Geetha told her classmate radha that (root2 - 1 upon root root2 + 1) is an irrational number. Radha told Geetha that she was wrong and further claimed that if there is a number x such that x3 is irrational then x5 is also irrational. Geetha said that Radha was wrong. Radha accepted her mistake.justify both these statements.

CBSE Class IX Chapters for Mathematics

Test Paper And Study Materials

IX Number System

IX Polynomial(Algebra)

IX Introduction to Euclid Geometry

IX Lines and Angles (Geometry)

IX Triangle(Geometry)

IX CO-Ordinate Geometry

IX Area of Triangle(Heron Formula)

IX Linear equations in two variables

IX Quadrilaterals

IX Area of Parallelogram

IX Geometry: Circles

IX Constructions

IX Surface Areas and Volumes

IX Statistics

IX Probability

9th[IX] Sample papers for Summative Assessment – 1 [links]
Mathematics	Science
Social Science	English, Hindi and Sanskrit
9th[IX] Sample papers for Summative Assessment – 2 [links]
Mathematics	Science
Social Science	English, Hindi and Sanskrit

X Real Number MCQ Assignments in Mathematics Class X (Term I)

X Real Number MCQ  Assignments in Mathematics Class X (Term I)

1. Euclid’s division algorithm can be applied to :

(a) only positive integers            (b) only negative integers

(c) all integers                            (d) all integers except 0.

2. For some integer m, every even integer is of the form :

(a) m (b) m + 1 (c) 2m (d) 2m + 1

3. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is :

(a) 1 (b) 2 (c) 3 (d) 4

4. If two positive integers p and q can be expressed as p = ab2 and q = a3b, a; b being prime numbers, then LCM (p, q) is :

(a) ab (b) a2b2 (c) a3b2 (b) a3b3

5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :

(a) 10 (b) 100 (c) 504 (d) 2520

6. 7 × 11 × 13 × 15 + 15 is :

(a) composite number                 (b) prime number

(c) neither composite nor prime  (d) none of these

7. 1.23 is :

(a) an integer (b) an irrational number (c) a rational number (d) none of these

8. If two positive integers p and q can be expressed as p = ab2 and q = a2b; a, b being prime numbers, then LCM (p, q) is :

(a) a2b2 (b) ab (c) ac3b3 (d) a3b2

9. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where :

(a) 0 < r ≤ b (b) 1 < r < b (c) 0 < r < b (d) 0 ≤ r < b

10. 3.24636363... is :

(a) a terminating decimal number (b) a non-terminating repeating decimal number

(c) a rational number                    (d) both (b) and (c)

11.(n + 1)2 – 1 is divisible by 8, if n is :

(a) an odd integer (b) an even integer (c) a natural number (d) an integer

12. The largest number which divides 71 and 126, leaving remainders 6 and 9 respectively is :

(a) 1750 (b) 13 (c) 65 (d) 875

13. For some integer q, every odd integer is of the form :

(a) 2q (b) 2q + 1 (c) q (d) q + 1

14. If the HCF of 85 and 153 is expressible in the form 85m – 153, then the value of m is :

(a) 1 (b) 4 (c) 3 (d) 2

15. According to Euclid’s division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid’s division lemma to a and b to find q and r such that a = bq + r, where r must satisfy :

(a) 1 < r < b (b) 0 < r < b (c) 0 ≤ r < b (d) 0 < r ≤ b