# Category Archives: School Learning

Question 1: Can a vector have direction angles 45Â°, 60Â°, and 120Â°. Solution: We know that if l, m and n are the direction cosines and ,  and  are the directionâ€¦ Read More
Factorize each of the following: Question 1. a3 + 8b3 + 64c3 â€“ 24abc Solution:  We know that a3 + b3 + c3 â€“ 3abcâ€¦ Read More
Question 1. Evaluate âˆ«1/ a2-b2x2 dx Solution: Let us assume I = âˆ« 1/ (a2-b2x2)dx take 1/b2 common from above equation = 1/b2 âˆ« 1/â€¦ 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: Weâ€¦ 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 ofâ€¦ Read More
Question 11. If a + ib =  , prove that a2 + b2 =  Solution: Given: a + ib =  On comparing the real andâ€¦ 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: â€¦ Read More
Question 11. Evaluate âˆ« sin2x/ âˆšcos4x-sin2x+2 dx Solution: Let us assume I =âˆ« sin2x/ âˆšcos4x-sin2x+2 dx =âˆ«sin2x/ âˆšcos4x-(1-cos2x)+2 dx (i) Put cos2x = t -2sinxcosxâ€¦ Read More
Evaluate the following integrals. Question 1. âˆ«(ex(cosx -sinx))dx Solution: Given expression isâˆ«(excosx)-(exsinx)dx=âˆ«(excosx) dx -âˆ«(exsinx)dx=ex(cosx )-âˆ«(exd(cosx)/dx-âˆ«exsinx dx=ex(cosx )+âˆ«exsinx dx-âˆ«exsinx dx=ex(cosx) + c Question 2. âˆ«ex(x-2+2x-3)dx Solution: Givenâ€¦ Read More
Question 1. Evaluate âˆ« x/ âˆšx4+a4 dx Solution: Let us assume I = âˆ« x/ âˆšx4+a4 dx = âˆ« x/ âˆš(x2)2+(a2)2 dx (i) Put x2â€¦ Read More
Question 1. Evaluate  Solution: = [-1 – i]3 = (-1)3 [1 + i]3 = -[13 + i3 + 3 Ã— 1 Ã— i (1 +â€¦ Read More
Question 33. Find the angle between the two vectors and , if (i) =âˆš3, = 2 and = âˆš6 Solution: We know,  â‡’ âˆš6 = 2âˆš3 cos Î¸ â‡’ cosâ€¦ Read More
Question 1. In the below fig, lines l1, and l2 intersect at O, forming angles as shown in the figure. If x = 45Â°. Findâ€¦ Read More
Question 1. In a parallelogram ABCD, determine the sum of angles C and D. Solution: In the given ||gm ABCD, âˆ C + âˆ D = 180Â°â€¦ 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 â€¦ Read More