##### Section D contains 11 questions of 4 marks each. Scroll down for explanatory answer and video solution to the 4-mark questions that appeared in CBSE Board Exam in 2016.

#### Due to heavy floods in a state, thousand were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs 120 per sq.m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (use = π \\frac{22}{7})

#### Prove that the lengths of two tangents drawn from an external point to a circle are equal.

The same question appeared in 2017 board paper.

#### Question to be added

#### In the figure given below, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with O, at the point C. O’D is perpendicular to AC. Find the value of \\frac{DO'}{CO})

#### Solve for x: \\frac{1}{x+1}) + \\frac{2}{x+2}) = \\frac{4}{x+4}), x ≠-1,-2,-4.

#### The angle of elevation of the top Q of a vertical tower PQ from a point x on the ground is 60

^{0}. From a point y, 40 m vertically above x, the angle of elevation of the top Q of tower is 45^{0}. Find the height of the tower PQ and the distance PX. (Use \\sqrt3) = 1.73).#### The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses proceeding the house numbered x is equal to sum of the numbers of houses following x.

#### In the figure below, the vertices of ∆ ABC are A (4, 6), B(1, 5) and C (7, 2). A line -segment DE is drawn to intersect the sides AB and AC at D and E respectively such that \\frac{AD}{AB}) = \\frac{AE}{AC}) = \\frac{1}{3}) calculate the area of ∆ ADE and compare it with area of ∆ABC.

#### A number x is selected at a random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.

#### In figure given below, is shown a sector OAP of a circle with centre O, containing ∠θ. AB perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tanθ + secθ + \\frac{πθ}{180-1}])

#### A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.