# CDS Maths(1) Questions and answers

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These are the list of questions asked in the previous year CDS Maths Exams. You can practice these questions as real time exam in this link.

51). If from the top of a post a string twice the length of the post is stretched tight to a point on the ground, then what angle will the string make with the post?
 A). $$\Large \frac{\pi}{6}$$ B). $$\Large \frac{\pi}{4}$$ C). $$\Large \frac{5\pi}{12}$$ D). $$\Large \frac{\pi}{3}$$
52). The price of a commodity increased by 5% from 2010 to 2011, 8% from 2011 to 2012 an 77% from 2012 to 2013. What is the average price increase (approximate) from 2010 to 2013?
 A). 26% B). 32% C). 24% D). 30%
53). A railroad curve is to be laid on a circle. What radius (approximate) should be used if the track is to change direction by $$25 ^{\circ}$$ in a distance of 120 m?
 A). 300 m B). 280 m C). 275 m D). 264 m
54). If $$0$$<$$\theta$$<$$\Large \frac{\pi}{4}$$, then what is $$\sqrt{1-2\sin \theta \cos \theta}$$ to?
 A). $$\cos \theta$$-$$\sin \theta$$ B). $$\sin \theta$$-$$\cos \theta$$ C). $$\pm$$$$\cos \theta$$-$$\sin \theta$$ D). $$\cos \theta \sin \theta$$
55). If $$\tan \theta$$ + $$\cot \theta$$ = $$2$$, then what is $$\sin \theta$$+$$\cos \theta$$ equal to ?
 A). $$\Large \frac{1}{2}$$ B). $$\Large \frac{1}{\sqrt{3}}$$ C). $$\sqrt{2}$$ D). 1

56). What is $$\Large \frac{\sec x}{\cot x+\tan x}$$ equal to ?
 A). $$\sin x$$ B). $$\cos x$$ C). $$\tan x$$ D). $$cot x$$
57). From a certain point on a straight road, a person observes a tower in the west direction at a distance of 200 m. He walks some distance along the road and finds that the same tower is 300 m south of him. What is the shortest distance of the tower from the road?
 A). $$300\sqrt{13}$$m B). $$500\sqrt{13}$$m C). $$600\sqrt{13}$$m D). $$900\sqrt{13}$$m
58). What is ($$\Large \frac{sin x-cos x+1}{sin x + cos x -1}$$ ) eqaul to?
 A). ($$\Large \frac{sin x-1}{ cos x}$$ ) B). ($$\Large \frac{sin x+1}{ cos x}$$ ) C). ($$\Large \frac{sin x-1}{ cos x+1}$$ ) D). ($$\Large \frac{sin x+1}{ cos x+1}$$ )
59). what is ($$sin^{2}x - cos^{2}x) ( 1-sin^{2}x cos^{2}x$$) equal to?
 A). ($$sin^{4}x - cos^{4}x)$$ B). ($$sin^{6}x - cos^{6}x)$$ C). ($$sin^{8}x - cos^{8}x)$$ D). ($$sin^{8}x - cos^{8}x)$$
60). What is (sin x cos y + cos x sin y)(sin x cos y - cos x sin y) equal to?
 A). $$cos^{2}x - cos^{2}y$$ B). $$cos^{2}x - sin^{2}y$$ C). $$sin^{2}x - cos^{2}y$$ D). $$sin^{2}x - sin^{2}y$$
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