CLASS 9 NUMBER SYSTEM DPP CH 1
CLASS - 9
1. Express in p/q (i) 0.5 ̅ (ii) 0.(34) ̅ (iii) 0.(47) ̅ (iv) 0.1(34) ̅
(vi) 5.2 ̅ (vii) 0.(001) ̅
2. Find 3 irrational Number b/w (i) 1/7 and 3/13 (ii) 2/7 and 4/11
(iii) 5/7 and 9/11 (iv) 1/9 and 2/10
3. Classify as rational and irrational No. (i) √23 (ii) √225
(iii) 0.3796 (iv) 7.478478... (v) 2-√3 (vi) 1/(√2)
(vii) 2+√23 (viii) 2π
4. Taking √2 = 1.414 find the value of (5√2)/2 , (3√2)/5
5. If x = √7+√5 and y = √7-√5, evaluate (i) x²+y² (ii) x2-y²
6. Simplify (i) √45 -3√20+4√5 (ii) (√24)/8+ (√54)/9
(iii) 3/(√8)+ 1/(√2) (iv) 4√12 x 7√6 (v) 2√27 + 1/(√3)+5√3
(vi) (√3)/3+(√3)/6
7. Simplify by rationalising the denominator:
(i) (2+√3)/(2-√3) (ii) (√3+√2)/(√3-√2) (iii) (√6)/(√2√3) (iv) (2√6+√5)/(3√5-2√6)
(v) (3√5+√3)/(√5-√3)
8. Simplify: (i) 〖(1²+2²+3²)〗^(1/2) (ii) (〖(8)〗^(1/3) X 〖(16)〗^(1/3))/〖(32)〗^(-1/3)
(iii) 〖(81/16)〗^(-3/4) [(25/9)^(-3/2)÷(5/2)^(-3) ]
9. Prove that (x^(1/(a-b)) )^(1/(a-c)) X(x^(1/(b-c)) )^(1/(b-a)) X(x^(1/(c-a)) )^(1/(c-b))=1
10. Prove that ((x^(a+b) )^2 X(x^(b+c) )^2 X(x^(c+a) )^2)/(x^a.x^b.x^c )^4 =1
