Q) If sin (A – B) = , cos (A + B) = ; 0 < A + B <= 90°, A > B; find ∠ A and ∠ B. Ans: Let’s take the components one by one: Step 1: sin (A – B) = Since we know that sin 300 = ∴ sin (A – […]
If sin (A – B) = 1/2, cos (A + B) = 1/2; 0 < A + B B; find ∠ A and ∠ B. Read More »
Q) In the given figure, O is the centre of the circle. If Ð AOB = 145°, then find the value of x. Ans: Step 1: From the given diagram, ∠ AOB = 1450 ∴ Reflex angle ∠ AOB = 3600 – 1450 = 215 0 Step 2: By the subtended angle theorem, “The angle
Q) In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC. Ans: Step 1: Since Δ AHK ~ Δ ABC (given) Therefore, ∴ AC = Step 2: It is given
In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, Read More »
Q) Prove that : Ans: Let’s start with LHS: LHS = = = = = = ∵ sin2 θ + cos2 θ = 1 ∴ LHS = = = = = = = By dividing the numerator & denominator by cos θ, we get: = = = = RHS Hence Proved ! Please press “Heart” button
Prove that : (sin θ – cos θ + 1) / (sin θ + cos θ – 1) = 1/ (sec θ – tan θ) Read More »
Q) Three coins are tossed simultaneously. What is the probability of getting (i) at least one head? (ii) exactly two tails? (iii) at most one tail? Ans: Since a coin has two possible outcomes (H, T) ∴ Total outcomes of 3 coins = 23 = 8 [i.e. (H, H, T), (H, H, H), (H, T,
Three coins are tossed simultaneously. What is the probability of getting Read More »
Q) A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a : (i) 2-digit number less than 40 (ii) number divisible by 5 and greater than 50 (iii) a perfect square number Ans: Total Number of discs
A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random Read More »
Q) Rehana went to a bank to withdraw Rs. 2,000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Rehana got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 did she receive. Ans: Let’s consider Notes of Rs. 50 = X and Notes of
Rehana went to a bank to withdraw Rs. 2,000. She asked the cashier to give her Read More »
Q) Find the zeroes of the polynomial 4×2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial. Ans: In the given polynomial equation, to find zeroes, we will start with f(x) = 0 Therefore, 4 x2 + 4 x – 3 = 0 Step 1: Let’s start calculating the
Q) If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of Ans: In the given polynomial equation f(x), to find zeroes, we will start with f(x) = 0 Therefore, x2 + x – 2 = 0 Step 1: Given that the roots of the polynomial are α and
If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of 𝛼/𝛽 + 𝛽 /𝛼. Read More »
Q) Prove that the parallelogram circumscribing a circle is a rhombus. Ans: Step 1: Let’s start by making a diagram for the given question: Here ABCD is a parallelogram and its is circumscribing a circle with center O. This parallelogram is touching the circle at points P, Q, R and S. Step 2: Let’s connect
Prove that the parallelogram circumscribing a circle is a rhombus. Read More »