Q. 1. Find the HCF and LCM

   1. 12(9x2 - 4) and 18 (6x2 - 5x - 6)
   2. (18x3 + 45 x2 - 27x) and (15x4 - 135 x2)
   3. 18(x3- x2+ x - 1) and 12(x4 - 1)
   4. 42(2x3 - 5x2 - 3x) and 60(8x4 + x)
   5. 8(x4-16) and 12(x3-8)
   6. (2x4 - 2y4) and (3x3 + 6x2 - 3xy2 - 6y3)
   7. (x4 - 1 ) and (x3 + x2 + x + 1)
   8. 36(3x4+5x3-2x2) and 54(27x4-x)
   9. (x3 - 1) and (x4 + x2 + 1)
  10. (x2 + x - 2) and (x3 + 4x2 + x - 6)
  11. (x4 - y4) and (x6 - y6)
  12. (6x4 - 13x3 + 6x2) and (8x4 - 36x3 + 54x2 - 27x)

 

Q. 2. For what value of k,the HCF of x2 + x - 2(k + 1)and (2x2+ kx - 12) is (x + 4).

Q. 3. if (x - k) is the HCF of (x2 + x - 12) and (2x2 - kx - 9) find the value of k.

Q. 4. Find the value of a and b so that x3 + ax2 + bx - 6 is completely divisible by x2 - 4x + 3.

Q. 5. If (x - 3) is the HCF of (x3 - 2x2 + px + 6) and (x2 - 5x + q) find the value of (6p +5 q).

Q. 6. Find the value of a and b so that f(x) = 3x3 + ax2 - 13x + b is divisible by (x2 - 2x - 3).

Q. 7. If (x + 1) (x - 4) is the HCF of the polynomial (x - 4) (2x2 + x - a) and (x + 1) (2x2 + bx - 12), find a and b.

Q. 8. The HCF and LCM of two polynomial p(x) and q(x) are 56(x4 + x) and 4(x2 - x + 1) respectively. If p(x) = 28 (x3 + 1) find q(x).

Q. 9. The HCF and LCM of the polynomial P(x) and Q(x) are respectively 5(x + 3) (x - 1) and 20 x (x2 - 9)(x2 - 3x + 2). If P(x) = 10 (x2 - 9) (x - 1) find q(x).

Q. 10. The HCF of the polynomial P(x) = (x - 3)(x2 + x - 2) and Q(x)=(x2 - 5x + 6), find the LCM of P(x) and Q(x).

Q. 11. (x2 + x - 2) is the HCF of the expression (x - 1)(2x2 + ax + 2) and (x + 2)(3x2 + bx + 1). Find the value of a and b.

Q. 12. If ( x + 3) (x - 2) is the G.C.D of f(x)=(x + 3)(2x2 - 3x + a) and g(x)=(x - 2)(3x2 + 10x - b) Find the value of a and b.

Q. 13. Find the L.C.M of the polynomials: x(8x2 + 27) and 2x2(2x2 + 9x + 9).

Q. 14. If (x - 1)(x + 4) is the HCF of the polynomials P(x)= (x2 + 2x - 3) (2x2 + 5x + a) and Q(x) = (x2 + x - 12) ( 3x2 - x + b) find the value of a and b

Q. 15. . If the HCF of P(x) = ( 2x2 - x - 1) (px2 + 8x - 3) and Q(x) = (x2 + x - 6) (3x2 + qx - 1)is (x2 + 2x - 3) , find the values of p and q.

Q. 16. Find the HCF of the polynomials: f(x) = 6 (x3 + 3x2) (x2 - 16) (x2 + 9x + 18) and g(x) = 8 (x4 + 4x3) (x2 + 6x + 9)2.

Q. 17. Find the HCF of the polynomials: f(x) = 9 (x4 – 1) (x + 5) and g(x) = 6 (x2 – 1) (x2+ 2x + 1) (x2 + 25).

Q. 18. Find the HCF of the polynomials: f(x) = 8 (x3 – x2 + x) (x3 – 8) and g(x) = 28 (x3 + 1) (x2 – 4).

Q. 19. Find the G.C.D. of the polynomials: f(x) = 2x4 – 2y4 and g(x) = 3x3 + 6x2y – 3xy2 – 6y3.

Q. 20. Find the L.C.M. of the polynomials: f(x) = 11x3 (x + 1)3 and g(x) = 121x (2x2 + 3x + 1).

Q. 21. Find the L.C.M. of the polynomials: f(x) = 35 (x4 – 27x) and g(x) = 40 (2x3 - 5x2 - 3x).

Q. 22. Find the L.C.M. of the polynomials: f(x) = 15x3 - 75x2 - 90x and g(x) = 6x4 – 18x3 – 108x2

Q. 23. The GCD and LCM of two polynomials are (x – 7) and (x3 - 10x2+ 11x + 70). If one is (x2 - 5x - 4), find the other.

Q. 24. If (x + 3) (x - 2) is the HCF of the polynomials f(x) = (x + 3) (2x2– 3x + p) and g(x) = (x - 2) (3x2 + 10x - q), find p, q.

Q. 25. For what value of k the HCF of x2 + x - (2k + 2) and (2x2 + kx - 12) is (x + 4)?

Q. 26. Simplify the following rational expressions: (i) (x4 - 6x3 + 36x2) / (x3 + 216). (ii) (x4 - 1) / (x - 1).

Q. 27. Which rational expression should be subtracted from (2x2 + 2x - 7) / (x2 + x - 6) to get (x - 1) / (x - 2).

Q. 28. Simplify: [ (2x – 1) / (x – 1) – (x + 1) / (2x + 1) ] + [ (x - 1) / (x + 2) – (x + 1) / (x – 2)].

Q. 29. If A = x2 – 7x + 12 and B = x2 – 5x + 6, then evaluate the sum their reciprocals to the lowest form.


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Some more....


CHAPTER - 1

   1. State Euclid division lemma.
   2. Prove that {root 5} is an irrational number.
   3. Prove that cube of any +ve integer is 9m, 9m+1 or 9m+8 where q is some integer

CHAPTER - 5

   1. find the nth term of the A.P. 2, 5, 8……………, find its 54 Th term
   2. What are an A.P. and a term?
   3. Find the sum of first n odd natural numbers.
   4. Find sum of first 22 terms of an A.P. in which d=22 and a22=149.
   5. A man is employed to count Rs 10710.He counts @ Rs 180/minute for half an hour. After it he counts @Rs 3 less than the preceding minute. What time he had taken to count the entire money?

CHAPTER - 7{Theorems only}

   1. Thale’s theorem.
   2. If 2 triangles ABC and PQR are similar then prove that ratios of their areas are in ratio of squares of their corresponding sides.
   3. Pythagoras theorem.


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