CBSE Class 8 - Maths - CH13 - Direct and Inverse Proportions (Ex 13.2)

Direct and Inverse Proportions

NCERT Exercise and Other Q & A

If there is an increase (↑) [decrease (↓)] in one quantity produces a proportionate decrease (↓) [increase (↑)] in another quantity, then we say that the two quantities are in inverse variation or inverse proportion.

If two quantities vary inversely, their product is a constant.
e.g. if  and y are two quantities which are in inverse proportion then,
       x × y = constant
or   x₁ × y₁ = x₂ × y₂

NCERT Exercise 13.2

Q1: Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.

Answer:
(i) With an increase in number of workers, the job will complete in lesser time. ∴ The number of workers on a job and the time to complete the job are in inverse proportion.

(ii) At constant (uniform) speed, more time means more distance will be covered. ∴ The time taken for a journey and the distance travelled in a uniform speed are in direct proportion.

(iii) An increase (↑) in the cultivated area means an increase  (↑) in the crop harvested. ∴ Area of cultivated land and the crop harvested are in direct proportion.

(iv) An  increase (↑) in speed of the vehicle means the distance will be covered in lesser  (↓) time. ∴ The time taken for a fixed journey and the speed of the vehicle. are in inverse proportion.

CBSE Class 10 - English (C) - Tenses

Tenses

Q1(CBSE class 10,  2011): Complete the following passage choosing the correct options given:

According to the NASA Astronaut Neil Armstrong, the Aliens (a)_____________  a base on the Moon and they (b)_______________ the American astronauts in no uncertain terms to (c) ....................... and stay away from the Moon. According to (d) ....................... unconfirmed reports, both Neil Armstrong and Edwin “Buzz” Aldrin saw UFOs shortly after that historic (e) ....................... on the Moon in Apollo 11 on 21 July 1969. Observers in the control room say that they remember (f) ....................... one of the astronauts refer to a “light” in or on a crater (g) ....................... the television transmission. The mission control (h) ....................... for more details.

(a)
   (i) are having
   (ii) have
   (iii) has
   (iv) is having

(b)
    (i) are telling
    (ii) tell
   (iii) told
    (iv) are saying

Online English Grammar Quiz Available

Eduvictors.com Basic English Grammar Quiz

200+ MCQs covering 17 topics on English Grammar are available at Eduvictors.com in quiz form.
You may access the quizzes on the following topics:

Nouns Quiz-1: Test your understanding about different types of Nouns

Nouns Quiz-2: Check your knowledge about cries of animals and birds.

CBSE Class 9 - SA-2 Sanskrit (संस्कृत) Sample Question Paper- 2012-13

Class 9 -संस्कृत Sample Paper (SA2) - 2012-13

Here follows a SA-2 संस्कृत Sample Question Paper (Solved) by CBSE

☛ See also The Fox and The Crow Story(लोमश: एवं काक:)

CBSE Class 8 - Maths - CH13 - Direct and Inverse Proportions (Ex 13.1)

Direct and Inverse Proportions

An increase (↑) in one quantity brings about an increase (↑) in the other quantity and similarly a decrease (↓) in one quantity brings about a decrease (↓) in the other quantity, the these two quantities are in direct proportion or direct variation.

In direct proportion the ratio of two quantities (say x and y) is a constant called constant of proportionality.
⇒ y/x = k          or       y = k × x



NCERT Chapter Solutions and other Q & A

NCERT Ex. 13.1

Q1: Following are the car parking charges near a railway station upto
       4 hours Rs 60
       8 hours Rs 100
     12 hours Rs 140
     24 hours Rs 180

Check if the parking charges are in direct proportion to the parking time

Answer: Calculating the ratio of parking charging wrt parting time:

No. of Hours (a)	Parking Charges(B)	Ratio (B/A)
4	60	60/4 = 15:1
8	100	100/8 =25:2
12	140	140/12 =35:3
24	180	180/24=15:2

Since the ratio of various parking charging vs parking time is not the same, the parking charges are NOT in direct proportion to the parking time.


Q2: A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base.
In the following table, find the parts of base that need to be added.

Parts of red pigment	1	4	7	12	20
Parts of base	8	...	...	...	...

CBSE Class 10 - संस्कृत (Sanskrit - Paper) - 2012-13

Class 10 -संस्कृत Sample Paper (SA2) - 2012-13

Here follows a SA-2 संस्कृत Sample Question Paper (Solved) by CBSE

☛ See also 2012 Papers: Paper-1 and Paper-2

CBSE Class 10 - English (C) - Unseen Passage with MCQs

Unseen Passage with MCQs

Q(CBSE 2010): Read the poem carefully. Choose the right option from the list of options given for each of the questions:

image credits: clker.com

When my shoulders are bent,
Saddled
With burdens
Of life;
When I am tired
So tired
(And when) I think, now - that now
my knees will give in,
a small little poem comes
and stands in front of me
holds my hand and says :
Give me your burden,
Come, give it to me,
my poet.

1. The ‘burden’ here refers to
(a) a heavy sack
(b) adversities that have plagued him
(c) his haversack
(d) none of the above


2. The word ‘tired’ here refers to
(a) fatigue
(b) the loss of will to carry on any further
(c) disillusionment
(d) the result of being exposed to the scorching sun