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Note for Applied Mathematics-1 - M-1 By Suraj Gautam

  • Applied Mathematics-1 - M-1
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SUBJECTIVE PAPER Instructions : Q.1 to Q. 6 carries 3 marks each, Q.7 to Q.10 carries 8 marks each. 3 . 16 1. Prove that : sin 20º sin 40º sin 60º sin 80º = 2. Find the image of the point ( – 8, 12) with respect to the line mirror 4x + 7y + 13 = 0. 3. If the angle of elevation of a cloud from a point 'h' metres above a lake is  and the angle of depression of its reflection in the lake is , prove that the distance of the cloud from the point of observation is 4. If r1 is the remainder when 3x4 – 8x3 + 5x2 – 7x – 13 is divided by x + k and r2 is when 9x3 – 4x2 – 3x + 8 is divided by x – 5. 2h sec  . tan   tan  3 1 k and if r – kr2 = , find the remainder when 32x3 + 27x2 – 43x + 100 is divided by 8 1 8 2 x – k. If two opposite vertices of a square are (5, 4) and (1, – 6), then find the coordinates of its remaining two vertices. 6. In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6 cm. Find the length of the chord BC. 7. (a) The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1 of the volume of the given cone, at what height above the base is the section made? 27 (b) A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal) 8. (a) In figure, M is mid-point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL = 2BL. (b) A villager X has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of plot from one of the corners to construct a Health Centre. X agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how his proposal will be implemented. 9. (a) Population of a town increased by 1200 persons in a year and then this new population decreased by 11% during the next year. If the town now has 32 persons less than it had before the increase, then find the original population of the town. (b) How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20% on the marked price, he still has a gain of 10% ? 10. (a) Solve for x : 1 + 6 +11 + 16 + ..... + x = 148. (b) The houses of a row are numbers consecutively from 1 to 49. Show that there is a value of 'x' such that the sum of the numbers of the houses preceding the house numbered 'x' is equal to the sum of numbers of the houses following it. Find the value of 'x'. PAGE # 1 1

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