The major product of the following reaction is :

The major product of the following reaction is :
$${\rm{C}}{{\rm{H}}_3}{\rm{CH = CHC}}{{\rm{O}}_2}{\rm{CH_3 }}\buildrel {LiAl{H_4}} \over \longrightarrow $$

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is :

The major product of the following reaction is :

The standard Gibbs energy for the given cell reaction in kJ mol^–1 at 298 K is :

Zn(s) + Cu²⁺ (aq) $$ \to $$ Zn²⁺ (aq) + Cu (s),

E° = 2 V at 298 K

(Faraday's constant, F = 96000 C mol^–1)

Among the following, the set of parameters that represents path function, is :
(A) q + w
(B) q
(C) w
(D) H–TS

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M BaCl₂ in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of XY (in mol L^–1) in solution is :

The correct IUPAC name of the following compound is :

The given plots represent the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are :

For a reaction,
N₂(g) + 3H₂(g) $$ \to $$ 2NH₃(g) ;
identify dihydrogen (H₂) as a limiting reagent in the following reaction mixtures.

The one that will show optical activity is :
(en = ethane-1,2-diamine)

Among the following, the molecule expected to be stabilized by anion formation is :
C₂, O₂, NO, F₂

Which of the following statements is not true about sucrose?

The organic compound that gives following qualitative analysis is :

	Test	Inference
(a)	Dil. HCl	Insoluble
(b)	NaOH solution	soluble
(c)	Br2/water	Decolourization

The major product of the following reaction is :

The degenerate orbitals of [Cr(H₂O)₆]³⁺ are :

The correct order of the oxidation states of nitrogen in NO, N₂O, NO₂ and N₂O₃ is :

The major product of the following reaction is :

For any given series of spectral lines of atomic hydrogen, let $$\Delta \mathop v\limits^\_ = $$ $$\Delta {\overline v _{\max }} - \Delta {\overline v _{\min }}$$ be the difference in maximum and minimum frequencies in cm^–1. The ratio Lyman Balmer $${{\Delta {{\overline v }_{Lyman}}} \over {\Delta {{\overline v }_{Balmer}}}}$$ is :

The element having greatest difference between its first and second ionization energies, is :

Aniline dissolved in dilute HCl is reacted with sodium nitrite at 0ºC. This solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is

Liquid 'M' and liquid 'N' form an ideal solution. The vapour pressures of pure liquids 'M' and 'N' are 450 and 700 mmHg, respectively, at the same temperature. Then correct statement is:
(x_M = Mole fraction of 'M' in solution ;
x_N = Mole fraction of 'N' in solution ;
y_M = Mole fraction of 'M' in vapour phase ;
y_N = Mole fraction of 'N' in vapour phase)

If the standard deviation of the numbers –1, 0, 1, k is $$\sqrt 5$$ where k > 0, then k is equal to

Let p, q $$ \in $$ R. If 2 - $$\sqrt 3$$ is a root of the quadratic equation, x² + px + q = 0, then :

Let ƒ(x) = 15 – |x – 10|; x $$ \in $$ R. Then the set of all values of x, at which the function, g(x) = ƒ(ƒ(x)) is not differentiable, is :

If ƒ(x) is a non-zero polynomial of degree four, having local extreme points at x = –1, 0, 1; then the set
S = {x $$ \in $$ R : ƒ(x) = ƒ(0)}
Contains exactly :

The value of $$\int\limits_0^{\pi /2} {{{{{\sin }^3}x} \over {\sin x + \cos x}}dx} $$ is

Let $$\overrightarrow \alpha = 3\widehat i + \widehat j$$ and $$\overrightarrow \beta = 2\widehat i - \widehat j + 3 \widehat k$$ . If $$\overrightarrow \beta = {\overrightarrow \beta _1} - \overrightarrow {{\beta _2}} $$, where $${\overrightarrow \beta _1}$$ is parallel to $$\overrightarrow \alpha $$ and $$\overrightarrow {{\beta _2}} $$ is perpendicular to $$\overrightarrow \alpha $$ , then $${\overrightarrow \beta _1} \times \overrightarrow {{\beta _2}} $$ is equal to

All the points in the set
$$S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )$$ lie on a :

If $$\left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]$$$$\left[ {\matrix{ 1 & 3 \cr 0 & 1 \cr } } \right]$$....$$\left[ {\matrix{ 1 & {n - 1} \cr 0 & 1 \cr } } \right] = \left[ {\matrix{ 1 & {78} \cr 0 & 1 \cr } } \right]$$,

then the inverse of $$\left[ {\matrix{ 1 & n \cr 0 & 1 \cr } } \right]$$ is

If the function ƒ : R – {1, –1} $$ \to $$ A defined by
ƒ(x) = $${{{x^2}} \over {1 - {x^2}}}$$ , is surjective, then A is equal to

If one end of a focal chord of the parabola, y² = 16x is at (1, 4), then the length of this focal chord is :

If the function ƒ defined on , $$\left( {{\pi \over 6},{\pi \over 3}} \right)$$ by $$$f(x) = \left\{ {\matrix{ {{{\sqrt 2 {\mathop{\rm cosx}\nolimits} - 1} \over {\cot x - 1}},} & {x \ne {\pi \over 4}} \cr {k,} & {x = {\pi \over 4}} \cr } } \right.$$$ is continuous, then k is equal to

The value of cos²10° – cos10°cos50° + cos²50° is

Let $$\sum\limits_{k = 1}^{10} {f(a + k) = 16\left( {{2^{10}} - 1} \right)} $$ where the function ƒ satisfies
ƒ(x + y) = ƒ(x)ƒ(y) for all natural numbers x, y and ƒ(1) = 2. then the natural number 'a' is

Four persons can hit a target correctly with probabilities $${1 \over 2}$$, $${1 \over 3}$$, $${1 \over 4}$$ and $${1 \over 8}$$ respectively. if all hit at the target independently, then the probability that the target would be hit, is :

Let $$\alpha $$ and $$\beta $$ be the roots of the equation x² + x + 1 = 0. Then for y $$ \ne $$ 0 in R,
$$$\left| {\matrix{ {y + 1} & \alpha & \beta \cr \alpha & {y + \beta } & 1 \cr \beta & 1 & {y + \alpha } \cr } } \right|$$$ is equal to

The area (in sq. units) of the region

A = {(x, y) : x² $$ \le $$ y $$ \le $$ x + 2} is

Let the sum of the first n terms of a non-constant A.P., a₁, a₂, a₃, ..... be $$50n + {{n(n - 7)} \over 2}A$$, where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a₅₀) is equal to

The integral $$\int {{\rm{se}}{{\rm{c}}^{{\rm{2/ 3}}}}\,{\rm{x }}\,{\rm{cose}}{{\rm{c}}^{{\rm{4 / 3}}}}{\rm{x \,dx}}} $$ is equal to (Hence C is a constant of integration)

The solution of the differential equation

$$x{{dy} \over {dx}} + 2y$$ = x² (x $$ \ne $$ 0) with y(1) = 1, is :

If the fourth term in the binomial expansion of $${\left( {{2 \over x} + {x^{{{\log }_8}x}}} \right)^6}$$ (x > 0) is 20 × 8⁷, then a value of x is :

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :

Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is :

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is :

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :

A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock-wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is :

If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is :

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be :

The magnetic field of a plane electromagnetic wave is given by :
$$$\overline B = {B_0}\widehat i\left[ {\cos (kz - \omega t)} \right] + {B_i}\widehat j\cos (kz + \omega t)$$$ B₀ = 3 × 10^–5 T and B1 = 2 × 10^–6 T.
The rms value of the force experienced by a stationary charge Q = 10^–4 C at z = 0 is closest to :

A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its (1/n)^th part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be :

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $$\theta $$, where $$\theta $$ is the angle by which it has rotated, is given as k$$\theta $$². If its moment of inertia is I then the angular acceleration of the disc is :

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y = 0.3 sin(0.157x) cos(200pt). The length of the string is : (All quantities are in SI units.)

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane. : (i) a ring of radius R, (ii) a solid cylinder of radius R/2 and (iii) a solid sphere of radius R/4 . If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is :

A rigid square loop of side 'a' and carrying current I₂ is lying on a horizontal surface near a long current I₁ carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be :

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index μ is put in front of one of the slits, the central maximum gest shifted by a distance equal to n fringe widths. If the wavelength of light used is $$\lambda $$, t will be :

A capacitor with capacitance 5μF is charged to 5μC. If the plates are pulled apart to reduce the capacitance to 2μF, how much work is done ?

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is :

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

The electric field of light wave is given as $$$\overrightarrow E = {10^{ - 3}}\cos \left( {{{2\pi x} \over {5 \times {{10}^{ - 7}}}} - 2\pi \times 6 \times {{10}^{14}}t} \right)\mathop x\limits^ \wedge {{\rm N} \over C}$$$ This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is :
Given, E (in eV) = 12375/$$\lambda $$(inÅ)

A moving coil galvanometer has resistance 50$$\Omega $$ and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a 5 k$$\Omega $$ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to :

The pressure wave, P = 0.01 sin [1000t – 3x] Nm^–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms^–1 . Approximate value of T is

A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be :

The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?

A system of three charges are placed as shown in the figure :

If D >> d, the potential energy of the system is best given by :

Determine the charge on the capacitor in the following circuit :

A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body ?

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :

Following figure shows two processes A and B for a gas. If $$\Delta $$Q_A and $$\Delta $$Q_B are the amount of heat absorbed by the system in two cases, and $$\Delta $$U_A and $$\Delta $$U_B are changes in internal energies, respectively, then :

A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is : (E is mid-point of arm CD)

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $$\overline v $$ , m is its mass and k_B is Boltzmann constant, then its temperature will be :

In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is :