CBSE Important Questions

CLASS X MATHS TEST (REAL NUMBERS, POLYNOMIALS)

Choose the correct option : EACH QUESTION 1 MARKS (SECTION A)

1. Every positive even integer is of the form:
   1. q
   2. 2q
   3. 2q + 1
   4. 2q -1
2. Every positive odd integer is of the form
   1. q
   2. 2q
   3. 2q + 1
   4. 2q -1
3. Decimal representation of an irrational number is always:
   1. non-terminating ,non-repeating
   2. terminating
   3. repeating
   4. non-terminating, repeating
4. n² - 1 is divisible by 8, if n is :
   1. an odd integer
   2. an integer
   3. a natural number
   4. an even integer
5. According to Euclid’s division algorithm using Euclid’s division lemma for any two positive integers a & b with a > b enables us to find:
   1. HCF
   2. LCM
   3. DECIMAL EXPANSION
   4. PROBABILITY
6. Sum of the zeroes of a quadratic polynomial p(x) = ax² + bx + c is given by :
   1. c/a
   2. a/c
   3. – b/a
   4. – a/b
7. The degree of the polynomial (x + 1) (x² - x - x⁴ + 1) is :
   1. 2
   2. 3
   3. 4
   4. 5
8. The quadratic polynomials whose sum of zeroes is +3 & product of zeroes is +2 is:
   1. x² + 3x -2
   2. x² - 2x + 3
   3. x² - 3x + 2
   4. x² - 3x - 2
9. If - 4 is a zero of the polynomial x² - x - (2 + 2k), then the value of k is :
   1. - 4/3
   2. 4/3
   3. 2/3
   4. - 2/3
10. The Q.P. p(y), the sum of whose zeroes is - 15 & one zeroes is -7, is :
    1. y² - 15y - 56
    2. y² + 15y + 56
    3. y² + 15y + 54
    4. y² + 15 - 56

Note : EACH QUESTION 3 MARKS (SECTION B)

11. Prove that √5 is irrational.
12. Show that (4 - √3) is irrational.
13. Divide 30x⁴ + 11x³ - 82x² - 12x + 48 by (3x² + 2x - 4) & verify the result by division algorithm.
14. Prove that 3+√5 is an irrational number.
15. Find a Q.P. the sum of whose zeroes is 7 & their product is 12. Hence find the zeroes of the polynomials.
16. Find all the zeroes of the polynomials x³ + 3x² - 2x - 6, if two of its zeroes are -√2 & √2.
17. If α,  β are the zeroes of the polynomials, such that α+ β = 6 α β = 4, then write the polynomials.
18. For what value of k, will the following system of linear equations have infinitely many solutions? 2x + 3y = 4 & (k+2)x + 6y=3k + 2.
19. Determine a & b for which the following system of linear equations has infinite number of solutions 2x - (a - 4) y = 2b + 1; 4x - (a -1) y = 5b -1.
20. If 6 years hence a man’s age will be 3times the age of his son & three years ago he was 9times as old as his son, find the present age of the man?