cbse math Linear Equations for class x

Linear Equations for class x 


1. For what value of k will the following system of linear equations have no solution?

3x + y = 1, (2k - 1)x + (k - 1)y = 2k +1

2. Determine the value of c for which the following system of linear equations has no solution:

cx + 3y = 3; 12x + cy = 6

3. For what value of k will the system of equations

x + 2y = 5; 3x + ky + 15 = 0

has (i) unique solution (ii) no solution.

4. For what value of k, the following system of equations have (i) a unique solution, (ii) no solutions:

kx + 2y = 5; 3x - 4y = 10

5. Find the value of a and b for which the following system of linear equations has infinite numbers of solutions:

2x - 3y = 7
(a + b)x - (a + b - 3)y = 4a + b.)

Solve the following system of linear equations

6. For the value of k, for which the following system of linear equations has in finite number of solutions:

2x + 3y = 7
(k - 1) x + (k +2)y = 3k

Solve the following system of linear equations:

7. 3x - 5y = -1, x - y = -1

8. x + y = 7, 5x + 12y = 7

9. 3x - 4y = 1, 4x - 3y = 6

10. x + y/2 = 4, x/3 + 2y = 5

11. x/3 + y/4 = 4, 5x/6 - y/8 = 4

12. 2/x + 2/3y = 1/6, 3/x + 2/y = 0

13. 2u + 15v = 17uv, 5u + 5v = 36uv

14. 3(a + 3b) = 11ab, 3(2a +b) = 7ab

15. 2x/a + y/b = 2, x/a - y/b = 4

16. x/a - y/b = 0, ax + by = a² + b²

17. (a - b)x + (a +b)y = a² - 2ab - b², (a +b) (x + y) = a² + b²

18. x/a + y/b = a +b, x/a² + y/b² = 2

19. ax + by = c, bx + ay = 1 + c

20. x + y = a - b, ax - by = a² + b²

GUESS QUESTION Real Numbers FOR CLASS X

CBSE TEST PAPER-02
MATHEMATICS (Class-10)
Chapter 1. Real Numbers

1. Express 3825 as a product of its prime factors.

2. Find the LCM and HCF of 8, 9 and 25 by the prime factorization method.

3. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.

4. State whether 29/343  will have a terminating decimal expansion or a non-terminating repeating decimal.

5. State whether 23/ 2³ 5²will have a terminating decimal expansion or a non-terminating repeating decimal

6. Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers

7. Use Euclid’s division algorithm to find the HCF of 867 and 255

8. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

9. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9lm + 1 or 9m + 8.

10. Prove that 7 √5 is irrational.

11. Prove that √5 is irrational.

12. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? 

CBSE MATH TEST PAPER ON REAL NUMBER

CBSE TEST PAPER-01
MATHEMATICS (Class-10)
Real Numbers


1. Express 156 as a product of its prime factors.

2. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.

3. Find the HCF and LCM of 12, 36 and 160, using the prime factorization method.

4. State whether 6/15 will have a terminating decimal expansion or a non-terminating repeating decimal.

5. State whether35/50 will have a terminating decimal expansion or a non-terminating repeating
decimal.

6. Find the LCM and HCF of 192 and 8 and verify that LCM × HCF = product of the two numbers.

7. Use Euclid’s algorithm to find the HCF of 4052 and 12576.


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

9. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

10. Prove that 3√2 5 is irrational.

11. Prove that 1/√2 is irrational. (3 marks)

12. In a school there are tow sections- section A and Section B of class X. There are 32 students in section A and 36 students in section B. Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.