# Category Archives: School Learning

Question 21. In figure, PSDA is a parallelogram in which PQ = QR = RS and AP || BQ || CR. Prove that ar (ΔPQE)… Read More
Question 12. Find the sum:  Solution: Given summation can be written as, S =   = (1 + 1/2 + 1/22 + . . . .… Read More
Question 1. Find the sum of the following geometric progressions: (i) 2, 6, 18, … to 7 terms Solution: Given G.P. has first term(a) =… Read More
Question11. If P is any point in the interior of a parallelogram ABCD, then prove that area of the triangle APB is less than half… Read More
Question 1. In the figure, compute the area of quadrilateral ABCD. Solution:  According to the question DC = 17 cm, AD = 9 cm and… Read More
Question 1. Evaluate ∫ sec2x/ 1 – tan2x dx Solution: Let us assume I = ∫ sec2x/ 1 – tan2x dx        … Read More
Question 11. A plane passes through the point (1, -2, 5) and is perpendicular to the line joining the origin to the point (). Find… Read More
Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum… Read More
Evaluate the following integrals: Question 1. ∫(x + 1)√(x2 – x + 1)dx Solution: We have, ∫(x + 1)√(x2 – x + 1)dx Let x… Read More
Question 25. A hemispherical depression is cut from one face of a cubical wooden block of the edge 21 cm such that the diameter of… Read More
Question 13. A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 and… Read More
Question 1. The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by… Read More
Question 1. Consider a tent cylindrical in shape and surmounted by a conical top having height 16 m and radius as common for all the… Read More
Question 11. Evaluate ∫ sin2x/ √cos4x-sin2x+2 dx Solution: Let us assume I =∫ sin2x/ √cos4x-sin2x+2 dx =∫ sin2x/ √cos4x-(1-cos2x)+2 dx (i) Put cos2x = t… Read More
Question 1. Evaluate ∫ x/ √x4+a4 dx Solution: Let us assume I = ∫ x/ √x4+a4 dx = ∫ x/ √(x2)2+(a2)2 dx (i) Put x2… Read More