# Category Archives: School Learning

Polynomials are of different types out of which degree two polynomials are in the form ax2 + bx + c, a ≠ 0. When we… Read More
Nowadays, managing and representing data systematically has become very important especially when the data provided is large and complex, This is when Data Handling comes… Read More
Question 1. Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram.… Read More
Evaluate the following integrals. Question 11. ∫ex(sin4x-4)/(2sin22x)dx Solution:  We have,  ∫ex(sin4x-4)/(2sin22x)dx =∫ex(2sin2xcos2x-4)/(2sin22x)dx =∫ex(((2sin2xcos2x)/(2sin22x))-4/(2sin22x))dx =∫ex(cot2x-2cosec22x)dx =∫excot2xdx-2∫excosec22xdx Integrating by parts, excot2x-2∫exd(cot2x)/dx-2∫excosec22xdx  = excot2x+2∫excosec22xdx-2∫excosec22xdx = excot2x+C Question 12. ∫ex(2-x)/(1-x)2dx… Read More
Question 23. At every point on a curve, the slope is the sum of the abscissa and the product of the ordinate and the abscissa,… Read More
Question 12. Experiments show that radium disintegrates at a rue proportional to the amount of radium present at the moment. Its half-life is 1590 years.… Read More
Question 1. The surface area of a balloon being inflated changes at a rate proportional to time t. If initially its radius is 1 unit… Read More
Question 1. Find the median of the following data: 83, 37, 70, 29, 45, 63, 41, 70, 34, 54 Solution: Ascending order sequence of the… Read More
Differentiate the following w.r.t x Question 1. y =  Solution:        () Question 2.  Solution: Question 3.  Solution: Question 4. y=sin(tan-1e-x) Solution: Question 5. y = log(cos… Read More
Question 1: Find the angles between each of the following pairs of straight lines. (i) 3x+y+12=0 and x+2y-1=0 Solution: Given equations of lines are,3x +… Read More
Prove That: Question 1. 2cos(π/13)cos(9π/13) + cos(3π/13) + cos(5π/13) = 0  Solution:  Let’s take L.H.S = 2cos(π/13)cos(9π/13) + cos(3π/13) + cos(5π/13) Rearranging terms, we get … Read More
Question 1. The following table shows the daily production of T.V. sets in an industry for 7 days of a week. Day Monday Tuesday Wednesday… Read More
Question 1. ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that… Read More
Question 1. In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove… Read More
Many times, it has been observed that we have some expressions which have radicals(i.e., an expression that uses roots, for e.g. √(x + y)) in… Read More