Q) If one zero of the polynomial p(x) = 6×2 + 37 x – (k-2) is reciprocal of the other, then find the value of k. Ans: Let’s consider the one zero of the given polynomial be , then other zero will be . We know that Product of the zeroes (α x β) = […]
September 2023
Q) The two numbers are in the ratio of 2 : 3 and their LCM is 180. What is the HCF of the these numbers? Ans: Let us consider, the two number be 2x & 3x in the ratio of 2 : 3. Therefore the LCM of these two numbers = 6x Since, its given
Q) Prerna saves Rs. 32 during the first, month, Rs. 36 in the second month and Rs. 40 in the third month. if she continues to save in this manner, in how many months will she save Rs. 2,000? Ans: From the given data, we get AP as, 32, 36, 40, ….. Let’s consider that
Q) The mode of the following frequency distribution is 55. Find the missing frequencies ‘a’ and ‘b’. Ans: Since we know that, the modal class is the class with the highest frequency. In the given data, class “45 – 60” has the highest frequency of 15. Hence, class “45 – 60” is the modal class. Now
Q) Prove that: = 1 + sinθ cosθ Ans: Let’s start from LHS LHS = = = = = We know that, a3 – b3 = (a – b) (a2 + b2 + ab) LHS = = (cos2 θ + sin2 θ + sin θ cos θ) = 1 + sinθ cosθ = RHS …………. Hence
Prove that: cos^2 θ/(1 – tan θ) + sin^3 θ/(sin θ – cos θ) = 1 + sin θ cos θ Read More »
Q) Prove that 6 – √7 is an irrational number, given that √7 is an irrational number. Ans: Let us assume that 6 – √7 is a rational number Let 6 – √7 = ; q ≠ 0 and p, q are integers √7 = Since, p and q are integers; Therefore 6q – p is
Q) From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angle of depression 300 and 450 respectively. Find the distance between the two cars. (use 3 = 1.73) Ans: Let PQ be the tower, A and B the two cars, man observes
Q) The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 600 and the angle of elevation of the top of the second tower from the foot of the first tower is 300. Find the distance between the two towers and
Q) Solve the equation for x: 1 + 4 + 7 + 10 + …. + x = 287 Ans: We can see that it is AP with first term a = 1 and common difference d = 3 Let x be the value of nth term and we need to find value of this
Solve the equation for x: 1 + 4 + 7 + 10 + …. + x = 287 Read More »
Q) Reeti prepares a rakhi for her brother Ronit. The Rakhi consists of a rectangle of length 8 cm and breadth 6 cm inscribed in a circle as shown in the figure. Find the area of the shaded region. (Use = 3.14) Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Since the rectangle is inscribed inside