# Calendar: 1899-1900 Page 765

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FACULTY OF SCIENCE cx111 prove that χ α α 2ύ 3c 2b 3c 2b 3c On what occasions is it possible in the process of solving an equation to introduce roots which are not sola- tions of the original equation Give an instance How many solutions ought there to be of χ x3 y2 x2 Find as many as you can Prove that the product of and ra -p is -l r-l State this theorem arithmetically if 10 number consisting of digits is multiple of the excess of the units7 digit over the tens' is twice the excess of the hundreds' over the tens' digit if the digits be written in the reverse order and the number thus obtained be added to the original one the sum is 1413 Find the number What is the index-law Find meaning in accordance therewith for ah a0 and a3 Given that is approximately the tenth root of thousand express 625 as power of ten Solve the equation 2מ gd ez fx2 having given that one root is zero Prove by mathematical induction that the sum of the series Ja 2B 2b ton terms is nAa -1 db aB ln -1 2n Bb Hence find the sum of the squares of the first η odd numbers Draw the graph of -- xl 2x Give an accurate definition of the cosine of an angle and obtain the relations connecting the cosine with the sine ii with the tangent iii with the secant iv with the cosecant with the cotangent of the angle Prove that sin 4Θ sin cos 2Θ tan cos 40 tan 40 sec 40

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