GSEB STD 10 Maths Paper Style 2021-Gujarat SSC Blueprint 2021 For Maths.

GSEB STD 10 Maths Paper Style 2021-Gujarat SSC Blueprint 2021 For Maths. 

Download GSEB STD 10 Maths Paper Style 2021-Gujarat SSC Blueprint 2021 For Maths. 

The Gujarat Secondary and Higher Secondary Education Board or GSEB is a government of Gujarat body responsible for determining the policy-related, administrative, cognitive, and intellectual direction the state's secondary and higher secondary educational system takes.

The main responsibilities of the Board include academics, conducting examinations, and research and development. The board is responsible for the registration and administration of higher secondary and secondary schools in the state of Gujarat.

The number of adults that make use of the integral 1 over 1 minus 3 X plus 4 x squared is small. Most people aren't planning on doing research in pure mathematics or becoming a rocket scientist. So why should you bother learning this stuff? Well, let me answer that with a story. During the Second World War, the American military was faced with a problem. You don't want your planes to get shot down by enemy fighters so you put armor on them but armor makes them heavier and heavier planes are slower and use more fuel. Not enough armor is a problem, too much armor is a problem. So what do you do? Somewhere there's a sweet spot, but where? That's the question the Army's best scientists were trying to answer. Among them was Abraham Wald, grandson of a rabbi, son of a baker, and a brilliant mathematician. 

The American military came to Wald with some data they thought would be helpful. When their planes returned from the battle they were covered in bullet holes but the holes weren't evenly spread. There were always more bullet holes in the fuselage, the main body of the plane, and barely any in the engine. The military thought this was a good opportunity to make the planes more robust while cutting down on armor. Put more armor where the planes get hit the most, the fuselage, and less armor where they get hit the least, the engines. But exactly how much more or less to put, they didn't know. That's why they came to Abraham Wald, but they didn't get the answer they expected. He told them that the armor doesn't go where the bullet holes are but where the bullet holes aren't the engines. After all, where were the missing bullet holes? Wald's answer? 

The missing bullet holes were on the missing planes. The reason planes were coming with fewer hits to the engines wasn't because they weren't getting hit in the engines, but because the ones that were didn't make it back. The fact that the majority of returning planes had more bullet holes in the fuselage meant that hits to the fuselage could be withstood, so if anywhere, armor could be spared there. It's the same reason there are a lot more patients in the hospital's recovery Ward with bullets in their legs than in their chest. It's not because people don't get shot in the chest, it's because when they do they don't end up in the recovery ward. The chest is the point of greatest vulnerability so it makes sense that we wear bulletproof vests there. The engine is the point of greatest vulnerability for a plane so that's where the extra armor goes. Wald's idea was quick to put into effect and was still being used by the Air Force during the Korean and Vietnam wars. This seems obvious once it's spelled out but why did it fool the military officers? They had much more experience with war, planes, and armor than Abraham Wald did. Why could he see what they couldn't? It all came down to the way they thought. 

Without knowing it the military officers were making the assumption that the planes that came back were a completely random sample of the planes that left.  If that were the case then it would make sense to assume that some areas were just getting hit more than others. But if you think about that for just a moment you realize that that assumption doesn't make sense. There's no reason at all to expect that all parts of the plane are getting hit except the engines, or that all parts of the plane are equally sensitive to gunfire. Wald thought "what assumptions am I making and why am I making them?". That's a nice story but where was the math? Abraham Wald didn't use any formula, trig identity, or integral to solve the problem. Wasn't it just common sense? The question still stands, why should you do page after page of integrals you're never going to use again? Well, look at it this way. Rote learning and formulas are to math as weight-training and repetitive drills are to soccer. 

If you want to be a professional soccer player you need to spend hundreds of hours lifting weights and zigzagging through traffic cones. You would never actually see a professional athlete doing any of these things on the field, but you do see the agility and strength they acquire from doing them. But say you don't want to be a professional soccer player you just want to play the friendly weekend game. That's fine, you can still play soccer and you're probably going to be a fitter and healthier person if you do. It's the same for math, you don't have to get into a career in mathematics but you can still do the math, and you're going to have better reasoning skills, more common sense, and make better life decisions if you do. 

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