CBSE Class 10 - Maths - CH1 - Real Numbers (Euclid's Division Lemma)

Euclid's Division Lemma

Important Questions asked in Examination...

Euclid (4th BC)
credits: wikipedia

Q1: State Euclid's Division Lemma.

Answer: Given positive integers a and b ( b ≠ 0 ), there exists unique integer numbers q and r satisfying a = bq + r, 0 ≤ r < |b|. where
    a is called dividend
    b is called divisor
    q is called quotient
    r is called remainder.

    e.g. 17 = 5 × 3 + 2

Q2: Prove Euclid's Division Lemma.

Answer: According to Euclid's Division lemma, for a positive pair of integers there exists unique integers q and r, such that
                      a = bq + r, where 0 ≤ r < b

Let us assume q and r are not unique i.e. let there exist another pair q0 and r0 i.e. a = bq0 + r0, where 0 ≤ r0 < b

⇒ bq + r = bq0 + r0
⇒ b(q - q0) = r - r0                                          ................ (I)

Since 0 ≤ r < b and 0 ≤ r0 < b, thus 0 ≤ r - r0 < b ......... (II)

The above eq (I) tells that b divides (r - r0) and (r - r0) is an integer less than b. This means (r - r0) must be 0.
⇒ r - r0 = 0 ⇒ r = r0

Eq (I) will be, b(q - q0) = 0
Since b ≠ 0, ⇒ (q - q0) = 0 ⇒ q = q0

Since r = r0 and q = q0, ∴ q and r are unique.

Q3: Prove that the product of two consecutive positive integers is divisible by 2?

CBSE Class 9 - CH 12 - Sound (Study Points)

Sound

Visual Representation of Sound Waveform
(image courtsey: openclipart)

Study Points

1. Sound travels from one point to another in the form of waves.

2. Sound is produced due to vibration of different objects.

3. Sound waves are longitudinal in nature.

4. Sound travels as a longitudinal wave through a material medium.

5. Sound travels as successive compressions and rarefactions in the medium.

6. In sound propagation, it is the energy of the sound that travels and not the particles of the medium.

7. Sound cannot travel in vacuum.

8. Sound waves cannot be polarised.

9. The change in density from one maximum value to the minimum value and again to the maximum value makes one complete oscillation.

10. The part or region of a longitudinal wave in which the density of the particles of the medium is higher than the normal density is known as compression.

11. The part or region of a longitudinal wave in which the density of the particles of the medium is lesser than the normal density is called a rarefaction.

12. The distance between two consecutive compressions or two consecutive rarefactions is called the wavelength, λ.

CBSE Class 12 - Chemistry - Question Paper (2014)

	CHEMISTRY (Theory) 2014
[Time allowed: 3hrs]		[Maximum Marks:70]

General Instructions :
(i)   All questions are compulsory.
(ii)  Questions numbers 1 to 8 are very short-answer questions and carry 1 mark each.
(iii) Questions numbers 9 to 18 are also short-answer questions and carry 2 marks each.
(iv)  Questions numbers 19 to 27 are long-answer questions and carry 3 marks each.
(v)   Questions numbers 28 to 30 are long-answer questions and carry 5 marks each.
(vi)  Use Log Tables,if neccessary.Use of calculators is not allowed.

1.	Give one example of sol and gel?	1
2.	Which reducing agent is employed to get copper from the leached low grade copper ore?	1
3.	Write the IUPAC name of the compound	1
	CH3 - CH - CH2 - CHO                            NH2
4.	Which of the following isomers is more volatile :	1
	o-nitrophenol or p-nitrophenol ?
5.	Some liquids on mixing form 'azeotropes'. What are 'azeotropes' ?	1
6.	Arrange the following in increasing order of basic strength :	1
	C6H5NH2, C6H5NHCH3, C6H5CH2NH2

CBSE Class 9 - Maths - CH 13 - Surface Area and Volume (Study Points)

Surface Area & Volume

Key Concepts

S.no.	Name	Figure	Lateral/ Curved Surface Area	Total Surface Area(TSA)	Volume(V)	Symbols use for
1	cuboid		2(l + b)xh	2(lb + bh + hl)	lbh	l=length b=breadth h=height
2	cube		4s2	6s2	s3	s = side
3	Right circular cylinder		2Πrh	2Πr(h + r)	Πr2h	h = height r = radius of base
4	Right circular cone		Πrl	Πr(l + r)	1 3 Πr2h	r = radius of base h = heightl = Slant height
5	Sphere		4Πr2	4Πr2	4 3 Πr3	r = OA = radius

CBSE Class 8/9/10 - Reading Comprehension (Set-5)

 Reading Comprehension

Read the following passages carefully and mark out the correct answers from among the alternatives given below each question in every passage:

PASSAGE - 1

The load was very heavy for the old camel. He tried his best to carry it as far as the next village. There his master would be able to get another camel to carry this heavy load. But he was so tired and exhausted that he could not go any further. His master took off the load from the camel’s back and put it on the back of another camel and went his way. A tiger was passing by at this time. He had been hurt by the tusk of an elephant. As the tiger was in pain, he found it difficult to walk. So he lay down by the side of the camel. The camel began licking the tiger’s wound with his long tongue and offered him food that his master had left behind. In a few days, the tiger and the camel recovered. As the tiger was very hungry the old camel told him to kill him and eat his meat. The tiger could not think of killing his friend.
At that time a deer came running towards them. A hunter had shot at him with an arrow. He lay down by the side of the tiger. He told the tiger to kill him and eat his flesh as he did not want the wicked hunter to take him away. The tiger did as he was told. Just then the hunter came on the spot. The angry tiger jumped on him and killed him also. Another young deer was in the bag that the hunter was carrying. The tiger set it free. The tiger and the camel lived happily ever after in the forest.

Q1: The camel began to lick the tiger’s wound because of the

(a) tiger was in pain
(b) tiger was tired
(c) tiger could not walk
(d) the camel was hungry
(e) camel’s tongue is long.

CBSE Class 9 - Maths - Ch 14 - Statistics (NCERT Ex 14.3)

Statistics

Exercise 14.3

Question 1:

A survey conducted by an organisation far the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures(in %):

S.no.	Causes	Female fatality rate(%)
1	Reproductive health conditions	31.8
2	Neuropsychiatric conditions	25.4
3	Injuries	12.4
4	Cardivasculor conditions	4.3
5	Respiratory conditions	4.1
6	Other Causes	22.0

(i) Represent the information given above graphically.

(ii)Which condition is the major cause of women's ill health and death worldwide?

(iii) Try to find out, with the help of your teacher, any two factors which play a major role ill the cause in (ii) above being the major causes.

Answer:

(i) By representing causes on x-axis and family fatality rate on y-axis and choosing an appropriate scale (1 unit 5% far y axis), the graph of the information given above can be constructed as follows:

In the graph, the rectangle bars are of the same width and have equal spacing among them.

(ii) As shown, Reproductive health condition is the major cause of women's ill health and death worldwide.

(iii) The factors are as follows.

1. Lack of medical facilities

2. Lack of awareness of  right medical treatment

Question 2:

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.

CBSE Class 9 Maths - CH14 - Statistics (NCERT Ex 14.1 and 14.2)

Statistics (NCERT Ex 14.1 and 14.2)

NCERT Exercise 14.1

Question:1

Give five examples of data that you can collect from day to day life.

Answer:

In our day to day life,we can collect the following data.

1. Numbers of girl students per class in a school.

2. Number of cars of different models in our colony.

3. Production of rice in last 20 years in our country.

4. Rainfall in our city in the last 10 years.
5. Scores made by a team in Indian Premier League tournament.

Question:2

Classify the data in Q1 above as primary or secondary data.

Answer:

The information which is collected by the investigator himself with defined objectives is called as primary data whereas when the information is gathered from a source which already had stored, is called as secondary data.
Item 1 and 2 are the primary data where as the data in 3, 4 and 5 is secondary data.

Exercise 14.2

Question:1

The blood groups of 30 students of class VIII are recorded as follows:

A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O

A,AB,O,A,A,O,O,AB,B,A,O,B,A,B,O.