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# Category Archives: School Learning

Question 1: Find the roots of the following quadratic (if they exist) by the method of completing the square: . Solution: Given:  We have to make… Read More
Question 1. Find the locus of a point equidistant from the point (2, 4) and the y-axis. Solution: Let C (a, b) be any point… Read More
Question 13. Prove that the tetrahedron with vertices at points O(0,0,0), A(0,1,1), B(1,0,1) and C(1,1,0) is a regular one. Solution: Given: The points O(0,0,0), A(0,1,1),… Read More
Question 1. Find the distance between the following pairs of points: (i) P(1, −1, 0) and Q (2, 1, 2) Solution: Given: The points P(1,… Read More
Question 16. A large window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 meters,… Read More
Question 1. Determine two positive numbers whose sum is 15 and the sum of whose squares is minimum. Solution: Let us assume the two positive… Read More
Question 1. Express the following complex numbers in the standard form a + ib: (i) (1 + i) (1 + 2i) Solution: We have, z… Read More
Question 1. A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the figure. If AB = 60… Read More
Question 12. Determine (8x)x, if 9x+2 = 240 + 9x. Solution: We have, => 9x+2 = 240 + 9x => 9x+2 − 9x = 240… Read More
Question 11. Find the points on the curve y = 3x2 − 9x + 8 at which the tangents are equally inclined with the axes.… Read More
Question 19. Divide 30x4 + 11x3 – 82x2 – 12x + 48 by 3x2 + 2x – 4 Solution: We have to divide 30x4 +… Read More
Question 1. Differentiate each of the following using first principles: (i) 2/x  Solution: Given that f(x) = 2/x By using the formula f'(x) =  We… Read More
Question 3. Differentiate each of the following using first principles: (i) xsinx Solution: Given that f(x) = xsinx By using the formula We get = … Read More
Question 1. Find the slopes of the tangent and the normal to the following curves at the indicated points: (i) y = √x3 at x… Read More
Question 1. Find the domain of each of the following real valued functions of real variable: (i) f (x) = 1/x  Solution: We are given,… Read More