Note Book

Welcome To Class : XI Subject : Maths Chapter : 2 Exercise : 2.2 Que 1 : Solve for " x "  (i) |3-x| < 7 |x| < r  -r < x < r |3-x|<7 -7 < (3-x) < 7 -7-3 < -x < 7-3 -10 < -x < 4 ∴ -4 < x < 10 (ii) |4x-5| ≥ -2 |x-a| ≥ r (x-a) ≥ -r  |4x-5| ≥ 2          ∵ r < 0 x ∈ R (iii) |3-(3/4)x| ≤ 1/4 |3-(3/4)x| ≤ 1/4 3|1-(1/4)x| ≤ 1/4 |1-(1/4)x| ≤ 1/12 |(4-x)/4| ≤ 1/12 1/4|4-x)| ≤ 1/12 |4-x| ≤ (1/12)(4/1) |4-x| ≤ 1/3 [-(x-4)] ≤ 1/3                      |x-a|≤ r -1/3 ≤ x-4 ≤ 1/3                  -r ≤ x-a ≤ r (-1/3)+(4) ≤ x ≤ (1/3)+(4) 11/3 ≤ x ≤ 13/3 (iv) |x|-10 < -3 |x|<7 -r < x < r |x|-10 < -3      |x| < -3+10      |x| < 7 -7 < x < 7    Que 2 : Solve (1/|2x-1|) < 6 and express the solution using the interval notation. Solution : (1/|2x-1|) < 6...

Welcome To Class : XI Subject : Maths Chapter : 2 Exercise : 2.1 Que 1 : Classify each element of {√7,-¼,0,3.14,4,(22/7)} as a member of ℕ, Q, ℝ, - Q or ℤ. Solution : √7 irrational number Q = R-Q √7 ∈ R-Q -¼ negative rational number -¼ ∈ Q 0 Integer & Rational Number 0 ∈ Z,Q 3.14 Rational Number 3.14 ∈ Q 4 Natural Number, Rational Number 4 ∈ N, Z, Q 22/7 Rational Number 22/7 ∈ Q             Que 2 : Prove That √3 is an irrational number. Solution : Let Assume That  √3 is Rational Number  i.e √3 = (m/n); m,n ∈ z ; n ∈ 0 n√3 = m Squaring on Both Side; (n√3)² = m² 3n² = m² ------------------------------ (1) Let m² is even m must be even m = 2k Substitute m = 2k in (1) 3n² = m² 3n² = 4k² n² = (4k²/3) n² & n also an even number m and n have common factor 2 This Contradiction that m and n have no factor greater than one  ∴ √3 is an irrational number. Que 3 : Are There Two Distinct irrational number, such that their difference i...