# Category Archives: School Learning

Question 1. Integrate ∫(2x – 3)5  + √3x + 2 dx Solution: Let I = ∫(2x – 3)5 + √3x + 2 dx    … Read More
Question 11. Integrate Solution: Let I = On simplifying the above equation, we get I =  =  = ∫ tan2 x/2 dx =  On integrating… Read More
Question 1. The following table shows the ages of the patients admitted in a hospital during a year: Age (in years) 5-15 15-25 25-35 35-45… Read More
Chapter 6 Application of Derivatives – Exercise 6.2| Set  1 Question 11. Prove that the function f given by f(x) = x2 – x +… Read More
Question 1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x2-3x+5=0 (ii) 3x2-4√3x+4=0 (iii) 2x2-6x+3=0 Solution: (i)… Read More
Solve the following inequalities graphically in two-dimensional plane: Question 1: x + y < 5  Solution: Now draw a dotted line x + y =… Read More
Question 1. Show that the function given by f (x) = 3x + 17 is increasing on R.  Solution: If for a function f(x), f'(x)… Read More
Question 1: Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.… Read More
Question 11.  Solution: Dividing numerator and denominator by x-a Applying the formula here,  for numerator and  for denominator Question 12. If , find the value of n. Solution: LHS… Read More
Evaluate the following limits: Question 1.  Solution: Let y = x + 2 and b = a + 2    [using formula ] Question 2.  Solution:… Read More
Question 1. Find the roots of the following quadratic equations by factorization: (i) x2– 3x – 10 = 0  Solution: Here, LHS = x2– 3x… Read More
Question 15.  A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of… Read More
Question 1. Can the mean of a binomial distribution be less than its variance? Solution: Let np be the mean and npq be the variance… Read More
Question 11: Show that y=(c-x)/(1+cx) is the solution of the differential equation. (1+x2)(dy/dx)+(1+y2)=0 Solution: We have,  y=(c-x)/(1+cx)                (i) Differentiating… Read More
Question 1: Show that y=bex+ce2x is the solution of the differential equation. d2 y/dx2-3(dy/dx)+2y=0 Solution: y=bex+ce2x (i) Differentiating equation (i)w.r.t x, dy/dx=bex +2ce2x dy/dx=bex+2ce2x (ii)… Read More