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Q)Â 250 logs are stacked in the following manner: 22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on (as shown by an example). In how many rows, are the 250 logs placed and how many logs are there in the top row? Ans:Â VIDEO […]
Q) The ratio of the 11th term to 17th term of an A.P. is 3:4. Find the ratio of 5th term to 21st term of the same A.P. Also, find the ratio of the sum of first 5 terms to that of first 21 terms. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION We know that nth term
Q) A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of cylindrical part. Find the total height of the room if it Contains m3 of air. Take Ans:Â Step1: Let h be the height of cylindrical part and r be the radius
Q) The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60°. The angle of elevation of the top of second tower from the foot of the first tower is 30°. Find the distance between two towers and the height of
Q) An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone, which is th of volume of the cone, is unfilled but hemisphere is formed on the top. Find volume of the of ice-cream. Ans:Â VIDEO SOLUTION STEP BY STEP SOLUTION
Q) Prove that, Ans: 2 methods to solve this question: 1st Method: LHS     =     =    Multiplying numerator & denominator by (sin θ + cos θ + 1), we get: x =      =      We know that sin2 θ + cos2 θ = 1 =           =     Â
Prove that, (tanθ + secθ-1)/(tanθ – secθ + 1) = (1 + sinθ)/cosθ Read More »
Q) In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle. Ans: In the above diagram, DR = DS = 3 cm Therefore, AR = AD –
Q) Two tangents TP and TQ are drawn to a circle with centre 0 from an external point T. Prove that ∠PTQ = 2∠OPQ. Ans: TP = TQ ⇒ ∠TPQ = ∠TQP Let ∠PTQ be θ ⇒ ∠TPQ = ∠TQP = = 90° –   Now, ∠OPT = 90° ⇒ ∠OPQ = 90° – [90° –
Q) If (-5,3) coordinates and (5,3) are two vertices of an equilateral triangle, then find of the third vertex, given that origin lies inside the triangle. (Take √3 = 1.7) Ans:  VIDEO SOLUTION STEP BY STEP SOLUTION Let the third vertex be (x, y)Hence, 3 vertex of the triangle will be A (-5,3)         B (5,3)         C
Q) Prove that √5 is an irrational number. Ans: Let √5 be a rational number. Therefore √5 = p/q, where q ≠0 and let p & q be co-primes. ⇒ 5q² = p² ⇒ p² is divisible by 5 ⇒ p is divisible by 5………………….. ……………….. (i) ⇒ p = 5a, where a is some