087/X/SA2/05/A1 Class - X SOCIAL SCIENCE Time : 3 hours â×Ø Ñ 3 æÅðU Maximum Marks : 80 ¥çÏ·¤Ì× ¥´·¤ Ñ 80 Total No. of Pages : 11 Instructions : 1. The question paper has 36 questions in all. All questions are compulsory. 2. Marks are indicated against each question. 3. Questions from serial number 1 - 16 are multiple choice Questions (MCQs) of 1 mark each. Every MCQ is provided with four alternatives. Write the correct alternative in your answer book. 4. Questions
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accepted axioms. An example that was often used to illustrate this was Euclidean geometry. When you have the five axioms defined and the postulates formed from the axioms you have basic geometry that you learned in high school (Euclidean). However you learn later on in the book‚ that if you ignore the 5th axiom than you have a whole new kind of geometry‚ called non-Euclidean geometry. What everyone thought they knew about geometry and axioms was completely changed by altering the original axiom. That is
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JTG- Ch.2 Euclid’s Proof of the Pythagorean Theorem Century and a half between Hippocrates and Euclid. Plato esteemed geometry to be the entrance to his Academy. Let no man ignorant of geometry enter here. “Logical scandal” Theorems were believed to be correct as stated but they lacked the material to prove them. Euclid’s Elements was said to become the staple of mathematics or the standard. 13 books‚ 465 propositions (not all Euclid but rather a collection of great mathematicians
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The VSEPR Model 10.33 Predict the shape or geometry of the following mole- cules‚ using the VSEPR model. a. SiF4 b. SF2 c. COF2 d. PCl3 10.34 Use the electron-pair repulsion model to predict the geometry of the following molecules: a. GeCl2 b. NF3 c. SCl2 d. XeO4 10.35 Predict the geometry of the following ions‚ using the electron-pair repulsion model. a. ClO3? b. PO43? c. SCN? d. H3O? 10.36 Use the VSEPR model to predict the geometry of the fol- lowing ions: a. N3? b. BH4? c. SO32? d. NO2
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Electronics. Answer X1 = Number of GE45 televisions produced per shift X2 = Number of GE60 televisions produced per shift MAX 50X1 + 75X2 S.T. 2X1 + 2X2 300 (Production hours) X1 + 3X2 240 (Assembly hours) X1‚ X2 0 Recap of Analytic Geometry
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outstanding genius who studied geometry as a child. At the age of sixteen he stated and proved Pascal’s Theorem‚ a fact relating any six points on any conic section. The Theorem is sometimes called the "Cat’s Cradle" or the "Mystic Hexagram." Pascal followed up this result by showing that each of Apollonius’ famous theorems about conic sections was a corollary of the Mystic Hexagram; along with Gérard Desargues (1591-1661)‚ he was a key pioneer of projective geometry. He also made important early
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with exactly two terms. 8. A pair of numbers in which the order is specified. 9. A comparison between two quantities. 10. The horizontal number line in a Cartesian coordinate plane. 11. The abscissa of the point of intersection of a line and the x-axis. 12. The vertical number line in a Cartesian coordinate plane. 13. The ordinate of the point of intersection of a line and the y-axis. 14. An angle with a measure greater than 90 but less than 180. 15. A space figure with
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di Pisa. There he was taught by Dini and Bianchi‚ who quickly influenced Guido to undertake research in geometry. He presented his doctoral thesis Clifford’s Parallelism in Elliptic Spaces in 1900. Most young doctoral students take a few years to make themselves well know in their area. However‚ Guido was lucky for his teacher Bianchi was about to publish an important work on differential geometry. Bianchi discussed the results of Guido’s thesis in his treatise‚ which appeared in 1902. Guido remained
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Alexander Grothendieck Alexander Grothendieck is a prominent mathematician who is well known for his theories in algebraic geometry‚ homological algebra and functional analysis. He was born in the capital of Germany‚ Berlin‚ in 1928‚ one year before the Wall Street Crash of 1929. Grothendieck’s parents were Sascha Shapiro and Hanka Grothendieck. Shapiro was a Russian anarchist of Jewish decent‚ prosecuted by the Czar and later by the Bolsheviks. He’d lost his left arm during an attempted prison
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amateur mathematician. He became known because of the contribution he made in mathematics and physics in the twentieth century. Hilbert is well remembered for landmark researches he conducted in algebra. He also left an indelible mark in axiomatic geometry and mathematics. Hilbert also profoundly contributed in other areas such as invariant theory and mathematical physics. Hilbert studied at the university of Konigsberg‚ and during his studies‚ he made several trips to abroad. He visited Europe on
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