Question Paper (Section wise)

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms^-1, at right angles to the horizontal component of the earth’s magnetic of field,

0.3 × 10^-4 Wb/m². The value of the induced emf in wire is:

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is l₁, and that below the piston is l₂, such that l₁ > l₂. Each part of the cylinder contains n moles of an ideal gas at equal temperature. T.

(R is universal gas constant and g is the acceleration due to gravity)

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 10³ kg/m³ and its Young’s modulus is 9.27 × 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

In a radioactive decay chain, the initial nucleus is . At the end there are 6 α- particles and 4β – particles with are emitted. If the end nucleus is , A and Z are given by:

Let l, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of  in SI units will be:

A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × 10^-4 A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of:

A paramagnetic material has 10²⁸ atmos/m³. Its magnetic susceptibility at temperature 350 K is 2.8 × 10^-4. Its susceptibility at 300 K is:

In the given circuit diagram, the currents, I₁ = -0.3 A, I₄ = 0.8 A and I₅ = 0.4 A, are flowing as shown. The currents I₂, I₃ and I₆, respectively are:

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. the coefficient of static friction between the block and the plane is:

[Take g = 10 m / s²]

Among the following, the false statement is:

An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is:

The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are:

i. They activate many enzymes

ii. They participate in the oxidation of glucose to produce ATP.

iii. Along with sodium ions, they are responsible for the transmission of nerve signals

The major product of the following reaction is:

The two monomers for the synthesis Nylon 6, 6 are:

The volume strength of 1M H₂O₂ is: (Molar mass of H₂O₂ = 34 g mol^–1)

Given:

C_(graphite) + O_2(g) → CO_2(g); ∆rH°= x kJ mol^-1

C_(graphite) +  O_2(g)  → CO_(g); ∆rH° = y kJ mol^-1

CO_(g) +  O_2(g)  → CO_2(g); ∆rH°= z kJ mol^-1

Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?

The aldehydes which will not form Grignard product with one equivalent Grignard reagents are:

The element that shows greater ability to form pπ - pπ multiple bonds, is:

The major product in the following conversion is:

If an angle between the line,  and the plane, x - 2y – kz = 3 is  then a value of k is:

If a straight line passing through the point P(-3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is:

The tangent to the curve y = x² - 5x + 5, parallel to line 2y = 4x + 1, also passes through the point:

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then probability that the student has opted neither for NCC nor for NSS is:

The set of all values of λ for which the system of linear equations

x – 2y – 2z =λx

x + 2y + z = λy

–x – y = λz,

has a non-trivial solution :

If the function f given by f(x) = x³ - 3(a - 2)x² + 3ax + 7, for some a ϵ R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation,  is:

The equation of a tangent to the parabola, x² = 8y, which makes an angle 𝛳 with the positive direction of X-axis, is:

If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is:

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is:

Let S be the set of all real values of λ such that a plane passing through the points (-λ², 1, 1), (1, - λ², 1) and (1, 1, - λ²) also passes through the point (-1, -1, 1). Then S is equal to: