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Important Questions – Some Applications of Trigonometry – If the angle of elevation of a cloud from point h meters above a lake is alpha and the angle of depression of its reflection in the lake is beta prove that height of the cloud is h Important Questions – Some Applications of Trigonometry – The angle of elevation of a cloud from a point 60 metres above a lake is 30o and the angle of depression of the reflection of the cloud in the lake is 60 o. Find the height of the cloud. Important Questions – Some Applications of Trigonometry – Amit standing on a horizontal plane. Find a bird flying at a distance of 200 M from him at an elevation of 30. Deepak standing on the roof of a 50 M high building Important Questions – Some Applications of Trigonometry – A fire in a building B is reported on telephone to two fire stations P and Q,20km apart from each other on a straight road. P observes that the fire is at an angle of60∘to the road Important Question – Related to Upstream & Downstream – A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hour 30 minutes. Determine the speed of the stream Important Questions – Surface Area and Volume – An ice–cream cone full of ice-cream having radius 5 cm and height 10 cm, as shown in figure. Calculate the volume of ice-cream, provided that its 1/6 part is left unfilled with ice–cream. Important Questions – Surface Area and Volume – Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide Find the time in which the level of water in the tank will rise by 21 cm Important Questions – Surface Area and Volume – Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed? Important Questions – Surface Area and Volume – Water is flowing at the rate of 2.52kmhr through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour Important Questions – Trigonometry – In a Triangle PQR, N is a point on PR, such that QN is perpendicular PR If PN x NR = QN^2 prove that angle PQR=90 Important Questions – Trigonometry – A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, find the height of the centre of the balloon. Important Questions – Trigonometry – If sin theta + cos theta = root 2 then tan theta + cot theta = Important Questions – Trigonometry – If sin theta – cos theta = 0 then value of sin^4 theta + cos^4 theta is Important Questions – Quadratic Equations – The roots of the equation (b-c)x^2 + (c-a)x + (a-b) = 0 are equal then …….. Important Questions – Coordinate Geometry – Rajiv decided to put a frame on a scenery which is quadrilateral in shape. He placed this scenery on coordinate axes such that one vertex coincides with origin O and one arm OA coincides with x axis Important Questions – Coordinate Geometry – The distance of the point P (2,3) from the x axis is Important Questions – Coordinate Geometry – The line segment joining points (-3 , -4) and (1 , -2) is divided by y axis in the ratio ……….. Important Questions – Coordinate Geometry – If x is a positive integer such that the distance between points P (x , 2) and Q (3 , -6) is 10 units the value of x is ………. Important Questions – Triangles – In the given figure ∠1=∠2 and ΔNSQ≅ΔMTR, then prove that ΔPTS∼ΔPRQ Important Questions – Triangles – Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD (produced) in E. 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Prove that 1/x + 1/z =1/y Important Questions – Triangles – In the given figure, the value of x in cm is Important Questions – Triangles – In the figure ∠BED = ∠BDE and E divides BC in the ratio 2:1 then prove that AF × BE = 2 AD × CF Important Questions – Triangles – In the given figure, DE BC, AE a units, EC b units, DE x units and BC y units Which of the following is true Important Questions – Arithmetic Progression – If the mth term of an AP is 1/n and nth term is 1/m ,then prove that the sum of mn terms is (mn+1)/2 Important Questions – Arithmetic Progression – Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first instalment of ₹ 1,000. If he increases the instalment by ₹ 100 every month, what amount will be paid by him in Important Questions – Arithmetic Progression – Find how many integers between 200 and 500 are divisible by 8. 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