# Solved papers for 10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-III

### done Solved Paper - Mathematics-2016 Outside Delhi Set-III

• question_answer1) Solve for $x:\sqrt{6x+7}-(2x-7)=0$

 There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80.

• question_answer3) Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.

• question_answer4) The sums of first n terms of three arithmetic progressions are ${{S}_{1}},{{S}_{2}}$ and ${{S}_{3}}$ respectively. The first term of each A.P. is 1 and their common differences are 1, 2 and 3 respectively. Prove that ${{S}_{1}}+{{S}_{3}}=2{{S}_{2}}$.

• question_answer5) Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

• question_answer6) From a point on the ground, the angle of elevation of the top of a tower is observed to be $60{}^\circ$. From a point 40 m vertically above the first point of observation, the angle of elevation of the top of the tower is $30{}^\circ$. Find the height of the tower and its horizontal distance from the point of observation.

• question_answer7) Draw a triangle with sides 5 cm, 6 cm. and 7 cm. Then draw another triangle whose sides are $\frac{4}{5}$ of the corresponding sides of first triangle.

• question_answer8) A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.

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