Solved papers for 10th Class Mathematics Solved Paper - Mathematics-2015 Delhi Term-II Set-II

1) Find the middle term of the A.P. 213, 205, 197, ......., 37.

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2) If the sum of the first n terms of an A.P. is \[\frac{1}{2}(3{{n}^{2}}+7n)\], then find its nth term. Hence write its 20th term.

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3)

Three distinct coins are tossed together. Find the probability of getting

(i) at least 2 heads

(ii) at most 2 heads

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4) Find that value of p for which the quadratic equation \[(p+1){{x}^{2}}-6(p+1)x+3(p+9)=0,p\ne -1\] has equal roots. Hence find the roots of the equation.

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5) To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

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6) Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are \[\frac{3}{4}\] times the corresponding sides of isosceles triangle.

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7) If \[P(-5,-3),Q(-4,-6),R(2,-3)\] and \[S(1,2)\] are the vertices of a quadrilateral PQRS, find its area.

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