**Physics:**

The diameter of a cylinder is measured using Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

(A) 5.112 cm (B) 5.124 cm

(C) 5.136 cm (D) 5.148 cm**Ans. (B)**

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is:

(A) 1 : 4 (B) 1 : 2

(C) 6 : 9 (D) 8 : 9**Ans. (D)**

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is:

(A) 1 m (B) 2 m

(C) 3 m (D) 4

**Ans. (C)**

**Chemistry:**

Concentrated nitric acid, upon long standing, turns yellow–brown due to the formation of:

(A) NO (B) NO2

(C) N2O (D) N2O4**Ans. (B)**

A tetrapeptide has – COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with – NH2 group attached to a chiral center is**Ans. (4)**

**Mathematics:**

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

(A) 24 (B) 32

(C) 45 (D) 60**Ans. (A, C)**

A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k-20 = _________**Ans. (5)**