# Category Archives: School Learning

Question 1: Can a vector have direction angles 45°, 60°, and 120°. Solution: We know that if l, m and n are the direction cosines and ,  and  are the direction… Read More
Factorize each of the following: Question 1. a3 + 8b3 + 64c3 – 24abc Solution:  We know that a3 + b3 + c3 – 3abc… Read More
Question 1. Evaluate ∫1/ a2-b2x2 dx Solution: Let us assume I = ∫ 1/ (a2-b2x2)dx take 1/b2 common from above equation = 1/b2 ∫ 1/… Read More
Question 1(i): Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses line through yz-plane. Solution: We… Read More
While solving and finding the Area of a Triangle, Certain parameters are expected to be provided beforehand, for example, the height and the base of… Read More
Question 11. If a + ib =  , prove that a2 + b2 =  Solution: Given: a + ib =  On comparing the real and… Read More
Question 17.  If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P. Solution: … 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 -2sinxcosx… Read More
Evaluate the following integrals. Question 1. ∫(ex(cosx -sinx))dx Solution: Given expression is∫(excosx)-(exsinx)dx=∫(excosx) dx -∫(exsinx)dx=ex(cosx )-∫(exd(cosx)/dx-∫exsinx dx=ex(cosx )+∫exsinx dx-∫exsinx dx=ex(cosx) + c Question 2. ∫ex(x-2+2x-3)dx Solution: Given… 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
Question 1. Evaluate  Solution: = [-1 – i]3 = (-1)3 [1 + i]3 = -[13 + i3 + 3 × 1 × i (1 +… Read More
Question 33. Find the angle between the two vectors and , if (i) =√3, = 2 and = √6 Solution: We know,  ⇒ √6 = 2√3 cos θ ⇒ cos… Read More
Question 1. In the below fig, lines l1, and l2 intersect at O, forming angles as shown in the figure. If x = 45°. Find… Read More
Question 1. In a parallelogram ABCD, determine the sum of angles C and D. Solution: In the given ||gm ABCD, ∠C + ∠D = 180°… Read More
Find the inverse of each of the following matrices by using elementary row transformation(Questions 1- 16): Question 1.   Solution: Here, A =  A = AI … Read More