The major product of the following reaction is :

The correct match between Item-I and Item-II is :

Item-I (drug)		Item-II (test)
A	Chloroxylenol	P	Carbylamine test
B	Norethindrone	Q	Sodium hydrogen carbonet test
C	Sulphapyridine	R	Ferric chloride test
D	Penicillin	S	Bayer's test

The major product of following reaction is :

The compounds A and B in the following reaction are, respectively :

The correct decreasing order for acid strength is :

Arrange the following amines in the decreasing order of basicity :

Which amongst the following is the strongest acid ?

The major product of the following reaction is :

The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of PbSO₄ electrolyzed in g during the process is : (Molar mass of PbSO₄ = 303 g mol^$$-$$1)

The one that is extensively used as a piezoelectric material is :

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T₁ and T₂ (T₁ < T₂). The correct graphical depiction of the dependence of work done (w) on the final volume (V) is :

A solution of sodium sulphate contains 92 g of Na⁺ ions per kilogram of water. The molality of Na⁺ ions in that solution in mol kg^$$-$$1 is :

The following results were obtained during kinetic studies of the reaction ;

2A + B $$ \to $$ Products

Experiment	[A] (in mol L$$-$$1)	[b] (in mol L$$-$$1)	Initial Rate of reaction (In mol L$$-$$1 min$$-$$1)
I	0.10	0.20	6.93 G 10$$-$$3
II	0.10	0.25	6.93 G 10$$-$$3
III	0.20	0.30	1.386 G 10$$-$$2

The time (in minutes) required to consume half of A is :

Two complexes [Cr(H₂O)₆]Cl₃ (A) and [Cr(NH₃)₆]Cl₃ (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is :

For emission line of atomic hydrogen from n_i = 8 to n_f = n, the plot of wave number $$\left( {\overline v } \right)$$ against $$\left( {{1 \over {{n^2}}}} \right)$$ will be (The Rydberg constant, R_H is in wave number unit)

Which one of the following statements regarding Henry's law is not correct ?

20 mL of 0.1 M H₂SO₄ solution is added to 30 mL of of 0.2 M NH₄OH solution. The pH of the resultant mixture is : [pk_b of NH₄OH = 4.7].

According to molecular orbital theory, which of the following is true with respect to Li₂⁺ and Li₂^$$-$$ ?

Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in + 1 and + 3 oxidation states. This is due to :

In general, the properties that decrease and increase down a group in the periodic table, respectively, are :

The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is :

The increasing order of pka of the following amino acids in aqueous solution is :

Gly, Asp, Lys, Arg

Let $${a_1},{a_2},.......,{a_{30}}$$ be an A.P.,

$$S = \sum\limits_{i = 1}^{30} {{a_i}} $$ and $$T = \sum\limits_{i = 1}^{15} {{a_{\left( {2i - 1} \right)}}} $$.

If $$a_5$$ = 27 and S - 2T = 75, then $$a_{10}$$ is equal to :

If $$A = \left[ {\matrix{ {\cos \theta } & { - \sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right]$$, then the matrix A^–50 when $$\theta $$ = $$\pi \over 12$$, is equal to :

For any $$\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$$, the expression

$$3{(\cos \theta - \sin \theta )^4}$$$$ + 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta $$

equals :

The system of linear equations
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a² – 1) z = a + 1 then

The maximum volume (in cu.m) of the right circular cone having slant height 3 m is :

If $${\cos ^{ - 1}}\left( {{2 \over {3x}}} \right) + {\cos ^{ - 1}}\left( {{3 \over {4x}}} \right) = {\pi \over 2}$$ (x > $$3 \over 4$$), then x is equal to :

Let $$0 < \theta < {\pi \over 2}$$. If the eccentricity of the

hyperbola $${{{x^2}} \over {{{\cos }^2}\theta }} - {{{y^2}} \over {{{\sin }^2}\theta }}$$ = 1 is greater

than 2, then the length of its latus rectum lies in the interval :

If y = y(x) is the solution of the differential equation,

x$$dy \over dx$$ + 2y = x², satisfying y(1) = 1, then y($$1\over2$$) is equal to :

Let
A = $$\left\{ {\theta \in \left( { - {\pi \over 2},\pi } \right):{{3 + 2i\sin \theta } \over {1 - 2i\sin \theta }}is\,purely\,imaginary} \right\}$$
. Then the sum of the elements in A is :

