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 […]
August 2023
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: 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 = =
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
Prove that root 5 is an irrational number. Read More »
Q) Half of the difference between two numbers is 2. The sum of the greater and twice the smaller number is 13. Find the numbers. Ans: Step 1: Let the numbers be x and y. Here, x is the greater number and y is the smaller number. Step 2: by 1st condition, we get: ½ (x-
Q) If sin α = 1/√2 and cot β = √3, then find the value of cosec α + cosec β. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Given that, sin α = 1/√2 ⇒ cosec α = 1 / sin α = 1/ (1/√2) ⇒ cosec α = √2 …………(i) Next, we have value
If Sin α = 1/√2 and Cot β = √3, then find the value of Cosec α + Cosec β. Read More »
Q) A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is (i) red (ii) yellow. Ans: