Test Paper Ch 1 and 2  (04/04/24)


  1.        Prove that 2 - 3√5 is an irrational number .                                                                [3M]

2.        The product of a non zero rational and an irrational number is

                  (a) always irrational (b) always rational   (c) rational or irrational        (d) one         [1M]       

3. Which of the following statement(s) is/are always true?                                                   [1M]

(a) The sum of two distinct irrational numbers is rational.

(b) The rationalizing factor of a number is unique.

(c) Every irrational number is a surd.

                                 (d) None of these

4.         Product of two co-prime numbers is 117. Their L.C.F. should be                                [1M]

(a) 1 (b) 117         (c) equal to their L.C.M.      (d) Lies between 1 to 117


5.        If α and β are the zeroes of the quadratic polynomial x²- 5x + k such that α – β = 1, then find the value of k.                                                                                                                                                        [3M]

6.         If zeroes of the polynomial x² + 4x + 2a are α and 2/α  , then find the value of a.            [2M]

7.        The pair of co-prime is                                                                                                [1M]

(a) 32,40       (b) 21, 28           (c) 18, 25          (d) 9,27

  8. .026     is       ( .026 bar above digit 6 )                                                                             [1M]

(a) an integer   (b) a rational number     (c) a natural number  (d) an irrational number

9.  If p is a prime number, then prove that √P is an irrational.                                                  [3M]

10.  If p is a prime number, then find LCM of p, p² and p³.                                                          [1M]

11.  Two positive integers a and b can be written as a = xy² and b = xy³, where x and y are prime numbers. Find LCM (a, b).                                                                                                     [1M]

12.  The graph of a polynomial P(x) cuts the x-axis at 3 points and touches it at 2 other points. The number of zeroes of P(x) is/are: ________                                                                             [1M]

13.  The graph of parabola opens upwards, if                                                                            [1M]

                           (a) b >0  (b) a<0   (c) a > 0   (d) b≥ 0