# Category Archives: School Learning

Question 1: A coin is tossed. Find the total number of elementary events and also the total number of events associated with the random experiment.… Read More
Question 1. Show that the relation R = {(a,b): a-b is divisible by 3;, a, b ∈ Z} is an equivalence relation.  Solution:  According to… Read More
General Formula Tn = a + (n – 1) * d where, Tn is the nth term a is the first term d = common… Read More
General Formula  Tn = a + (n – 1)*d where, Tn is the nth term a is the first term d = common difference Question… Read More
Represent to solution set of the following inequations graphically in two-dimensional plane: Question 1. x+2y-4 <=0 Solution: Step 1. Convert the given inequation into equation… Read More
Question 11: Differentiate sin-1(2x√(1-x2)) with respect to tan-1(x/√(1-x2)) if -1/√2<x <1/√2. Solutions: Let u = sin-1(2x√(1-x2)) Substitute x = sin θ ⇒ θ = sin-1x… Read More
Question 1: Differentiate x2 with respect to x3. Solution: Let u = x2, and let v = x3 Differentiating u with respect to x, du/dx… Read More
Question 1. Solve the following Quadratic Equations: i) x2 + 10ix – 21 = 0 Solution: x2 + 10ix – 21 = 0    … Read More
Question 1. A bag A contains 5 white and 6 black balls. Another bag B contains  4 white balls and 3 black balls. A ball… Read More
Question 1. Find the perpendicular distance of the point (3, -1, 11) from the line  Solution: Let the foot of the perpendicular drawn from P… Read More
Question 11. In a survey of 60 people, it was found that 25 people read newspaper H, 26 people read newspaper T, 26 read newspaper I,… Read More
Question 1. If A and B are two sets such that n (A ∪ B) = 50, n (A) = 28 and n (B) =… Read More
Find dy/dx in each of the following. Question 16. If x√(1+y) +y√(1+x) =0  then prove that (1+x)2dy/dx +1=0 Solution: We have,  x√(1+y) +y√(1+x) =0 =>x√(1+y)=-y√(1+x)… Read More
Find dy/dx in each of the following: Question 1. xy = c2 Solution:  We have xy=c2 Differentiating both sides with respect to x. d(xy)/dx =… Read More
Question 1.  Find the position vector of a point R which divides the line joining the two points P and Q with position vectors and   respectively… Read More