Q) A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the total area of grass field that can be grazed by them. […]
A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners Read More »
Q) Find the zeroes of the polynomial f(t) = t2 + 4 √3 t – 15 and verify the relationship between the zeroes and the coefficients of the polynomial. Ans: In the given polynomial equation, to find zeroes, we will start with f(x) = 0 Therefore, t2 + 4√3 t – 15 = 0 Step
Find the zeroes of the polynomial f(t) = t2 + 4 √3 t – 15 and verify the relationship Read More »
Q) If 𝛼, β are zeroes of quadratic polynomial f(x) = 6 x2 + 11 x – 10, find the value of Ans: In the given polynomial equation, to find zeroes, we will start with f(x) = 0 Therefore, 6 x2 + 11 x – 10 = 0 Step 1: Given that the roots of
Q) The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves 2500 per month, find the monthly income of each. Ans: Let the income of A and B be 8 X and 7 X Since Saving = Income
Q) A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle Ans: Let’s first draw a diagram for the given question: By Pythagorus theorem, AC = = = = 25 cm Method 1: OP = OQ (radius of
Q) Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ Ans: Here, let’s start by simplifying the LHS in given equation: LHS = = = Let’s make the denominators equal: LHS = = = We know that a3
Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ Read More »
Q) Calculate the mean of the following data : Ans: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency: We know that, mean of grouped data is given by: Mean of grouped data = Therefore, Mean value = = 10.57 Hence, the mean value of the given data is
Calculate the mean of the following data : Read More »
Q. Solve for X : Ans: Given equation is: ∴ ∴ 4 (2 X + 3) – 5 X = 3 X (2X + 3) ∴ 8 X + 12 – 5 X = 6 X 2 + 9 X ∴ 12 = 6 X 2 + 6 X ∴ 6 X 2 + 6 X
Solve for x : 4/x – 5 / (2x + 3) = 3 Read More »
Q. The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers. Ans: Let the numbers be X and Y Step 1: By 1st condition: X + Y = 18 or X = 18 – Y ….. (i) Step 2: By 2nd condition: By simplifying this equation, we
The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers. Read More »
Q) ABCD is a trapezium with AB ǁ DC. AC and BD intersect at E. If Δ AED ~ Δ BEC, then prove that AD = BC. Ans: Let’s start with the diagram for he given question: Step 1: We are given AB ǁ DC, hence let’s look at △AEB and △CED: Here we