# Category Archives: School Learning

Question 41. Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex. Solution: Let the coordinates of… Read More
Question 23. Solve the following system of linear equations graphically and shade the region between the two lines and the x-axis. (i) 2x + 3y… Read More
Question 11. If – 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² +… Read More
Question 21. Find the ratio in which the point P(-1, y) lying on the line segment joining A(-3, 10) and B(6, -8) divides it. Also, find… Read More
Question 27. If the 3rd, 4th, 5th and 6th terms in the expansion of (x + α)n be respectively a, b, c, and d, prove… Read More
Question 1. Determine the nature of the roots of following quadratic equations : (i) 2x² – 3x + 5 = 0 (ii) 2x² – 6x… Read More
Question 14. Find the middle terms in the expansion of: (i) (3x – x3/6)9 Solution: We have, (3x – x3/6)9 where, n = 9 (odd… Read More
Question 1. Find the 11th term from the beginning and the 11th term from the end in the expansion of (2x – 1/x2)25. Solution: We… Read More
Question 16: In △ABC, prove the following: a2 (cos2 B – cos2 C) + b(cos2 C – cos2 A) + c(cos2 A – cos2 B)… Read More
Question 14. Solve the following of equation graphically X – 2y + 11 = 0 3x + 6y + 33 = 0 Solution:  Given that,… Read More
Question 1. Find the coordinates of the point which divides the line segment joining (-1, 3) and (4, – 7) internally in the ratio 3:… Read More
Question 1. Solve the following of equation graphically x + y = 3 2x + 5y = 12 Solution:  Given that, 2x + 5y =… Read More
Question 1: If in △ABC, ∠A=45°, ∠B=60°, and ∠C=75°, find the ratio of its sides. Solution: According to the sine rule Hence, we get Using… Read More
Question 1. Determine a point that divides a line segment of length 12 cm internally in the ratio 2 : 3. Also, justify your construction.… Read More
Evaluate the following integrals: Question 21. ∫(log⁡x)2 x dx Solution: Given that, I = ∫(log⁡x)2 x dx Using integration by parts,        ∫u… Read More