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Use Euclid’s division algorithm to find the HCF of:

Sol:

(i) 135 and 225

Since 225 > 135, we apply the division lemma to 225 and 135 to obtain

225 = 135 × 1 + 90

Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to obtain

135 = 90 × 1 + 45

We consider the new divisor 90 and new remainder 45, and apply the division lemma to obtain

90 = 2 × 45 + 0

Since the remainder is zero, the process stops.

Since the divisor at this stage is 45,

Therefore, the HCF of 135 and 225 is 45.

(ii)196 and 38220

Since 38220 > 196, we apply the division lemma to 38220 and 196 to obtain

38220 = 196 × 195 + 0

Since the remainder is zero, the process stops.

Since the divisor at this stage is 196,

Therefore, HCF of 196 and 38220 is 196.

(iii)867 and 255

Since 867 > 255, we apply the division lemma to 867 and 255 to obtain

867 = 255 × 3 + 102

Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain

255 = 102 × 2 + 51

We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain

102 = 51 × 2 + 0

Since the remainder is zero, the process stops.

Since the divisor at this stage is 51,

Therefore, HCF of 867 and 255 is 51.

CBSE/NCERT TEXT BOOK Problem Solutions

1. Real Numbers

2. Polynomials

3. Pair of Linear Equations in Two Variables

4. Quadratic Equations

5. Arithmetic Progressions

6. Triangles

7. Coordinate Geometry

8. Introduction to Trigonometry

9. Some Applications of Trigonometry

10. Circles

11. Constructions

12. Areas Related to Circles

13. Surface Areas and Volumes

14. Statistics

15. Probability

1. Complete the following statements:

(i) Probability of an event E + Probability of the event ‘not E’ = _______.

(ii) The probability of an event that cannot happen is _________. Such as event is called _________.

(iii) The probability of an event that is certain to happen is _________. Such as event is called ________.

(iv) The sum of the probabilities of all the elementary events of an experiment is _________.

(v) The probability of an event is greater than or equal to _______ and less than or equal to _______.

(i) 1

(ii) 0, impossible event

(iii) 1, sure event or certain event

(iv) 1

(v) 0, 1

Mathematics Intermediate INDEX

INTERMEDIATE FIRST YEAR INDEX(IA)
UNIT I	Functions
UNIT II	Mathematical Induction
UNIT III	Additions of Vectors
UNIT IV	Multiplication of Vectors 1) Products of Vectors 2) Scalar Triple Product 3) Multiple Products -1 4) Multiple Products -2 5) Additional Exercise
UNIT V	Trigonometric Ratios and Transformations 1) Trigonometric Ratios 2)  Periodicity and Extreme values 3) Trigonometric ratios of Compound Angles 4) Multiple and Sub-Multiple Angles 5) Transformations
UNIT VI	Trigonometric equations
UNIT VII	Inverse Trigonometric Functions
UNIT VIII	Hyperbolic Functions
UNIT IX	Properties of Triangles 1)  In circle and Ex-circles of a Triangle
UNIT X	Height And Distances
UNIT XI	Complex numbers 1) Fundamental Operations 2) Conjugate of Complex Numbers, Square Roots of Complex Numbers, And      Nth Roots of Complex Numbers 3) Mod-Amplitude Form Of Complex Number  4)  Geometrical Representation of Complex Numbers
UNIT XII	De Moivre’s Theorem
UNIT XIII	Trigonometric Expansions