
(I) At pH = 2
(highly acidic), the structure of the peptide will be as shown below.
Net charge +2
|Z1| = 2 at pH = 2
(ii) At pH = 6 (neutral solution)
In neutral medium, the given tripeptide exists as Zwitter ion.
net charge = 0
|Z2| = 0 at pH = 6
(iii)At pH = 11 (basic medium)
In basic medium the given tripeptide exists in anionic form.
Net charge = β3
So, |Z3| = |-3|
|Z1| + |Z2| + |Z3| = 2 + 0 + 3 = 5
Fat soluble vitamins are :
A. Vitamin B\( _1 \)
B. Vitamin C
C. Vitamin E
D. Vitamin B\( _{12} \)
E. Vitamin K
Choose the correct answer from the options given below :
The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____. 
Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hookeβs law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 