Kaliyuga Ekalavya

NCERT Class X Chapter 7: Coordinate Geometry Example 8 Question: Find the coordinates of the points of trisection (i.e., points dividing in three equal parts) of the line segment joining the points A(2, –2) and B(–7, 4). Given: Points \( A(2, -2) \) and \( B(-7, 4) \). To Find: Coordinates of the points of trisection of the line segment \( AB \). Formula: Section formula: If a point \( P \) divides the line segment joining \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), then the coordinates of \( P \) are: \[ P = \left( \frac{mx_2 + nx_1}{m+n},\ \frac{my_2 + ny_1}{m+n} \right) \] Solution: Step 1: Let the points of trisection be \( P \) and \( Q \). Point \( P \) divides \( AB \) in the ratio \( 1:2 \), and point \( Q \) divides \( AB \) in the ratio \( 2:1 \). Step 2: Find the coordinates of \( P \) (dividing \( AB \) in \( 1:2 \)). \[ \begin{align*} x_P &= \frac{1 \times (-7) + 2 \times 2}{1 + 2} = \frac{-7 + 4}{3} = \frac{-3}...

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 8 Question: The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, find their monthly incomes. Use elimination method Given: Ratio of incomes = 9 : 7 Ratio of expenditures = 4 : 3 Savings of each person = Rs 2000 per month To Find: Monthly incomes of the two persons Formula: Income - Expenditure = Savings Solution: Let the incomes be 9x and 7x, and expenditures be 4y and 3y. 9x - 4y = 2000 ...(1) 7x - 3y = 2000 ...(2) Multiply (1) by 3 and (2) by 4 to eliminate y: 27x - 12y = 6000 ...(3) 28x - 12y = 8000 ...(4) Subtract (3) from (4): x = 2000 Substitute x = 2000 in (2): 7(2000) - 3y = 2000 14000 - 3y = 2000 3y = 12000 y = 4000 Incomes are 9x = 9(2000) = 18000 and 7x = 7(2000) = 14000 Result: The monthly incomes of the two persons are Rs 18000 and Rs 14000. Next question s...

NCERT Class X Chapter 14: Probability Example 8 Question: A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be (i) white? (ii) blue? (iii) red? Given: Number of blue marbles = 3 Number of white marbles = 2 Number of red marbles = 4 To Find: Probability of drawing a white, blue, and red marble. Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: Total number of marbles = 3 + 2 + 4 = 9 (i) Probability of drawing a white marble ⇒ 2 9 (ii) Probability of drawing a blue marble ⇒ 3 9 = 1 3 (iii) Probability of drawing a red marble ⇒ 4 9 Result: (i) Probability of drawing a white marble = 2 9 (ii) Probability of drawing a blue marble = 1 3 (iii) Probability of drawing a red marble = 4 9 Next question solution: NCERT Class X Chapter 14: Probability Example 9 Explore ...

NCERT Class X Chapter 4: Quadratic Equation Example 8 Question: A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?. Given: A circular park with diameter AB = 13 metres. A pole (P) is erected on the boundary. The difference of its distances from two diametrically opposite fixed gates A and B is 7 metres.                                 To Find: 1. Is it possible to erect the pole under these conditions? 2. If yes, at what distances from the two gates should the pole be erected? Formula: WKT, an angle inscribed ...