CBSE Class 8 - Mathematics - Factorisation - NCERT Exercise (14.2)

Factorisation

NCERT Exercise 14.2

Q1: Factorise the following expressions.

(i) a² + 8a + 16

(ii) p² − 10p + 25

(iii) 25m² + 30m + 9

(iv) 49y² + 84yz + 36z²

(v) 4x² − 8x + 4

(vi) 121b² − 88bc + 16c²

(vii) (l + m)² − 4lm (Hint: Expand (l + m)² first)

(viii) a⁴ + 2a²b² + b⁴


Answer:

(i) a² + 8a + 16 = (a)² + 2 ☓ a ☓ 4 + (4)²

= (a + 4)² [(x + y)² = x² + 2xy + y²]


(ii) p² − 10p + 25 = (p)² − 2 ☓ p ☓ 5 + (5)²

= (p − 5)² [(a − b)² = a² − 2ab + b²]


(iii) 25m² + 30m + 9 = (5m)² + 2 ☓ 5m ☓ 3 + (3)²

= (5m + 3)² [(a + b)² = a² + 2ab + b²]

(iv) 49y² + 84yz + 36z² = (7y)² + 2 ☓ (7y) ☓ (6z) + (6z)²

= (7y + 6z)² [(a + b)² = a² + 2ab + b²]

(v) 4x² − 8x + 4 = (2x)² − 2 (2x) (2) + (2)²

= (2x − 2)² [(a − b)² = a² − 2ab + b²]

= [(2) (x − 1)]² = 4(x − 1)²

(vi) 121b² − 88bc + 16c² = (11b)² − 2 (11b) (4c) + (4c)²

= (11b − 4c)² [(a − b)² = a² − 2ab + b²]

(vii) (l + m)² − 4lm = l² + 2lm + m² − 4lm

= l² − 2lm + m²

= (l − m)² [(a − b)² = a² − 2ab + b²]

(viii) a⁴ + 2a²b² + b⁴ = (a²)² + 2 (a²) (b²) + (b²)²

= (a² + b²)² [(a + b)² = a² + 2ab + b²]

CBSE Class 9/10 - English Grammar - Editing Exercise - 4

Editing Exercise

The following sentences have not been edited. There is one error in each line. Write the incorrect word and correction. Remember to underline the word you have supplied.

-	Incorrect	Correct Word
1. Radha sat in a tree.	________	________
2. He likes cutting jokes.	________	________
3. I want a pen to write on.	________	________
4. Mohan needs not worry.	________	________
5. Are you a member in the committee?	_______	_______
6. What is the cost of this pen?	_______	_______
7. Verbal orders will not be obeyed.	_______	_______
8. I saw a bad dream last night.	_______	_______

CBSE Class8 - Mathematics - Ch 14 - Factorisation (NCERT Ex 14.1)

Factorisation

NCERT Exercise 14.1 Solutions

Q1: Find the common factors of the terms

(i)   12x, 36

(ii)  2y, 22xy

(iii)  14pq, 28p²q²

(iv) 2x, 3x², 4

(v) 6abc, 24ab², 12a²b

(vi) 16x³, −4x², 32x

(vii) 10pq, 20qr, 30rp

(viii) 3x²y³, 10x³y², 6x²y²z

Answer:

(i) 12x = 2 ☓ 2 ☓ 3 ☓ x

36 = 2 ☓ 2 ☓ 3 ☓ 3

The common factors are 2, 2, 3.

And, 2 ☓ 2 ☓ 3 = 12

(ii) 2y = 2 ☓ y

22xy = 2 ☓ 11 ☓ x ☓ y

The common factors are 2, y.

And, 2 ☓ y = 2y

(iii) 14pq = 2 ☓ 7 ☓ p ☓ q

28p²q² = 2 ☓ 2 ☓ 7 ☓ p ☓ p ☓ q ☓ q

The common factors are 2, 7, p, q.

And, 2 ☓ 7 ☓ p ☓ q = 14pq

(iv) 2x = 2 ☓ x

3x² = 3 ☓ x ☓ x

4 = 2 ☓ 2

The common factor is 1.

CBSE Class 9 - English (C) - CH 12 - Song of the Rain - A summary

Song of the Rain

Summary

Poet: Khalil Gibran

Khaill Gibrain, a Lebanese poet and writer. In his young age, he settled in America. The style of his poems s very formal and it offers a deep insight into various facts of human life. 'The Prohet' his one of the famous works.

                     
Summary:

CBSE Class 12 - NEET - Biology - The Living World (MCQs)

Biology - The Living World

7 MCQs from previous AIPMT/NEET question papers

Q1: The living organisms can be unexceptionally distinguished from the non-living things on the basis of their ability for

(a) responsiveness to touch
(b) interaction with the environment and progressive evolution
(c) reproduction
(d) growth and movement



Q2: There is no life on the moon due to the absence of 

(a) oxygen
(b) water
(c) light
(d) temperature



Q3: Praying Mantis is the example of 

(a) warning coluration
(b) social insects
(c) camouflage
(d) Mullerian mimicry

JEE 2017 - Main and Advanced Examination Dates Announced

JEE 2017 - Main and Advanced Examination Dates Announced

JEE is the topmost examination conducted to get admissions in UG engineering or architecture courses in NITs, IITs and other institutions. It is a 2 stage  examination i.e.

Ist Stage - JEE Mains examination - to get admission in NIT, IIITs and other engineering colleges.
2nd Stage - JEE Advanced to get admission to IITs, IIS and other premier institutes.

Important Changes Made in JEE Main 2017

Class 7 - Science - Weather, Climate and Adaptation of Animals to Climate (MCQs)

 Weather, Climate and
Adaptation of Animals to Climate 

Protect Our Environment

Class 7 - Science - NCERT Exemlar MCQs Answers

Q1: The maximum and minimum temperature displayed daily in the weather bulletin refer to the –

(a) highest day temperature and lowest night temperature of the day.
(b) highest day temperature and highest night temperature of the month.
(c) temperature recorded at 12 noon and at mid night (00.00 hrs).
(d) average highest temperature of day and average lowest temperature of night.




Q2: Paheli went to a wildlife sanctuary where she saw dense vegetation of trees, shrubs, herbs and also a variety of animals like monkeys, birds, elephants, snakes, frogs, etc. The most likely location of this sanctuary is in the –

(a) temperate region
(b) tropical region
(c) polar region
(d) coastal region




Q3: Out of the given definitions, which is the most appropriate definition of climate?

(a) Changes in weather conditions in a year.
(b) Average weather pattern of many years.
(c) Change in weather pattern in a few years.
(d) Weather conditions during summer.



Q4: Which of the following briefly describes the desert climate?

(a) Hot and humid
(b) Dry and humid
(c) Hot and dry
(d) Hot and wet