# Category Archives: School Learning

Question 1. Evaluate the integral: Solution: Let  On dividing numerator and denominator by cos2x, we get Let us considered tan x = t So, sec2x… Read More
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis,… Read More
Question 13. Find the value of k if x – 3 is a factor of k2x3 – kx2 + 3kx – k Solution: Let, f(x) = k2x3… Read More
Question 14. The dimensions of a cinema hall are 100 m, 50 m, 18 m. How many persons can sit in the hall, if each… Read More
Chapter 1 Relations and Functions – Exercise 1.4 | Set 1 Question 7: Is ∗ defined on the set {1, 2, 3, 4, 5} by… Read More
Question 11. If 28C2r : 24C2r-4=225:11, find r. Solution: (28!/(28-2r)!2r!)/(24!/(24-2r+4)!(2r-4)!)=225/11 28x27x26x25/2r(2r-1)(2r-2)(2r-3)=225/11 28x27x26x25x11=225x(2r)(2r-1)(2r-2)(2r-3) 28x3x26x11=2r(2r-1)(2r-2)(2r-3) 14x2x3x13x2x11=2r(2r-1)(2r-2)(2r-3) 14x13x12x11=2r(2r-1)(2r-2)(2r-3) 2r=14 r=7 Question 12. If nC4,nC5 and nC6 are in… Read More
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x), or not(Question 1-7): Question 1. f(x)… Read More
Solve the inequalities in Exercises 1 to 6. Question 1. 2 ≤ 3x – 4 ≤ 5  Solution: In this case, we have two inequalities,… Read More
In each of the following using the remainder theorem, find the reminder when f(x) is divided by g(x)and verify by actual division:(1-8) Question 1. f(x)… Read More
Question 8. Find sets A, B and C, such that A ∩ B and B ∩ C and A ∩ C are non-empty sets, and… Read More
Question 1. Find the smallest set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9}. Solution: A ∪ {1, 2} =… Read More
Question 9. Write down all subsets of the following subsets:  (i) {a} (ii) {0,1} (iii){a,b,c} (iv){1,{1}} (v) {ϕ} Solution: We know, if A is a… Read More
Question 1. Which of the following statements are true? Give a reason to support your answer. (i) For any two sets A and B either… Read More
Find the mean deviation about the mean for the data in questions 1 and 2.  Question 1.  4, 7, 8, 9, 10, 12, 13, 17… Read More
Question 1. If A and B are two sets such that A ⊂ B, then Find: (i) A ⋂ B (ii) A ⋃ B Solution:… Read More