List of practice Questions

The equation of the straight line representing the tangent to the curve \(y = x^2\) at the point (1, 1) is
Let \(\hat{i}, \hat{j}, \hat{k}\) be the unit vectors in the x, y, and z directions, respectively. If the vector \(\hat{i} + \hat{j}\) is rotated about positive \(\hat{k}\) by \(135^\circ\), one gets
The point of maximum entropy on a Fanno-curve in a Temperature–Entropy (T–s) diagram represents the
Consider steady, two-dimensional, incompressible flow over a non-porous flat plate as shown in the figure. For the control volume PQRS, the speed \(u_{\infty}\) at section PQ is uniform and the speed at section RS is given by \(u(y)=A_0\left(\frac{y}{h}\right)^n\), where \(n\) is a positive integer. The value of \(A_0\) for which the flow through section PS will vanish is:
Consider the velocity distribution $u(y)$ shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is _________.
The prevalence of flu in a population is 1%. A diagnostic test has a false positive rate of 10% and a false negative rate of 10%. The probability that a randomly chosen person tests positive is ________ (Round off to three decimal places).
In a deer population, the male-to-female ratio is 1 : 2. The probability that a randomly formed group of size three has 2 males and 1 female is ________ (Round off to two decimal places).
The fitness \( f(n) \) of an individual in a group of size \( n \) is given by \[ f(n) = n(10 - n). \] At evolutionary equilibrium, groups are found in two different sizes. If one group size is 6, the other group size must be ________ (Answer in integer).
Which one or more of the following conditions can lead to an increase in tree densities in tropical savannas?
Gene conversion can lead to which one or more of the following evolutionary outcomes?
If the observed heterozygosity at a locus is 0.6, which one or more of the following could produce this outcome?
Which one or more of the following reasons has/have been invoked to explain high species diversity in the tropics?
In a linear regression with a single continuous predictor and 100 data points, the residual degrees of freedom are ________ (Answer in integer).
The genome of an organism has 60% GC (Guanine-Cytosine) content. The Adenine in this genome is ________% (Answer in integer).
Which one or more of the following genes/markers is/are typically used for species identification?
A bee species forages for nectar on a plant species which has yellow flowers. To find out what cues the bees use to recognize the flowers, researchers performed the following experiment. They presented individual bees with the stimuli given below and examined the proportion of bees that approached and landed on the stimuli. The results are shown below.
Which one or more of the following interpretation(s) of the experiment is/are correct?
Which one or more of the following reason(s) explain(s) why whales use low frequencies (infrasound) for mate-finding and high frequencies (ultrasound) for hunting prey?
The table shows the relative abundance of three potential prey species in the environment and in the diet of a bat predator.
Which one or more of the following options represent(s) an evolutionary arms race?
The figure shows an \(F\) probability density function. The two dotted lines represent critical values corresponding to a two-tailed \(F\)-test at a level of significance of 0.05. The observed \(F\)-statistic for two samples is indicated by the solid line.
Some lizard species show positive allometry in head width, with larger individuals investing disproportionately more in musculature leading to wider heads. To test for positive allometry in a study population, a researcher measures body size and head width for 100 individuals and fits a straight line to a log-log plot of these two traits. Which one of the following estimated values of the slope indicates support for positive allometry?
A team of ecologists laid 100 plots of 50 m \(\times\) 50 m in a forest and counted the number of individuals of a tree species in each plot. They then calculated the mean and variance of the number of individuals per plot. If trees are randomly distributed, then which one of the following relationships between the variance and mean is expected?
The following graphs show rank abundance data for species in three different communities P, Q and R. Based on both species richness and relative abundance, which one of the following options correctly represents the ordering of communities according to their species diversity?
Which one of the following cladograms represents the correct phylogenetic relationships in the Kingdom Animalia?
\(\beta\)-diversity quantifies the difference in species composition between two ecological communities. Which one of the following statements is correct about \(\beta\)-diversity?