFKulDPwwjCjtOTgcJixSkEG3mxl3gERi4U6xpE3ST9I9xNS0h6moBrXZgcNmRv0vBhDqlO6eKyEp9ejsenT2PHIoozDQg2JqiLev/YwNTTMzG+PDLws+TxRaNOYsXOYsXL/8S6A2oLMZ0NnyyE5RaZl3rr+ndKEurKG0OJdVhRP4c5dhySklS61ecIMtyZiLY0Ujm8t3sn7HK4a/t/B//+cxX/e20/emlv5IBbkZGbxKkFSolAqUCpDlpFhC8veSE8ihMLFIjJikRVKrUamkDJ+s0qFz5LO8ooDigJNJkw6xj8CHkXnn+hwlktaCXq/HYlCiN+hQaXQL5bv25yTlu4dE1KAzrGZF02bWtnt41BdB6fXijyeJopjXvsHfJ44cjxCLxojLCtRaAxqtLnPXw8hkkgI0alQqFcqkTCIWJx5PImf6g9uyGpVSR3Z+DtrSPCymBXkGZpwMDl7erS2A9OPB+W50IGVm/9hvoACnC0dJEdk5CcwmMzallJltcfIs8ckRxicDzODEkptNVq4RVUYWm+EUZhSOfBwOKw7lJH3eSabcPqLyv1p2RoZkgiQKUCjmJ6ZjPqKeEYbGZhj1q1AZTVhNajREmX3rpjtYQF75ClbX5JBrFcH7IWR08MqJOIl4glg8STweI56IE1/wV7phmAmQUBnQlOWSW7iMQrWU2hadv9uuWvql7aunB5l600XPhIzfVkztimWUFmlQZ/RRk6lsqGyVFJYUUuoao3u6j6HePiZnV1Nm+KU3VCYRCBCNx5G1BpQ6DRrmoYc6OEzw9XmuXXrJlW4TxuIyVldYsCtCzHoSRIybKF+5hrWVWvLmeYHwpSJDT6EwsdkxJrqf8fpNF+3dw3R52zG/esmr5atxLLdjM6gytXjePTI8jbe/k1ePexmcUaLKzcNp12JITBMdGaQv4KRoSz119UXkahQpfC1qUKlQK5UoJQVKlRqVVo/u74dSsQGG77Xy3aXntPnzMdfvYPPaEla7pBStK7HYaFAYy6lY38Dm9n5e3m2j69Z3tK7JIndXAcX/MJD0k5geoWc0xiw2cgt0uOYr9JRaFHoHtqw88kN69Fl27DYzVkmHzp6NNqeaNZX5lC2MBt4FIUOzK0wsOMbEwBATASVRgxMDQWR3P8PjebgLzZgzOniTgBvf8GMeXbjG7V4Jxcpaysod5CpjRPwqtHmVNGxaTk25DX3KbvPJyIkQydlZZn2z+ENB/JpZfO4p3LMGgu+fXEtMEuy+za1bT/m+S0myYhub9+5hV3UWpcqMPWgyn8JFXu02tjaP8WbkDj8M3uXerXJybFtpWq7HqpBQKH7cSXemn+nRPnqmzETMdhxJJWrm6YlBwzJMNZ+wtzzK9pgCSaVGq1agkGRkSY1CrUMvGrc/qAw9h7So9Nm4Sjay6eMccjaH8Ckd2AorqCiyYdUqM/Oe6BwJsGJyVVBVN0XA6sfvcOC055Jls2DUWskqWEZpmZPsVLZoJCJEp3oYb3/Os7Z2OoZ66Zm2YG+9iCNUzJgmhjI2i88zxvRQP52DNqTa9Rzc9hG7d1axOkudqQfMAqFE6VpD+fYkx4N6LLc7ePn6LJcmH/N2mROH2YjNqEWv06NRK1HrTeid2RTmW7DqlfP3mLZCg0KvwaIHy3z9P4SfkWSxZ/T8iYeIeCeYmvYwHVKQ1DuwuVxkWXQY0zFHEQ8QGnnFwPNWrl+7zeVHUwxL+SyrWcnykhzytDFUEQ/Tkx6mA1pU+WuobtjM1rUlrHCqMn3+fQGJIE+85M3DH/j+5gseD4Twa52YbFayrHpMRiM6Zyk5pauprS6kKle7MLt5hF8kgjcVkhGi0SRxSYNaq0zfSZSMEw968HsmGJ9wM+mLEkaL1mDAoNehUSRQJKOEQ1GishaNLY/s/FzyLJnYY7zQRYh7hhkZHGPUEyaIFqVGg16jQqVSodLbMNpcZNv1iA6uxUcEryAIQoqJq0dBEIQUE8ErCIKQYiJ4BUEQUkwEryAIQoqJ4BUEQUgxEbyCIAgpJoJXEAQhxUTwCoIgpJgIXkEQhBQTwSsIgpBiIngFQRBSTASvIAhCiongFQRBSDERvIIgCCkmglcQBCHFRPAKgiCkmAheQRCEFBPBKwiCkGIieAVBEFJMBK8gCEKKieAVBEFIMRG8giAIKSaCVxAEIcVE8AqCIKSYCF5BEIQUE8ErCIKQYiJ4BUEQUkwEryAIQoqJ4BUEQUgxEbyCIAgpJoJXEAQhxUTwCoIgpJgIXkEQhBQTwSsIgpBiIngFQRBSTASvIAhCiongFQRBSDERvIIgCCkmglcQBCHFRPAKgiCkmAheQRCEFBPBKwiCkGIieAVBEFJMBK8gCEKKieAVBEFIMRG8giAIKSaCVxAEIcVE8AqCIKSYCF5BEIQUE8ErCIKQYv8/1myySqgm50QAAAAASUVORK5CYII=)
Maths-General
Maths-
In the figure, ABCD is a kite with AB = AD, BC = CD and
intersects
at O. If
and
then a – b + c – d + e – f =
![](data:image/png;base64,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)
In the figure, ABCD is a kite with AB = AD, BC = CD and
intersects
at O. If
and
then a – b + c – d + e – f =
![](data:image/png;base64,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)
Maths-General
Maths-
The expression
where
when simplified is.
The expression
where
when simplified is.
Maths-General
Maths-
Suppose you drop a die at random on the rectangular region shown. The probability that it will land inside the circle with diameter 1m is
![](data:image/png;base64,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)
Suppose you drop a die at random on the rectangular region shown. The probability that it will land inside the circle with diameter 1m is
![](data:image/png;base64,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)
Maths-General
Maths-
In the spinner shown, pointer can land on any of three parts of the same size. So there are three outcomes. What part of the whole is coloured ?
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)
In the spinner shown, pointer can land on any of three parts of the same size. So there are three outcomes. What part of the whole is coloured ?
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General