Mathematics and Statistics in Ecology - Mathematics and Quantitative Ecology - Ecology and Evolution Previous Year Questions

1

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences.
The word closest in meaning to comprehension is

A

understanding

B

meaning

C

concentration

D

stability

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2

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

Choose the most appropriate word from the options given below to complete the following sentence.
One of his biggest _____ was his ability to forgive.

A

vice

B

virtues

C

choices

D

strength

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3

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above sentences?

A

Rajan has decided to work only in a group.

B

Rajan and Sajan were formed into a group against their wishes.

C

Sajan had decided to give in to Rajan’s request to work with him.

D

Rajan had believed that Sajan and he would be working together.

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4

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

If \( y = 5x^2 + 3 \), then the tangent at \( x = 0 \), \( y = 3 \)

A

passes through \(x = 0, y = 0 \)

B

has a slope of +1

C

is parallel to the x-axis

D

has a slope of -1

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5

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

A

ALRVX

B

EPVZB

C

ITZDF

D

OYEIK

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6

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?

A

3.0

B

2.5

C

1.5

D

1.25

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7

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)
(i) On average, it rains more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall

A

(i) and (ii)

B

(i) and (iii)

C

(ii) and (iii)

D

(iii) and (iv)

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8

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

A researcher measures the height of 100 trees of a species. The mean of these observations is 50 and the variance is 16. The standard error of the mean calculated from these observations is ______________

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9

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

The slope of a function is zero

A

only at the maxima

B

only at the minima

C

at both maxima and minima

D

exactly mid-way between maxima and minima

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10

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

The coefficient of determination, \( R^2 \), represents how well a linear model fits the data. \( R^2 \) is the sum of squared deviations of observations from the regression line divided by the total sum of squared deviations from the mean value. For the figure below, \( R^2 \) is closest to

A

-1

B

0

C

0.05

D

1

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11

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

To evaluate the relationship between two variables (e.g., resource abundance and population density), a linear regression can be used. Here, the statistical null hypothesis which allows us to evaluate whether there is a relationship between these variables is

A

intercept = 0

B

slope = 0

C

sample size = 0

D

mean = 0

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12

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

The doubling time for a bacterial population is 60 minutes. Given a density of 35 cells/ml in a population in its exponential growth phase and assuming unlimited resources, the number of hours that the population will take to grow to 560 cells/ml is ______________

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13

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

Consider the following frequency distribution of an ecological variable:

Such a distribution with two peaks is called a bi-modal distribution. Here, the peak with the higher frequency is called the major mode and the one with the lower frequency is called the minor mode. A student has marked four points on the x-axis, i.e., P, Q, R and S. Match the points with the most appropriate statistic: Mean, Median, Major mode, and Minor mode

A

P–Major mode, Q–Mean, R–Median

B

P–Major mode, Q–Median, S–Minor mode

C

P–Minor mode, R–Mean, S–Major mode

D

Q–Median, S–Major mode, S–Mean

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14

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

Find the matching triplet

A

2, r, i

B

1, q, iv

C

3, s, iii

D

4, p, ii

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15

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

There are two coins in a bowl. Because of differences in the size of the two coins, the probability of picking the bigger coin is 0.6. The bigger coin is unbiased, whereas the smaller coin has a probability of 0.6 of yielding heads. A blind-folded student picks a coin from the bowl and tosses the coin. The probability (expressed using decimal notation, not as a fraction or percentage) that the coin yields a head is ______________.

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16

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

A recently discovered fossil contains 3.125% of \(^{14}C\) found in present day organisms. If the half-life of \(^{14}C\) is 5730 years, the age of the fossil in years is ______________

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17

2014 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2014

Assume that a piece of bamboo is a hollow cylinder of negligible wall thickness. The numerical value (in cm) of the ratio of the volume to surface area of such a bamboo, measuring 6 cm in diameter, is ______________

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18

2015 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2015

Fill in the missing value

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19

2015 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2015

A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

A

1 : 4

B

1 : 3

C

1 : 2

D

2 : 3

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20

2015 · Ecology and Evolution · Mathematics and Quantitative Ecology · Mathematics and Statistics in Ecology

Ecology and Evolution (EY) 2015

Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks.

Which one of the statements below is logically valid and can be inferred from the above sentences?

A

Humpty Dumpty always falls while having lunch

B

Humpty Dumpty does not fall sometimes while having lunch

C

Humpty Dumpty never falls during dinner

D

When Humpty Dumpty does not sit on the wall, the wall does not break

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