List of practice Questions

The arc length of the parametric curve: \( x=\cos\theta,\; y=\sin\theta,\; z=\theta \) from \( \theta=0 \) to \( \theta=2\pi \) is equal to _________ (round off to one decimal place).

The service ceiling of an airplane is the altitude

Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?

A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised:

A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force \( F \) as shown. The force in QR is

The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

The region of highest static temperature in a rocket engine and the region of highest heat flux are _______, respectively.

If $\hat{a}, \hat{b}, \hat{c}$ are three mutually perpendicular unit vectors, then $\hat{a} \cdot (\hat{b} \times \hat{c})$ can take the value(s):

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 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?