Physics-
General
Easy
Question
The magnitude of I in ampere is
![](data:image/png;base64,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)
- 0.1
- 0.3
- 0.6
- None of the above
The correct answer is: 0.1
All the resistances are in parallel order, so voltage across them will be equal.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/900283/1/971869/Picture1129.png)
![therefore blank 60 I equals open parentheses 15 plus 5 close parentheses I subscript 1 end subscript](data:image/png;base64,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)
![⟹ 60 I equals 20 I subscript 1 end subscript](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGEAAAARCAYAAADNJMJiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAg5JREFUeNrtl0FEREEYx5+11sqKDkk6RFbSqUtWVhJZSZJI0jE6dOoQHZJO0TF7iJW1hyRW1kq6JSsdliSd0q1Dh710WFnrie0b/vGMmffm2XnTO7w/v8P73uf5z/tm5puxrGA1SZSJJtEmrokZLqeXOCXqoICYTC0iptFjlriCR5t4ITYkuf/t1be28NNHHQNgg3vg8u6IJcfzImIipYlXzT5rxDqRwvM48YiYFTKvvsQG8qSQt0rkBfETyU9YJi4N+B8W/MDQeN31WH5/KkiM8WLbQE4Qn8U7XofEnqGJ1A6r133iA/uom96IQYXvfREJQZzFGoJ4GTNMpI4CqprClhSUV091FDlyaTpt9IIKmpON7YlveD8uPmxB7J0YCngFJNF0s2H3WkQhLlwK+UwsEHEUKwtj24oD47eDGAoapPqIqmTbMepVdSUcu6yEpmQWTBCfjueGZIknBUs8Q9x36dtNIyhAWvJep1cjPeHWpUA21+zmBTk5QbNjjb4U0LjGiDOix+MQ0a1XtkUf4C7S1ekopZDHtpw1yWDrjucVDJ5XSXC6yuPuoVsDaKJxjzwdXs8R71gGlMAlaNMxuAzO3nNcLlu2O8hLYLXVBN+soMfo1g0mh4p0eTVSBKZ+zJxvNDVmdlrSDItobi3cMVKS42wyAJ9+eogur8aKECkqQlSESFERoiJE8ncIsH4BS5+5c3eZZNcAAACbdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDI3Rjk7PC9tbz48bW4+NjA8L21uPjxtaT5JPC9taT48bW8+PTwvbW8+PG1uPjIwPC9tbj48bXN1Yj48bWk+STwvbWk+PG1uPjE8L21uPjwvbXN1Yj48L21hdGg+ezHt5QAAAABJRU5ErkJggg==)
![⟹ I subscript 1 end subscript equals 3 I](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAARCAYAAACGjBGPAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAASVJREFUeNpjYKA9+AbETAz0A45AvA1q7w8gvgXEE4BYeKDdqALElxjoC/YDcRAQsyGJGQDxjoF2YwAQL2cYHOATtd1YAsR8JKivB+LyQRAQSkB8g9purAbih0BsTaT6VdCQJwf8JwITAuJAnAgtN7zIceN/InErEYUOyBHSA5AS0N1aQEs3zoVashSPGiZoKT2QQBAa6yeB2J4cNxKbMjoIpAxzaMnOMIDZBAZ4oAFCVTeSUmZEAvF8LOJqQFwLxBfonEp+kOBGomsTHiLVTgLiNCzii6Hi/+kYEHrQsoFYN1IdrMNTgjPQMDAOAnEoELNAszGoRXofiOPJcCPVwDsg5hiAwLAF4i3QbPEDWib4kOlGulZ/o2A0MEYDYzQwyGlMDQoAAAk4bBPw87kvAAAAj3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyN0Y5OzwvbW8+PG1zdWI+PG1pPkk8L21pPjxtbj4xPC9tbj48L21zdWI+PG1vPj08L21vPjxtbj4zPC9tbj48bWk+STwvbWk+PC9tYXRoPsTgRFkAAAAASUVORK5CYII=)
![A g a i n blank open parentheses 15 plus 5 close parentheses I subscript 1 end subscript equals 10 open parentheses 1 minus I minus I subscript 1 end subscript close parentheses](data:image/png;base64,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)
![⟹ 2 I subscript 1 end subscript equals 1 minus I minus I subscript 1 end subscript](data:image/png;base64,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)
![⟹ 2 open parentheses 3 I close parentheses equals 1 minus I minus 3 I](data:image/png;base64,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)
![⟹ blank 6 I plus 4 I equals 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAANCAYAAACw26D4AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAaJJREFUeNpjYKA/MAXiVUD8CYh/APEmILbHofYbEDPR0C0+QPyfgBpauUENiGuB+ALDAIM0aCSoQfl8QBwNxIexqFUB4ks0dAsPEF8jECm0dMNiaHj8H8gI0QLiMySoDwDi5USqJcdjM4E4mYBeUtxALqA4UkqgqZuBzECIJEF9PRCX08hj1kC8lwi9pLhhwCKlGogfQj1FKrgBxJIkqF8FTanU9hgbtEiSJ0IvPjf8JwJTze3/icStJFaAP6B1yTpo5fkLWpxF41B/C4ilaRApHUCcQ6ReUtwwYDkFBuZCDVtKouXngNgLiFmgEWoN9XgWmlomaMQxUDmV6gHxUSIDhZAb6BopxOaUDhJzyiccqc4AiJ+iiZkD8X4apLaT0BYVMXoJuYGuxRet6pRteCLxFxof1CCYT4NIISUQSXXDgLa+eMjUCyqiwrGIa0BTMDKYBG3D08NjuPSS6oYBr1PIAaBWz0Fo34AFqYgAtYRc0NSug9Y9AxkppLphSEYKCIgC8Wwg/gLEf6CRZItF3Tsg5qCTm3AFCq3dQG4dNAoGAgAAHeed2pbowLIAAACldEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDI3Rjk7PC9tbz48bWk+JiN4QTA7PC9taT48bW4+NjwvbW4+PG1pPkk8L21pPjxtbz4rPC9tbz48bW4+NDwvbW4+PG1pPkk8L21pPjxtbz49PC9tbz48bW4+MTwvbW4+PC9tYXRoPtP1S1wAAAAASUVORK5CYII=)
![⟹ 10 I equals 1](data:image/png;base64,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)
![therefore I equals fraction numerator 1 over denominator 10 end fraction equals 0.1 A](data:image/png;base64,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)
Related Questions to study
physics-
A cord of length 64 m is used to connect a 100 kg astronaut to a space-ship whose mass is much larger than that of the astronaut. Estimate the value of the tension in the cord. Assume that the space-ship is orbiting near earth surface. Also assume that the space-ship and the astronaut fall on a straight line from the earth’s centre. The radius of the earth is 6400 km.
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)
A cord of length 64 m is used to connect a 100 kg astronaut to a space-ship whose mass is much larger than that of the astronaut. Estimate the value of the tension in the cord. Assume that the space-ship is orbiting near earth surface. Also assume that the space-ship and the astronaut fall on a straight line from the earth’s centre. The radius of the earth is 6400 km.
