JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q89

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MathematicsSingle correct+4 / -1Question 89 of 90

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from O is 'a' ; then the distance between two consecutive poles, is :

\dfrac{h\sin\alpha+a\cos\alpha}{9\sin\alpha}

\dfrac{h\cos\alpha-a\sin\alpha}{9\cos\alpha}

\dfrac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}

\dfrac{h\sin\alpha+a\cos\alpha}{9\cos\alpha}

Answer and worked solution

Official answer: C

Equal angles mean all the tops lie on one line from O: $h_k=(a+kd)\tan\alpha$ for $k=0,\dots,9$ . The longest pole gives $h=(a+9d)\tan\alpha$ , so
$d=\frac{h\cot\alpha-a}9=\frac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}.$

Topics:Heights and distances

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 89