# Category Archives: School Learning

Question 1. Maximize Z = 5x + 2y,  Subject to 3x + 5y ≤ 15 5x + 2y ≤ 10 x, y ≥ 0 Solution:… Read More
Question 11. Minimize Z = 5x + 3y Subject to 2x + y ≥ 10 x + 3y ≥ 15 x ≤ 10 y ≤… Read More
Question 21: Maximize Z = 3x + 3y, if possible, Subject to the constraints x − y ≤ 1 x + y ≥ 3  x, y ≥ 0… Read More
While thinking about functions, we always imagine that a function is a mathematical machine that gives us an output for any input we give. It… Read More
We encounter a lot of situations in real life where we encounter some variable for which we want to know its rate of change. For… Read More
Derivatives of the functions express the rate of change in the functions. We know how to calculate the derivatives for standard functions. Chain rule, product… Read More
Derivatives are an essential part of calculus. They help us in calculating the rate of change, maxima, minima for the functions. Derivatives by definition are… Read More
Evaluate the following definite integrals as limits of sums: Question 23.  Solution: We have, I = We know, , where h = Here a =… Read More
Evaluate the following definite integrals as limits of sums: Question 12.  Solution: We have, I = We know, , where h = Here a =… Read More
Evaluate the following definite integrals as limits of sums: Question 1.  Solution: We have, I = We know,, where h = Here a = 0,… Read More
Question 53. From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp… Read More
Prove the following identities: Question 35. = 4xyz Solution: Considering the determinant, we have R1⇢R1 – R2 – R3 C2⇢C2 – C3 △ = [-2x((z)(-y) –… Read More
Question 27. A T.V. tower stands vertically on a bank of a river of a river. From a point on the other bank directly opposite… Read More
Prove the following identities: Question 18. = -2 Solution: Considering the determinant, we have R2⇢R2 – R1 and R3⇢R3 – R2 △ = 1[2(a + 2)… Read More
Question 1. A tower stands vertically on the ground. From a point on the ground, 20 m away from the foot of the tower, the… Read More