The ecological niche of an organism relates to
UPSC CAPF
12. Which one of the following is NOT a favourable condition for occurrenc
Which one of the following is NOT a favourable condition for occurrence of a thunderstorm ?
13. Which one of the following statements about the Himalayas is NOT corre
Which one of the following statements about the Himalayas is NOT correct ?
14. Which of the following statements about the Equatorial region are corr
Which of the following statements about the Equatorial region are correct ?
- 1. It is a megathermal region
- 2. It is a sclerophyll region
- 3. It is a region of high development
- 4. It is a region of aerial streamlets
Select the correct answer using the code given below :
15. If the product of $n$ positive numbers is unity, then their sum is
If the product of $n$ positive numbers is unity, then their sum is
We are given that their product is unity: $x_1 \times x_2 \times \dots \times x_n = 1$.
We want to determine the property of their sum: $S = x_1 + x_2 + \dots + x_n$.
According to the Arithmetic Mean – Geometric Mean (AM-GM) inequality, for a set of non-negative numbers, the arithmetic mean is always greater than or equal to the geometric mean. Since the numbers are positive, this inequality applies:
$\frac{x_1 + x_2 + \dots + x_n}{n} \ge \sqrt[n]{x_1 x_2 \dots x_n}$
Substitute the given product into the inequality:
$\frac{S}{n} \ge \sqrt[n]{1}$
$\frac{S}{n} \ge 1$
$S \ge n$
The sum of the n positive numbers whose product is unity is always greater than or equal to n.
Equality holds if and only if all the numbers are equal. If $x_1 = x_2 = \dots = x_n = x$, and their product is 1, then $x^n = 1$. Since they are positive, $x$ must be 1. In this case, the sum is $n \times 1 = n$. If the numbers are not all equal, the sum is strictly greater than n. Therefore, the sum is never less than n.
16. 5% of income of A is equal to 15% of income of B and 10% income of B i
5% of income of A is equal to 15% of income of B and 10% income of B is equal to 20% of income of C. If the income of C is Rs. 2,000, then what is the total income of A, B and C ?
1) 5% of A = 15% of B
(5/100) * A = (15/100) * B
0.05 A = 0.15 B
Divide both sides by 0.05: A = (0.15 / 0.05) B => A = 3B
2) 10% of B = 20% of C
(10/100) * B = (20/100) * C
0.10 B = 0.20 C
Divide both sides by 0.10: B = (0.20 / 0.10) C => B = 2C
We are given the income of C is Rs. 2,000.
Substitute the value of C into the equation for B:
B = 2 * C = 2 * 2000 = Rs. 4,000.
Substitute the value of B into the equation for A:
A = 3 * B = 3 * 4000 = Rs. 12,000.
The total income of A, B, and C is the sum of their individual incomes:
Total Income = A + B + C = 12000 + 4000 + 2000 = Rs. 18,000.
17. In an examination, 25% of the candidates failed in Mathematics and 12%
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination ?
Given: M = 25%, E = 12%, B = 10%.
The percentage of candidates who failed in at least one subject is given by the formula:
P(M U E) = P(M) + P(E) – P(M ∩ E)
Percentage failed in at least one subject = 25% + 12% – 10% = 37% – 10% = 27%.
The percentage of candidates who passed in both subjects is the remaining percentage:
Percentage passed in both = 100% – Percentage failed in at least one subject = 100% – 27% = 73%.
We are given that 292 candidates passed in both subjects.
Let T be the total number of candidates.
So, 73% of T = 292
(73 / 100) * T = 292
T = (292 * 100) / 73
T = 29200 / 73
Dividing 29200 by 73: 292 / 73 = 4 (since 73 * 4 = 292).
So, 29200 / 73 = 400.
The total number of candidates is 400.
18. Study of a single species and the environmental factors in its habitat
Study of a single species and the environmental factors in its habitat is called
B) Synecology is the study of ecological relationships within biological communities, focusing on the interactions among different species and the structure and function of entire ecosystems.
D) Ethology is the scientific study of animal behavior, usually in natural conditions.
19. NPP (Net Primary Productivity) is highest for
NPP (Net Primary Productivity) is highest for
* Tropical forests: 1000-3500
* Swamps and Marshes: 800-3500
* Algal beds and reefs: 1000-2500
* Woodland and shrub land: 200-2000
While the ranges overlap, many ecological sources point to swamps/marshes and estuaries as having the absolute highest peak NPP values per unit area.
20. Presence of ozone in the atmosphere is important because it absorbs
Presence of ozone in the atmosphere is important because it absorbs