Q) If A and B are acute angles such that sin(A-B) = 0 and 2 cos (A+B) -1 = 0, then find angles A and B. Ans: Given that sin(A – B) = 0 Since we know that, sin 00 = 0 A – B = 0 ……….. (i) […]
Q) Evaluate Ans: Since sin2θ + cos2θ = 1 = = 5 cos2 60 + 4 sec2 30 – tan2 45 = = = =
Evaluate (5cos^2 60 + 4 sec^2 30 – tan ^2 45) / (sin^2 30 + cos^2 30) = 1 + sin θ cos θ Read More »
Q) If a fair coin is tossed twice, find the probability of getting ‘at most one head’. Ans: When we toss 2 fair coins, here are the possible outcomes: HH, HT, TH, TT Here, we need to get at most 1 head. It means we will include outcomes of getting 1 head and no head. Since
If a fair coin is tossed twice, find the probability of getting ‘at most one head’. Read More »
Q) Find the sum and product of the roots of the quadratic equation 2×2 – 9x + 4 = 0. Ans: We know that sum of roots (α + β) = Sum of roots = = Next, we know that the product of the roots (α x β) = Product of the roots
Find the sum and product of the roots of the quadratic equation 2x^2 – 9 x + 4 = 0. Read More »
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) =
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