chapter 1 number system

                                Chapter 1 Real number

Q.1 Express the following in the form :

(i) 18.  (ii)23.  (iii)0.0002  (iii) 32.12 (iv) 0.3+0. +0.4

Q.2 show that is not a rational number.

Q.3 Represent  on the number line.

Q.4 Locate on number line 3+  .  Q.5 Locate on number line 1+

Q.6 Evaluate the following :

(i)     (ii)3⁵⁵x3⁴⁹-3⁶⁰x3⁴⁴ (iii)( )^1/11(iv) [5{8^1/3+27^1/3}]^1/4(v)  (vi) (vii)

Q.7 Prove that + = .

Q.8 show that =1

Q.9 if pqr =1 Show that  =1.

Q.10 if =  show that m=1+n.

Q.11 if x= 3^1/3 + 3^-1/3 , then prove that 3x³ – 9x = 10.

Q.12 if a^1/x = b^1/y = c^1/z and abc=1 prove that x+ y+ z= 0.

Q.13 if x= 3^1/3 + 3^-1/3 then prove that 3x³ -9x = 10.

Q.14 express 3 as a surd of fifth order .

Q.15 simplify .

 Q.16  if x = ,prove that bx²-ax+b=0.

Q.17 if x= , find the value of x³-2x²-7x+5.

Q.18  find the value of

Q.19 Find the simplest rationlizing factor of the following:

(i)2+                (ii)      

Q.20 Show that

(i)        

(ii)      

Q.21 if  =1.732  =2.236 and =2.449 find the value of                        

Q.22 find the value - 5=0

Q.23 smiplify :(i) (ii)        

Q.24 if a + b  = find a and b.

Q.25 if a +b√3   find the value a and b .

Q.26 if x =6-√35 ,find the value of x²+

Q.27 if x =3+2√2 ,find the value of x⁴ +

Q.28 if x =  and y =  find the value of x²+y²+xy

Q.29 if p =  ,show that p²+q²+pq=99

Q.30 if x =1-√2 ,find the value of

Q.31 if x =  ,find the value of x²-y²

Q.32 if x =  and y = ,find the value of x²+xy-y²

Q.33 if x =  ,find the value of bx²-ax+b =0

Q.34 if x =  ,find the value of x³-2x²-7x+5

Q.35 if x =  ,y= find the value of x²y +xy²

Q.36 if x =2+  ,find the value of x³+1/x³

Q.37 if x = 3+ ,find the value of x²+1/x²

Q.38 if x = ,y = find the value of 3x²+4xy-3y²

Q.39 if x = ,find the value of 4x³+2x²-8x+7.

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