Question Paper (Section wise)

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing through their mid-point P, at angle θ = 45° with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimension of the dipole).

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x – axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time).

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity form the earth is closest to:

[Boltzman’s Constant k_B = 1.38 × 10^-23 J/k

Avogadro number N˄ = 6.02 × 10^{26 /} kg

Radius of Earth: 6.4 × 10⁶ m

Gravitation acceleration on Earth = 10 ms²]

A common emitter amplifier circuit, built using an npn transistor, is shown in the figure. Its dc current gain is 250, R_c = 1kΩ and V_cc = 10V. What is the minimum base current for V_CE to reach saturation?

The ratio of mass densities of nuclei of ⁴⁰C_a and ¹⁶O is closed to:

A rectangle solid box of length 0.3 m is held horizontally, with one of its sided on the edge of a platform of height 5. When released, it slips off the table in a very short time =0.01 s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

A body of mass m₁ moving with an unknown velocity of  undergoes a collinear collision with a body of mass m₂ moving with a velocity  After collision m₁ and m₂ move with velocities of  and  respectively.

An electric dipole is formed by two equal and opposite charges q with separation d. The charges the same mass m. It is kept in a uniform electric field E. If it slightly rotated from its equilibrium orientation, then its angular frequency ω is:

The magnetic field of an electromagnetic wave is given by: 

The associated electric field will be:

In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70m, then the minimum height of the transmitting antenna should be: (Radius of the Earth = 6.4 × 10⁶m).

The Mond process is used for the:

The covalent alkaline earth metal halide

(X = Cl, Br, l) is:

The major product obtained in the following reactions is

For the following reactions, equilibrium constant are given:

The equilibrium constant for the reaction

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temprature becomes 200 K. If C_v = 28 JK^-1 mol^-1, calculate ΔU and ΔpV for this process. ( R = 8.0 J K^-1 mol^-1 )

Which of the following compounds will show the maximum ‘enol’ content?

The IUPAC symbol for the element with atomic number 119 would be:

0.27 g of a long chain fatty acid was dissolved in 100 cm³ of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. What is the height of the monolayer?

The calculated spin only magnetic moments (BM) of the anionic and cationic species of  and , respectively, are:

The major product in the following reaction is:

Let f : [ -1, 3 ] → R is defined as

Where [t] denotes the greatest integer less than or equal to t. Then f is discontinuous at:

If a point R( 4, y, z ) lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10), then the distance of R from the origin is:

The number of four – digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is:

The number of integral values of m for which the equation

( 1 + m² ) x² – 2 ( 1 + 3m ) x + ( 1 + 8m ) = 0 has no real root is:

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0, 5), then the length of its latus rectum is:

The vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0 is:

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is:

If the eccentricity of the standard hyperbola passing through the point (4, 6) is 2, then the equation of the tangent to the hyperbola at (4, 6) is:

The tangent to the parabola y² = 4x at the point where it intersects the circle x² + y² = 5 in the first quadrant, passes through the point: