CLASS X SOLUTION

 MATHS UNIT TEST

1. Which of the following rational number have terminating decimal?

 a. 16/225              b. 5/18             c. 2/21             d. 7/250

Ans:  7/250.  Since 7/250 = 7/5³x2

3

2. The H.C.F and L.C.M of two rational nos. are equal then the nos. must be

 a. prime                b. co-prime      c. composite    d. equal

Ans:  Equal

3. Given that H.C.F (306,657) = 9. Find the L.C.M.

Ans:  Since we know that H.C.F x L.C.M = a x b

          9 x L.C.M = 306 x 657

          L.C.M = (306 x 657)/9

                      = 22338.

4. Express 3825 as the product of its prime factors.

Ans:  3825 = 5 x 5 x 3 x 3 x 17

                  = 5² x 3² x 17

5. Find a quadratic polynomial if sum and product of its zeros are -1/4 and 1/4.

Ans:  Equation for quadratic polynomial is

          X²- (sum) x + product = 0

          X²- (-1/4) x + (1/4) = 0

          X² + 1/4x + ¼ = 0

6. Use Euclid’s division algorithm to find the H.C.F of 210 and 55.

Ans:  H.C.F of 210 and 55

          210 = 55 x 3 + 45

          55 = 45 x 1 + 10

          45 = 10 x 4 + 5

          10 = 5 x 2 + 0

          So, H.C.F = 5.

7. Prove that √3 is irrational number.

Ans:  Let us consider √3 is rational = p/q = where p and q are co-primes.

         Squaring: (√3)² = p²/q²

                                  3 = p²/q²

                             q² = p²/3                                 (1)

                       = 3 divides p²

                       = 3 divides p                                 (2)

         Let us suppose   p=3p’

Inserting value of p in (1)

         3q² = (3p’)

           q² = 3p’

           p2 = q2/3

= 3 divides p2

= 3 divides p                                                      (3)

From (2) and (3)

3 divides p and q

= H.C.F of p and q is 3

But p and q are co-primes

= our supposition is wrong

= √3 is irrational.

8. Show that any positive odd integer is of the form 4q+1 and 4q+3 where q is some integer.

Ans:  Let a be any positive integer, b=4

         Acc. To Euclid’s division algorithm

         A=bq+r where 0_< r < b

         R=0,1,2,3

         When r = 0

         A=bq+0

         When r = 1

         A=bq+1

         When r = 2

         A=bq+2

         When r = 3

         A=bq+3

So, the positive odd integer among this is 4q+1 and 4q+3.

9. Divide the polynomial p(x) = x⁴-3x²+4x+5 by the polynomial g(x) = x²+1-x. Find the ques. and rem.

Ans:  p(x) = x⁴-3x²+4x+5

         g(x) = x²+1-x = x²-x+1

                                                                                                       

Rem = 8, quest = x²+x-3.

10. Obtain all other zeros of 3x⁴+6x³-2x²-10x-5 if two of it’s zeros are √5/3 and -√5/3.

Ans:  p(x) = 3x⁴+6x³-2x²-10x-5

         Given zero = (x-√5/3) (x+√5/3)

               Product = (x²-5/3)

       

  

                       

P(x) = (x²-5/3)(3x²+6x+3)

Now: 3x²+6x+3

          3x²+3x+3x+3

          3x(x+1)+3(x+1)

          (3x+3)(x+1)

Now x = -1, -1                                                                                                                                                                                                                                                                                                                              YOU ARE MOST WELCOME TO ASK ANY DOUBT