List of practice Questions

Hosts of parasites evolve effective immune responses to infection, which in turn results in those parasites evolving increased infectiousness towards the hosts. Which one of the following processes describes this type of interaction between hosts and parasites?

In primates, males are often larger than females. If sexual dimorphism evolved to enable males to compete for access to multiple females, in which mating system would we expect to see the greatest sexual dimorphism?

Fly larvae of a species feed simultaneously on a shared rotting fruit. If the density of fly larvae is high, then all the larvae grow up to be smaller sized adults than if the larval density were low. Which one of the following processes best describes this observation?
In a linear regression, a line of best fit can be obtained by
There are 9 different rock lizard species, each with a unique colour. Lizards of 2 different species sit on a rock at any given time. The number of possible colour combinations of rock lizards seen together on a rock is:
Rotting leaves of mango are composed of 25% of compound P which decomposes exponentially at a rate \( k_P = 0.5 \, {yr}^{-1} \) and 75% of compound Q which decomposes exponentially at a rate \( k_Q = 0.1 \, {yr}^{-1} \). What percentage of the initial amount of compound Q remains when half of the initial amount of compound P has decomposed? Choose the closest numerical value from the options provided.

The effect of temperature on the spontaneity of reactions are represented as:  Which of the following is correct?

The correct order of basic strength of the following molecules is:
(A) \(\text{C}_6\text{H}_4\text{NH}_2\text{O}\)
(B) \(\text{C}_6\text{H}_4\text{NH}_2\text{MeO}\)
(C) \(\text{C}_6\text{H}_4\text{NH}_2\text{NO}_2\)
(D) \(\text{C}_6\text{H}_4\text{NH}_2\text{CH}_3\)

The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from \( \pm 15 \, {V} \) supplies. If a \( +1 \, {V} \) signal is applied at the input, the output voltage (rounded off to one decimal place) is:


 

Consider the following oxides: 
V_2O_5, Cr_2O_3, Mn_2O_7, V_2O_3, VO_2 
A number of oxides which are acidic is \( x \). 
Consider the following complex compound: 
[Co(NH_2CH_2CH_2NH_2)_3](SO_4)_3 
The primary valency of the complex is \( y \). 
What is the value of \( x + y \) is?

If \( \text{Re} \left( \frac{2z + i}{z + i} \right) + \text{Re} \left( \frac{2z - i}{z - i} \right) = 2 \) is a circle of radius \( r \) and centre \( (a, b) \), then \( \frac{15ab}{r^2} \) is equal to:

If two vectors \( \mathbf{a} \) and \( \mathbf{b} \) satisfy the equation:

\[ \frac{|\mathbf{a} + \mathbf{b}| + |\mathbf{a} - \mathbf{b}|}{|\mathbf{a} + \mathbf{b}| - |\mathbf{a} - \mathbf{b}|} = \sqrt{2} + 1, \]

then the value of

\[ \frac{|\mathbf{a} + \mathbf{b}|}{|\mathbf{a} - \mathbf{b}|} \]

is equal to:

If a box contains 19 unbiased coins and 1 biased coin with both faces heads, and a coin is randomly chosen from this box and tossed. If the head appears, then the probability that the unbiased coin was selected is:
If \( f(\theta) = \frac{\tan(\tan(\theta)) - \tan(\sin(\theta))}{\tan(\theta) - \sin(\theta)} \) is continuous at \( \theta = 0 \), then the value of \( f(\theta) \) at \( \theta = 0 \) is equal to.
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A magnetic monopole does not exist.
Reason (R): Magnetic lines are continuous and form closed loops.
In the light of the above statements, choose the correct answer from the options below:
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Refractive index of glass is more than air.
Reason (R): Optical density of a medium is directly related to its mass density.
In the light of the above statements, choose the correct answer from the options given below.
Which of the following is the correct hybridization of \( \text{XeF}_4 \)?
Which of the following is the correct order of acidic character of oxides of vanadium?
If \( x |x - 3| + 3 |x - 2| + 1 = 0 \), then the number of real solutions is.
A system of five identical, non-interacting particles with mass \( m \) and spin \( \frac{3}{2} \) is confined to a one-dimensional potential well of length \( L \). If the lowest energy of the system is \[ E_{{min}} = \frac{N \pi^2 \hbar^2}{2m L^2}, \] the value of \( N \) (in integer) is:

In the transistor circuit shown in the figure, \( V_{BE} = 0.7 \, {V} \) and \( \beta_{DC} = 400 \). The value of the base current in \( \mu A \) (rounded off to one decimal place) is:


 

Cyclotrons are used to accelerate ions like deuterons (\( d \)) and \( \alpha \) particles. Keeping the magnetic field the same for both, \( d \) and \( \alpha \) are extracted with energies 10 MeV and 20 MeV with extraction radii \( r_d \) and \( r_\alpha \), respectively. Taking the masses \( M_d = 2000 \, {MeV}/c^2 \) and \( M_\alpha = 4000 \, {MeV}/c^2 \), the value of \( \frac{r_\alpha}{r_d} \) (in integer) is:
A linear magnetic material in the form of a cylinder of radius \( R \) and length \( L \) is placed with its axis parallel to the \( z \)-axis. The cylinder has uniform magnetization \( M \hat{k} \). Which of the following option(s) is/are correct?
A point charge \( q \) is placed at the origin, inside a linear dielectric medium of infinite extent, having relative permittivity \( \epsilon_r \). Which of the following option(s) is/are correct?
A neutral conducting sphere of radius \( R \) is placed in a uniform electric field of magnitude \( E_0 \), that points along the \( z \)-axis. The electrostatic potential at any point \( r \) outside the sphere is given by: \[ V(r, \theta) = V_0 - E_0 r \left(1 - \frac{R^3}{r^3} \right) \cos \theta \] where \( V_0 \) is the constant potential of the sphere. Which of the following option(s) is/are correct?