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)
physics-General
Maths-
If for a matrix A, A3 = I then A–1 equals -
If for a matrix A, A3 = I then A–1 equals -
Maths-General
physics-
The temperature of the two outer surfaces of a composite slab, consists of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x respectively
and ![text end text T subscript 1 end subscript open parentheses T subscript 2 end subscript greater than T subscript 1 end subscript close parentheses](data:image/png;base64,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)
The rate of heat transfer through slab, in a steady state is
with f equals to
![](data:image/png;base64,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)
The temperature of the two outer surfaces of a composite slab, consists of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x respectively
and ![text end text T subscript 1 end subscript open parentheses T subscript 2 end subscript greater than T subscript 1 end subscript close parentheses](data:image/png;base64,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)
The rate of heat transfer through slab, in a steady state is
with f equals to
![](data:image/png;base64,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)
physics-General
physics-
Three rods of material x and three rods of material y are connected as shown in figure all the rods are of identical length and cross section If the end A is maintained at 60
C and the junction E at 10
C, find effective Thermal Resistance Given length of each rod=l, area of cross-section=A, conductivity of x=K and conductivity of y=2K
![](data:image/png;base64,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)
Three rods of material x and three rods of material y are connected as shown in figure all the rods are of identical length and cross section If the end A is maintained at 60
C and the junction E at 10
C, find effective Thermal Resistance Given length of each rod=l, area of cross-section=A, conductivity of x=K and conductivity of y=2K
![](data:image/png;base64,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)
physics-General
physics-
One end of a copper rod of uniform cross section and of length 1.5m is kept in contact with ice and the other end with water at 100
C At what point along its length should a temperature of 200
C be maintained so that in steady sate, the mass of ice melting be equal to that of the steam produced in same interval of time? Assume that the whole system is insulated from surroundings
and ![text end text open L subscript text steam end text end subscript equals 540 c a l divided by g m close parentheses](data:image/png;base64,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)
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)
One end of a copper rod of uniform cross section and of length 1.5m is kept in contact with ice and the other end with water at 100
C At what point along its length should a temperature of 200
C be maintained so that in steady sate, the mass of ice melting be equal to that of the steam produced in same interval of time? Assume that the whole system is insulated from surroundings
and ![text end text open L subscript text steam end text end subscript equals 540 c a l divided by g m close parentheses](data:image/png;base64,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)
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)
physics-General
Maths-
If A =
, then the value of adj (adj A) is -
If A =
, then the value of adj (adj A) is -
Maths-General
physics-
The curves for potential energy (U) and kinetic energy
of a two particle system are shown in figure. At what points the system will be bound?
![](data:image/png;base64,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)
The curves for potential energy (U) and kinetic energy
of a two particle system are shown in figure. At what points the system will be bound?
![](data:image/png;base64,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)
physics-General
physics-
Suppose, the acceleration due to gravity at the earth’s surface is 10 m/s2 and at the surface of Mars it is 4.0 m/s2. A 60 kg passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force)of the passenger as a function of time.
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VbjuxCAub+NgmJ/iGU5TBW5JQNLxN9cYWO7gnMCcvp4RALDEPKUxmZDI0GRIVmbgSght2cF3xgFHzcQZMr/swhpV4I91/AQCqIsPEJOhmc4JoKNMN80lXi9PDFjWVxxbctjDJ28GuTKA5GenYBj1kjqIb0T/PRUM9BrnQutrflpON/AT6uyfIhZx7ZWd8GByPK4ILOKJuLhVjgrzyQBTAMRgukeWx6Nic2zt5ABw/t5PzicmAHFGoXLMTyG44I9xuGhFqh5RlN0TvYmMAH5kFkZah5ArgmOTmXiRj0Dx/aiHWZ8T1n06MMhIZiWZ5eKDwhMyvkEYzmysF/BlxKN9x7xahcponzlpK5iPWWYhnWb8mfVCQxfOiZw85gm508g7AcVZxgfcTesspFR8aZF49+/qfByjLtiNxRozSfxglrq/nxeSQt6Q6/O/FEJA/cZ9lm8liGA+5gcfcLgwESa+Necdr1rzgiZITQh+JN5Hvey0eGF0YsVvsRLbofkDaguQwMqy8vyoXq2EjqqWL/uZT0O2LJFlz1xJ5QJWdSA5gGQC5L8e7AwCQhbea7cgGQX7C4r2PBFpifqT1hVXd5FVKte0UunEiQ2+GZKN4W5uo9McmJCENvNbJ8HGwcAT8/XOZzQG8S6cUlmSjR/vM3grnXAbHMLxvx3SRnEWe0kIv46UmVahc0tj3b6rANP9R8HutV/G0sbAs+OwQxelBe1aPnIIkol2fXR8eIYH+QoIn9rxRbvoClbREzO9EbTmJcZJcAsqwe6dPD8TmgkUi723vZgWS5tU9+6S2w9ERActMyLomxEmiwvPtkeIOVW6kMDnIwqbshajkDWR7ZQr2Z8iOHug/XYmhJZaGtcmABDrMi4x6pgncK/edthXpvCLJl8TmZ0034IbHLmnml39301KzmNc1gawWM6T5/IfL/Eh7ZwruKYGVyk2dluhGstTVtsBxXKIcItoklGhUhUzkI4G2bG/Oisv/WeLQt0CKYk8ldnla+ZxA96Vt2b0vCIcjTyR+bFFiVaGQGyhnwELcALE1NPj7Zs2FcxaqyS47FDIIrZ7I5t6NQykkZCHZushhK2X9vrLClyKHsiFHox+LUHIYFL3CjBz2IvLU2xQhZRc8Qpuy+OdbYktVmShcmBFu3WdraQZC+kX/SYLniuWC5u2GlpffHGlsMJ7lO2E6zsBecGtEdIgRo0+L55Bkcxu4WNfM3xoonAtIwNSJjpR61gBhbo6RFbvXK8Q6cDHsO97wWtxAwurOxaoYy37ki/BkExU9nzL4P1tmyiHTpRpZDZy9BcZUl2OKz6NBKTkSwIj2LVSZNHl8A/gosMRTxJH5oiy3Z+UzEQCf99QCV+aZnsPzood4U62yh8+EI9PgSGzterGzfISMrkXWccuD9sRa3EPOabqbLox+RcP8pA1jLClwx5zQ6RLasioUNhtMQzmjEMstTDZ9XshnnDaChauMwBf0cWJS47xArOaMLi7xzujCMSxy63BeM5BLTDugTYEsszKNnRvfDLAoM0nVlFeSyTwLYW6RCC/K9OzY8EaDdvG3pgT86OiTWRq8G+3fw17rIkvBZghZgI24BjOGVTK+YMd0kA2bfnIht/2rzb3Eu5HkM7h5bFsVLALd8Msqj3CEbSpNkuTjkaQJ/YJstlMIwrbOAmfRoNzWXq3sGY2TFKbr7ExncPbZQCotQg8Py91gXYhFrsXu1rPe2msWW8wT+xKYnwiU9tP2AW6PlhFgQzLOWkPfXIL8QFVz0/I3eHltRLsHIdu5Vp6kRYle2We32LrB7ymnFZqITWRZgx7bgRQTs87us6G3zEcS9jsW4HanQasOmyJDKzmlviB3bIuRY2AQOst71QSkQYScnKipE6Z7L4O56IkA8SNnOYP3yaIWBLIHQhSwninCJXbYwcF9YF0jqYBhvhpmgHHY6F1mELXtiWcsP54Nrm+CJNCnCr3MZ3GdsKfWFspMhlZfnakTDwiiZBvdk3hnYty2DLyl7AoQzkwdrbGII/cRsn40su3ELIUNEiwCVonomF/bXiXPnYt+nI8sztkAXmAeVnQwjl7xvREXT5BSOxJ0q7hc8Y4uUo5buVTzvnnnhxAchlKSK5yPLU7bQujyu5g4HtZf70TVnL07b9Dtz8L6HJ54ImKz+c0dZv2TjcuXVzCYpfT75A2+IJ3GLgOHY8obTvGzNiBCuFB2bLAVzKjxnS3ZGS2ZwzsRqP6EEt4NU2G92KCR+MzzJiQRiH5ZmE/mzzLgquwPYt027khnCIPlEQ4kTHGCLGIhHx8OxQpmJdgc2ZRr5sOYGHzX8MPEmnyZfb4wDbFkp0wnyhJiZXLT14NB99siaE/s+/vc3XMHTuEXARPrRH4MvnD6V+5/w3aTQSotyfjkPuK1dBGud37m6n298OMIWnrV622lfOmeTZj1Ky6PSJk/6yul32ZnAKBv48OGy+zIM/tZPm/FjbGFMtzYHXLHJsuWiH8H5FpsjVbJJWkud4Ny5TNTXY1+V4k8vpUSxGLYDbn4RHOhh+DY/CmguRNg0DXtuy0MiBpTQJm9PfzPJE8s54jR/4eCXrL/Vei48+3OSUfgLuXl0F75rbl3ZngF6c/v85MOT+Wh2WZ9jADkx3R/QUio4/cjfXYfvb1Mb9gOA2WSvH/if/z1u5B1w4sanjA+H8pfs8qt8m/xaPn/xPtjFeRQkH1k+Pf7SP7x38/K045fAqQs2ybpX8m9tA/8TnUzjYz4yfOVvU+Sj+GH5YE+XD5Szywsp4qWbTC3JRw5/3Tdh2/PC1uUifhb3v/K4AfGt1KMy5CR8y1/ld8BChICyOUE+lWvGsgdkOPAiOIMr7o7a/Uusx3Rb4MjbZiSn9LeehcVffxOh4Ca9Mr7OxrCd1Px7FwVvVLbeAXkYrOzsg074bGNDXwUz6WNqxMXdtiSIW30JceEiynUcHmjNJ5adBRTMStl8BonXyrc3g/lQRN5m+eSAGgmt1lUIMa6sJ1V2d8BoVsDQthx7H7AjGbFC5sgxNZLGjQ17KyvVHYvD+IflTx9bT+ifApkNYgT8zzd/O3iZIFetys4CBrm4O5Y8q8SV8kQspEv+Kur0k+nQISSun6qHXlNWGJ6pEWdRbHoho2WBTdmUA9tAHhpk0jCtEQD58JuISKfffaCusfII/uRKWQFqJGHa9kfikPy2H4eCcTlWZsLlyDaMiUwHIR2Lm4O8Mlgrq5jyqY6u8Pd3gE9GeeBzFJNCNdobD6Nh2TnBIG7nIr6H7nYWC1dZ5YKLwXsH4QSwJobIBSp/jS+wkGJK9LjIKQcUNwfOKLbdkSFZWZLLTz9OlH4E7wneyfrA1fO09Z5rdcYUfcTPw8uu/gBUFOOpx9U86Y22GwRlkGjH01CHkLPTyexQruDOFq4mqBUXoIX+QJ+QhXo4tN9mi8H9uV/q2IzwiCyzHR5AzLAQtOKsrj0BxYKTyBY+ugYGhssAQyxS7jq4OtVPAOYOJldbsZMDJIZdlQtHiWQoYBO4LPr7BO/7IlvghbiuIMRiYXAZzxwx2z8DOh7YObK3HAEYe6wmAZTKZtBfwNhVI0qj5y2HNlHEIrYlZrHgT8hyzlwheYeUPwxWjCIw/wjsSEBUt7wscUJTWm1BIucDKgC3xbM0YjpKEe6LQQxoAsrh2PM3+DEwIWG1vewWiGHNS8mNwI3sj7YnHEyjy1k8m6FS+cb/j5/pHVDkMvlojEk5Jv2GH/YfQlEuk8jB4ECH+Pf39P09QLlQZTK1YYPa/ieG4U+HLBeE4lD0vEbUb4ad7wNWJikYOFvX8aHzf12BChBI8FnzHChsWz7Ytxz/66D2sFGBK2QdCEP+DgwjVgZYVSgL5FiroqKioqKioqKioqKioqKioqKioqKioqKioqKioqKioqKiouI5Pj7+A1KtOSXIAIhOAAAAAElFTkSuQmCC)
Suppose, the acceleration due to gravity at the earth’s surface is 10 m/s2 and at the surface of Mars it is 4.0 m/s2. A 60 kg passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force)of the passenger as a function of time.
![](data:image/png;base64,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)
physics-General
physics-
A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as ![left parenthesis 0 less or equal than r less or equal than infinity right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as ![left parenthesis 0 less or equal than r less or equal than infinity right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
Maths-
If A is skew symmetric matrix & C is column matrix then
A C =
If A is skew symmetric matrix & C is column matrix then
A C =
Maths-General
Maths-
If A,B,C, are three matrices, then AT + BT + CT is -
If A,B,C, are three matrices, then AT + BT + CT is -
Maths-General
maths-
If A and B are matrices of order m × n and n × m respectively, then the order of matrix BT (AT)T is -
If A and B are matrices of order m × n and n × m respectively, then the order of matrix BT (AT)T is -
maths-General
Maths-
If A =
and B =
, then (AB)T is
If A =
and B =
, then (AB)T is
Maths-General
Maths-
If A =
, then A5 equals-
If A =
, then A5 equals-
Maths-General
maths-
If A =
, then for what value of x, A2 = 0-
If A =
, then for what value of x, A2 = 0-
maths-General