For $$x \in R - \left\{ {0,1} \right\}$$, Let f₁(x) = $$1\over x$$, f₂ (x) = 1 – x

and f₃ (x) = $$1 \over {1 - x}$$ be three given

functions. If a function, J(x) satisfies

(f₂ o J o f₁) (x) = f₃ (x) then J(x) is equal to :

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

$$\mathop {\lim }\limits_{y \to 0} {{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 } \over {{y^4}}}$$

If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be

5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is :

If the fractional part of the number $$\left\{ {{{{2^{403}}} \over {15}}} \right\} is \, {k \over {15}}$$, then k is equal to :

Let f : R $$ \to $$ R be a function defined as
$$f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} & ; & {1 < x < 3} \cr {b + 5x} & ; & {3 \le x < 5} \cr {30} & ; & {x \ge 5} \cr } } \right.$$

Then, f is

For x² $$ \ne $$ n$$\pi $$ + 1, n $$ \in $$ N (the set of natural numbers), the integral

$$\int {x\sqrt {{{2\sin ({x^2} - 1) - \sin 2({x^2} - 1)} \over {2\sin ({x^2} - 1) + \sin 2({x^2} - 1)}}} dx} $$ is equal to :

(where c is a constant of integration)

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is :

Let $$\alpha $$ and $$\beta $$ be two roots of the equation x² + 2x + 2 = 0 , then $$\alpha ^{15}$$ + $$\beta ^{15}$$ is equal to :

The value of $$\int\limits_0^\pi {{{\left| {\cos x} \right|}^3}} \,dx$$ is :

The area (in sq. units) bounded by the parabolae y = x² – 1, the tangent at the point (2, 3) to it and the y-axis is :

If $$\theta $$ denotes the acute angle between the curves, y = 10 – x² and y = 2 + x² at a point of their intersection, the |tan $$\theta $$| is equal to :

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 10¹⁹ m^$$-$$3 and their mobility is 1.6 m²/(V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to :

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The corecivity of the bar magnet is :

Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm², is $$\upsilon $$. If the electron density in copper is 9 $$ \times $$ 10²⁸/m³ the value of $$\upsilon $$. in mm/s is close to (Take charge of electron to be = 1.6 $$ \times $$ 10^$$-$$19C)

A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d < < a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is :

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $$\alpha $$/^oC. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $$\Delta $$TK. Young's modulus, Y, for this metal is :

A gas can be taken from A to B via two different processes ACB and ADB.


When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is :

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, $$\overrightarrow E = 6.3\widehat j\,V/m.$$ The corresponding magnetic field $$\overrightarrow {B,} $$ at that point will be :

A particle is moving with a velocity

$$\overrightarrow v \, = K(y\widehat i + x\widehat j),$$ where K is a constant.

The general equation for its path is :

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is given an initial speed $$\upsilon $$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically $${5 \over 6}$$th of the initial kinetic energy is lost in whole process. What is value of M/m ?

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop a applies a force F on the wire then :

Two masses m and $${m \over 2}$$ are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k, at the centre of mass of the rod-mass system(see figure). Because of torsional constant k, the restoring torque is $$\tau $$ = k$$\theta $$ for angular displacement $$\theta $$. If the rod is rotated by $$\theta $$₀ and released, the tension in it when it passes through its mean position will be :

A conducting circular loop made of a thin wire, has area 3.5 $$ \times $$ 10^$$-$$3 m² and resistance 10 $$\Omega $$. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50$$\pi $$t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to :

A block of mass m, lying on a smooth horizontal surface, is attached to a sring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is :

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $$\mu $$. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $$\mu $$ is :

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms^$$-$$1. When the car has acceleration a, the wave-speed increases to 60.5 ms^$$-$$1. The value of a, in terms of gravitational acceleration g, is closest to :

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :

Surface of certain metal is first illuminated with light of wavelength $$\lambda $$₁ = 350 nm and then, by light of wavelength $$\lambda $$₂ = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to :

(Energy of photon n = $${{1240} \over {\lambda (in\,mm)}}$$eV)

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is $$\theta $$, thrown :

Temperature difference of 120^oC is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length $${{3L} \over 2},$$ is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to :

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio :

When the switch S, in the circuit shown, is closed, then the value of current i will be :

Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms^$$-$$2)

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is :

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $$\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$$ is close to :