Grade 10 _ Real Numbers & Pair of linear equations

Real Numbers & Pair of linear equations

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Class : 10

1. If HCF (336, 54) = 6, find LCM (336, 54).

2. Find the nature of roots of the quadratic equation 2x2 – 4x + 3 = 0.

3. Write the smallest number which is divisible by both 306 and 657.

4. Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution.

5. Prove that 2 + 5 √3  is an irrational number, given that 3 is an irrational number.

6. Using Euclid’s Algorithm, find the HCF of 2048 and 960.

7. HCF of 168 and 126 is

8. The pair of lines represented by the equations 2x+y+3 = 0 and 4x+ky+6 = 0 will be parallel if value of k is ______.

9.If the quadratic equation x2 – 2x + k = 0 has equal roots, then value of k

10. Prove that 5 - √3 is irrational, given that √3 is irrational.

11. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march ?

ANSWERS

 1. 3024

2. Equation has NO real roots

3. LCM (306, 657) = 22338

4. k ≠ 6

5. Refer cbse text book

6. HCF (2048, 960) = 64 

7. 42

8. 2

9.1

10. Refer cbse text book

11.616 =32 x 19+8 

⇒ r = 8≠0

 32 = 8 x 4+0 

⇒ r = 0 

The HCF of 32 and 616 is 8