List of practice Questions

Let \( \mathbb{N} \) be the set of natural numbers and \( f : \mathbb{N} \to \mathbb{N} \) be defined by 

Let \( f^n(x) \) denote the \( n \)-fold composition of \( f(x) \). What is the smallest integer \( n \) such that \( f^n(13) = 1 \)? 
 

The characteristic oxygen binding profile of hemoglobin shown below arises due to the ......... 

H\(_2\) reacts with trans-(Ph\(_3\))\(_2\)Ir(CO)Cl to primarily produce .......... 

Match the entries in Group I with entries in Group II 

The following reaction is an example of ............ 

Match the entries in Group I with the entries in Group II 

Which one of the following figures represents the correct sequence of phases in adult eukaryotic cell cycle? 

Two identical, infinite conducting plates are kept parallel to each other and are separated by a distance \( d \). The uniform charge densities on the plates are \( +\sigma \) and \( -\sigma \). The electric field at a point between the two plates is \( E = n \left( \frac{\sigma}{\epsilon_0} \right) \), where \( n \) is ........
The concentration of NaCl (in mM) formed at the stoichiometric equivalence point when 10 mL of 0.1 M HCl solution is titrated with 0.2 M NaOH solution is ............
An infinitely long solenoid of radius \( r \) and number of turns per unit length \( n \) carries a steady current \( I \). The ratio of the magnetic fields at a point on the axis of the solenoid to a point \( r/2 \) from the axis is ..............
The total number of multiplet peaks in the \( ^1 \)H NMR spectrum of 1,3,5-tri-isopropylbenzene in CDCl\(_3\) is ..........
The value of \( \int_0^\pi x \sin x \, dx \) is .......
Phosphoglucoisomerase catalyzes the following reaction: \[ \text{Glu-6-P} \rightleftharpoons \text{Fru-6-P} \] If 0.05% of the original concentration of Glu-6-P remains at equilibrium, then the equilibrium constant of this reaction is ............
In a bacterium, a mutation resulted in an increase of \( K_s \) (substrate-specific constant) for ammonium from 50 \( \mu M \) to 5000 \( \mu M \) without affecting \( \mu_{max} \). The specific growth rate (\( \mu \)) of the mutant growing on 0.5 mM ammonium in the medium decreases by a factor of ..........
The total number of DNA molecules present after 5 cycles of polymerase chain reaction (PCR) starting with 3 molecules of template DNA is .................
Proinsulin is an 84 residue polypeptide with six cysteines. How many different disulfide combinations are possible?
The refractive index of a liquid relative to air is 1.5. Calculate the ratio of the real depth to the apparent depth when the liquid is taken in a beaker.
A metallic wire of electrical resistance 40 \( \Omega \) is bent in the form of a square loop. The resistance between any two diagonally opposite corners is ....... \( \Omega \).
The total number of lone pairs of electrons in NO\(_2\)F is ............
C\(_3\) plants utilize 18 molecules of ATP to synthesize one molecule of glucose from CO\(_2\). How many molecules of ATP equivalents are used by C\(_4\) plants to synthesize one molecule of glucose from CO\(_2\)?
A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. What fraction of light is transmitted if the concentration is increased to 0.4%? [Correct to two decimal places]
Let XYZ be an equilateral triangle and let P, Q, R be the midpoints of YZ, XZ, and XY, respectively.
Let \( r = \frac{\text{Area of } \Delta PQR}{\text{Area of } \Delta XYZ} \).
Which of the following statement(s) is/are true?
BF\(_3\) reacts readily with ...........
The reaction of \( (R)-2-bromobutane \) with CN\(^-\) proceeds by ..........