PRACTICE PAPER (IX)

       PRACTICE PAPER (IX)
------------------*********--------------------

1) Simplify : (√5 +√2)².

2) Rationalise the denominator:
     (√3+1)/(√7-2).

3) If a - b√3={(2-√3)/(2+√3)}
    find a,b.

4) Expand (x+2y+4z)².

5) Without multiplying, find the
     product of 105 x 106.

6) Factorise:
a) 64a³-27b³-144a²b + 108ab².
b) 25a² - 35a+12.
c) a(a- 1) - b(b -1).
d) x² - 5x/12 + 1/12.

7) Find five Rational numbers
     between 2 and 1.

8) Rationalise the denominator
     (x+√y)/(x-√y).

9) Factorise: 3x²-x-4

10) If x- 1/x= -1 find x² + 1/x²

11) Simplify with the help of formula: 541² - 540².

12) If a+b+2=0 find ab=5
i) a² +b²
ii) a²-b²
iii) a-b
iv) a⁴+b⁴

13) Simplify: (x+y)³ - (x³+y³)

14) Find three rational numbers between 0 and 0.1

15) Rationalise the denominator:
       5/(3√3 +√3)

16) Factorise:
a) 6x²+5x-6
b) 2y³+y²-2y-1

17) If x - 1/x = -1 find x²+ 1/x²

18) When the polynomial
kx³+9x²+4x -8 is divided x+3, then a reminder 7 is obtained. Find k.

19) Find the measure of an angle which is 26° more than its complement.

20) If Tan A=1 and Tan B=√3 find
Cos A CosB - Sin A Sin B.

21) Calculate the compound interest on Rs 8000 for 1 year at 11% p.a compounded half-yearly.

22) Find the measure of an angle if four times its complement is 10° less than twice its complement.

23) If x+ 1/x = 1 find x² + 1/x².

24) If x+y+z=0, then find x³+y³+z³ .

25) Factorise: a)  x²-x-12
b) 25x²/4  - y²/9

26) For what value of k, the polynomial x²+ (4- k)x + 2 is Divisible by x- 2 ?

27) If (3+√8)/+(3-√8) = a+ b√8, then find the value of a and b.

28) Write in simplest value of
        1.1010101010101 .....

29) Write four rational equivalent
   to 5/7.

30) Calculate the compound interest for the 2nd year on Rs6000 invested for 3 years at 10% p.a.

31) If 2 tan²A -1=0 prove
      Cos3A= 4cos³A - 3cosA

32) Ashok borrows Rs20000 at 12% Compound interest p.a., interest payable every six months. He pays back Rs6200 at the end of every six months. Calculate the 3rd payment Ashok has make at the end of 18 months in order to clear the entire loan.

Continue........