The probability of finding a green signal on a busy crossing X is 30 % . What is the probability of finding a green signal on X on two consecutive days out of three?

Let A be the event of finding a green signal on a busy crossing X The probability of finding a green signal on a busy crossing X is 30 % . P A = 30 100 = 3 10 The probability of not finding a green signal on a busy crossing X is P A ¯ = 1 - 3 10 = 7 10 . The probability of finding a green signal on X on two consecutive days out of three = P A P A P A ¯ + P A ¯ P A P A = 3 10 × 3 10 × 7 10 + 7 10 × 3 10 × 3 10 = 63 500 .

If in a population of size ”N” the birth rate is represented as “b” and the death rate as “d”, the increase or decrease in “N” during a unit time period ”t” will be: The equation given above can also be represented as: What does ”r” represent. Write any one significance of calculating ”r” for any population?

r here represents the intrinsic rate of increase of population and it is equal to the difference in the natality (birth rate) and mortality (death rate). The 'r' is called the 'intrinsic rate of natural increase. It' is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth. If the value of 'r' is increasing it signifies the growth of the population and if it is going down then the population growth has slowed down.

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In the two-sector model, what is the primary function of households?

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Important Questions on Relations and Functions

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Describe the DDT biomagnification occurring in an aquatic food chain. State the negative effects the process has on the organisms at the last trophic level of the food chain.

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How is the detritus food chain connected with the grazing food chain in a natural ecosystem?

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Mathematics>Algebra>Relations and Functions>Composition of Functions

Explain the role of the ‘first trophic level’ in an ecosystem.

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Mathematics>Algebra>Relations and Functions>Composition of Functions

An association of individuals of different species living in the same habitat and having functional interactions is:

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Mathematics>Algebra>Relations and Functions>Composition of Functions

Four persons can hit a target correctly with probabilities

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

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Mathematics>Algebra>Relations and Functions>Composition of Functions

Explain energy flow in ecosystem.

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Mathematics>Algebra>Relations and Functions>Composition of Functions

What is a trophic level in an ecosystem ? What is ‘standing crop’ with reference to it?

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Mathematics>Algebra>Relations and Functions>Composition of Functions

If 8 individuals in a population of 80 butterflies die in a week, calculate the death rate of population of butterflies during that period.

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Mathematics>Algebra>Relations and Functions>Composition of Functions

A die marked

1, 2, 3

in red

4, 5, 6

in green tossed. Let

A

be the event "number is even" and

B

be the event "number is marked red". Find whether the events

A

and

B

are independent or not.

EASY

Mathematics>Algebra>Relations and Functions>Composition of Functions

The probability of finding a green signal on a busy crossing

X

30 %

. What is the probability of finding a green signal on

X

on two consecutive days out of three?

EASY

Mathematics>Algebra>Relations and Functions>Composition of Functions

The principle of competitive exclusion was stated by

EASY

Mathematics>Algebra>Relations and Functions>Composition of Functions

f (x) = x + 1

, find

\frac{d}{d x} (fof) (x)

HARD

Mathematics>Algebra>Relations and Functions>Composition of Functions

Match the following and select the correct option:

(a)	Earthworm	(p)	Pioneer species
(b)	Succession	(q)	Detrivore
(c)	Ecosystem service	(r)	Natality
(d)	Population growth	(s)	Pollination

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Mathematics>Algebra>Relations and Functions>Composition of Functions

Give a diagrammatic representation of energy flow through different trophic levels.

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Mathematics>Algebra>Relations and Functions>Composition of Functions

State two observations made by the German naturalist, Alexander von Humboldt during his extensive explorations in South American Jungles.

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Mathematics>Algebra>Relations and Functions>Composition of Functions

If in a population of size ”N” the birth rate is represented as “b” and the death rate as “d”, the increase or decrease in “N” during a unit time period ”t” will be:

Question Image

The equation given above can also be represented as:

Question Image

What does ”r” represent. Write any one significance of calculating ”r” for any population?

HARD

Mathematics>Algebra>Relations and Functions>Composition of Functions

Differentiate between an ‘Expanding age pyramid’ and a ‘Stable age pyramid’. Substantiate your answer with diagrams.

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Mathematics>Algebra>Relations and Functions>Composition of Functions

If 20J of energy is trapped at producer level, then how much energy will be available to peacock as food in the following chain?
plant

\to

mice

\to

snake

\to

peacock

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Mathematics>Algebra>Relations and Functions>Composition of Functions

A problem in mathematics is given to three students

A, B, C

and their respective probability of solving the problem is

\frac{1}{2}, \frac{1}{3}

and

\frac{1}{4}

, the probability that the problem will be solved is

EASY

Mathematics>Algebra>Relations and Functions>Composition of Functions

For

x ϵ (0, \frac{3}{2}),

let

f (x) = \sqrt{x}, g (x) = t a n x

and

h (x) = \frac{1 - x^{2}}{1 + x^{2}}

. If

ϕ (x) = (h o f) o g) (x),

then

ϕ (\frac{π}{3})

is equal to:

In the two-sector model, what is the primary function of households?

Important Questions on Relations and Functions

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