The electric field inside a uniformly charged spherical shell of radius R is:

• (A) directly proportional to the charge within the shell
• (B) inversely proportional to \( R^{2} \)
• (C) same as that outside the shell
• (D) zero
• (E) maximum at the centre

The distance between two charges \( q_1 = +2\mu \)C and \( q_2 = +8\mu \)C is 15 cm. Calculate the distance from the charge \( q_1 \) to the points on the line segment joining the two charges where the electric field is zero.

• (A) 1 cm
• (B) 2 cm
• (C) 3 cm
• (D) 4 cm
• (E) 5 cm

Three point charges 4q, Q, and q are placed in a straight line of length L at points 0, L/2, and L respectively. The net force on charge q is zero. The value of Q is:

• (A) 4q
• (B) −q
• (C) −0.5q
• (D) −2q
• (E) 3q

A galvanometer of resistance 100 Ω gives a full scale deflection for a current of 1 mA through it. The resistance required to convert it into a voltmeter which can read up to 2 V is:

• (A) 1175 Ω
• (B) 1200 Ω
• (C) 1525 Ω
• (D) 1900 Ω
• (E) 2025 Ω

The magnetic force acting on a charged particle carrying a charge of \( 3\mu \)C in a magnetic field of 5 T acting in the y-direction, when the particle velocity is \( (\hat{i} + \hat{j}) \times 10^{5} \) ms⁻¹, is:

• (A) 0.5 N in +x direction
• (B) 0.2 N in +y direction
• (C) 2 N in −x direction
• (D) 1.5 N in +z direction
• (E) 1 N in +z direction

Which of the following compounds has the highest boiling point?

• (A) n-Butane
• (B) Propan-1-ol
• (C) Methoxy methane
• (D) Propanal
• (E) Acetone

The major product obtained in the dehydration of ethanol in the presence of H\(_2\)SO\(_4\) at 413 K is:

• (A) Ethanoic acid
• (B) Ethanal
• (C) Ethyne
• (D) Ethane
• (E) Ethoxyethane

Compound ’A’ is obtained by the reaction of benzyl chloride with magnesium metal in dry ether followed by treatment with water. What is the compound ’A’?

• (A) Toluene
• (B) Benzyl alcohol
• (C) Phenol
• (D) Benzene
• (E) Benzaldehyde

The products obtained by the ozonolysis of 2-methylbut-1-ene are:

• (A) Propanone and ethanal
• (B) Propanone and methanal
• (C) Butanone and methanal
• (D) Ethanal and propanal
• (E) Butanone and methanol

On heating an aldehyde with Fehling’s reagent, a reddish-brown precipitate is obtained due to the formation of:

• (A) Cupric oxide
• (B) Cuprous oxide
• (C) Carboxylic acid
• (D) Silver
• (E) Copper acetate

The 25th term of 9, 3, 1, \( \frac{1}{3} \), \( \frac{1}{9} \), ... is:

• (A) \( \frac{1}{3^{24}} \)
• (B) \( \frac{1}{3^{25}} \)
• (C) \( \frac{1}{3^{23}} \)
• (D) \( \frac{1}{3^{22}} \)
• (E) \( \frac{1}{3^{26}} \)

Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:

• (A) 360
• (B) 240
• (C) 120
• (D) 480
• (E) 520

Let U be the universal set and let A and B be any two subsets of U. If n(U) = 25, n(A) = 14, n(A\(\cap\)B) = 6 and n(A\(\cup\)B) = 20, then n(B′) is equal to:

• (A) 12
• (B) 13
• (C) 14
• (D) 15
• (E) 16

A straight line passing through (6,1,3) meets the line \( \frac{x-1}{2} = \frac{y}{1} = \frac{z-2}{3} \) at Q. If the lines are perpendicular to each other, then the coordinates of Q are:

• (A) (2, 1, 3)
• (B) (1, 2, 3)
• (C) (3, 1, 5)
• (D) (2, -1, 3)
• (E) (-1, 2, 3)

The three vertices of a triangle are (0,0), (3,1) and (1,3). If this triangle is inscribed in a circle, then the equation of the circle is:

• (A) \( 2x^{2} + 2y^{2} - 2x - 6y = 0 \)
• (B) \( x^{2} + y^{2} - 3x - y = 0 \)
• (C) \( x^{2} + y^{2} - x - 3y = 0 \)
• (D) \( 2x^{2} + 2y^{2} - 6x - 2y = 0 \)
• (E) \( 2x^{2} + 2y^{2} - 5x - 5y = 0 \)