# Category Archives: School Learning

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
Question 1. If , prove that  Solution: We have,  ⇒  Squaring both sides, we get, y2 = x + y Question 2. If , prove that  Solution:… Read More
Question 1: Let A = and B = verify that (i) (2A)T = 2AT (ii) (A + B)T = AT + BT (iii) (A − B)T =… Read More
Question 1: Divide the first polynomial by the second polynomial in each of the following. Also, write the quotient and remainder: (i) 3x2 + 4x… Read More
The dictionary meaning of “disguise” is “unrecognizable”. Disguised derivative means “unrecognized derivative”. In this type of problems, the definition of derivative is hidden in the… Read More
Three dimensions can be measured, length, width, and height, for any object that you can see or touch. There are certain dimensions of our home… Read More