Solved papers for 10th Class Mathematics Solved Paper - Mathematics 2017 Outside Delhi Set-III

1) For what value of n, are the nth terms of two A.Ps 63, 65, 67,.... and 3, 10, 17,.... equal ?

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2) A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

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3) How many terms of an A.P. 9, 17, 25, .., must be taken to give a sum of 636?

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4) If the roots of the equation \[\left( {{a}^{2}}+{{b}^{2}} \right){{x}^{2}}-2(ac+bd)x+\left( {{c}^{2}}+{{d}^{2}} \right)=0\] are equal, prove that \[\frac{a}{c}=\frac{c}{d}\].

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5) Solve for x: \[\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=2\], where \[x\ne -\frac{1}{2},1\]

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6) A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

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7) From the top of a tower, 100 m high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angles of depression \[30{}^\circ \] and \[45{}^\circ \]. Find the distance between the cars. [Take \[\sqrt{3}=1.732\]]

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8)

In the given figure, O is the centre of the circle with \[AC=24\text{ }cm,\,\,AB=7\text{ }cm\] and \[\angle BOD=90{}^\circ \]. Find the area of the shaded region.

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