For the solution of the gases w, x, y and z in water at 298K, the Henrys law constants (K_H) are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is :-

Polysubstitution is a major drawback in:

If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $$\lambda $$, then for 1.5 p momentum of the photoelectron, the wavelength of the light should be: (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

Fructose and glucose can be distinguished by :

The major product obtained in the following reaction is

The correct statement about ICl₅ and $$ICl_4^-$$ is

Which of the following compounds will show the maximum 'enol' content?

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If C_V = 28 JK^–1mol^–1, calculate $$\Delta $$U and $$\Delta $$pV for this process. (R = 8.0 JK^–1 mol^–1]

The major product obtained in the following reaction is :

The statement that is INCORRECT about the interstitial compounds is :

For a reaction scheme $$A\buildrel {{k_1}} \over \longrightarrow B\buildrel {{k_2}} \over \longrightarrow C$$,

if the rate of formation of B is set to be zero then the concentration of B is given by :

The major product of the following reaction is:

Among the following molecules / ions, $$C_2^{2 - },N_2^{2 - },O_2^{2 - },{O_2}$$ which one is diamagnetic and has the shortest bond length?

The calculated spin-only magnetic moments (BM) of the anionic and cationic species of [Fe(H₂O)₆]₂ and [Fe(CN)₆], respectively, are :

Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product?

The covalent alkaline earth metal halide (X = Cl, Br, I) is :

The compound that inhibits the growth of tumors is :

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

The percentage composition of carbon by mole in methane is :

The major product of the following reaction is:

The ion that has sp³d² hybridization for the central atom, is :

For the following reactions, equilibrium constants are given :

S(s) + O₂(g) ⇋ SO₂(g); K₁ = 10⁵²

2S(s) + 3O₂(g) ⇋ 2SO₃(g); K₂ = 10¹²⁹

The equilibrium constant for the reaction,

2SO₂(g) + O₂(g) ⇋ 2SO₃(g) is :

The major product in the following reaction is :

Calculate the standard cell potential in (V) of the cell in which following reaction takes place :

Fe²⁺(aq) + Ag⁺(aq) $$ \to $$ Fe³⁺(aq) + Ag (s)

Given that

$$E_{A{g^ + }/Ag}^o = xV$$

$$E_{Fe^{2+ }/Fe}^o = yV$$

$$E_{Fe^{3+ }/Fe}^o = zV$$

Let $$\mathop a\limits^ \to = 3\mathop i\limits^ \wedge + 2\mathop j\limits^ \wedge + x\mathop k\limits^ \wedge $$ and $$\mathop b\limits^ \to = \mathop i\limits^ \wedge - \mathop j\limits^ \wedge + \mathop k\limits^ \wedge $$ , for some real x. Then $$\left| {\mathop a\limits^ \to \times \mathop b\limits^ \to } \right|$$ = r is possible if :

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$$\sqrt 3$$), then the length of its latus rectum is :

If $$z = {{\sqrt 3 } \over 2} + {i \over 2}\left( {i = \sqrt { - 1} } \right)$$,

then (1 + iz + z⁵ + iz⁸)⁹ is equal to :

Let $$f(x) = \int\limits_0^x {g(t)dt} $$ where g is a non-zero even function. If ƒ(x + 5) = g(x), then $$ \int\limits_0^x {f(t)dt} $$ equals-

If three distinct numbers a, b, c are in G.P. and the equations ax² + 2bx + c = 0 and dx² + 2ex + ƒ = 0 have a common root, then which one of the following statements is correct?

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 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 :

Let the number 2,b,c be in an A.P. and
A = $$\left[ {\matrix{ 1 & 1 & 1 \cr 2 & b & c \cr 4 & {{b^2}} & {{c^2}} \cr } } \right]$$. If det(A) $$ \in $$ [2, 16], then c lies in the interval :

Let ƒ : R $$ \to $$ R be a differentiable function satisfying ƒ'(3) + ƒ'(2) = 0.
Then $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + f(3 + x) - f(3)} \over {1 + f(2 - x) - f(2)}}} \right)^{{1 \over x}}}$$ is equal to

If the fourth term in the binomial expansion of
$${\left( {\sqrt {{x^{\left( {{1 \over {1 + {{\log }_{10}}x}}} \right)}}} + {x^{{1 \over {12}}}}} \right)^6}$$ is equal to 200, and x > 1, then the value of x is :

If ƒ(1) = 1, ƒ'(1) = 3, then the derivative of ƒ(ƒ(ƒ(x))) + (ƒ(x))² at x = 1 is :

Let S($$\alpha $$) = {(x, y) : y² $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ $$\alpha $$} and A($$\alpha $$) is area of the region S($$\alpha $$). If for a $$\lambda $$, 0 < $$\lambda $$ < 4, A($$\lambda $$) : A(4) = 2 : 5, then $$\lambda $$ equals

If the system of linear equations

x – 2y + kz = 1
2x + y + z = 2
3x – y – kz = 3

has a solution (x,y,z), z $$ \ne $$ 0, then (x,y) lies on the straight line whose equation is :

Let ƒ(x) = a^x (a > 0) be written as
ƒ(x) = ƒ₁ (x) + ƒ₂ (x), where ƒ₁ (x) is an even function of ƒ₂ (x) is an odd function.
Then ƒ₁ (x + y) + ƒ₁ (x – y) equals

A student scores the following marks in five tests :

45, 54, 41, 57, 43.

His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests 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 :

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 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 :

Let ƒ : [–1,3] $$ \to $$ R be defined as

$$f(x) = \left\{ {\matrix{ {\left| x \right| + \left[ x \right]} & , & { - 1 \le x < 1} \cr {x + \left| x \right|} & , & {1 \le x < 2} \cr {x + \left[ x \right]} & , & {2 \le x \le 3} \cr } } \right.$$

where [t] denotes the greatest integer less than or equal to t. Then, ƒ is discontinuous at:

Suppose that the points (h,k), (1,2) and (–3,4) lie on the line L₁ . If a line L₂ passing through the points (h,k) and (4,3) is perpendicular to L₁ , then $$k \over h$$ equals :

If $$\int {{{dx} \over {{x^3}{{(1 + {x^6})}^{2/3}}}} = xf(x){{(1 + {x^6})}^{{1 \over 3}}} + C} $$
where C is a constant of integration, then the function ƒ(x) is equal to

A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when :-

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

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)

Two very long, straight, and insulated wires are kept at 90° angle from each other in xy-plane as shown in the figure. These wires carry currents of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be :

A circuit connected to an ac source of emf e = e₀sin(100t) with t in seconds, gives a phase difference of $$\pi $$/4 between the emf e and current i. Which of the following circuits will exhibit this ?

The magnetic field of an electromagnetic wave is given by :-

$$\mathop B\limits^ \to = 1.6 \times {10^{ - 6}}\cos \left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\mathop i\limits^ \wedge + \mathop j\limits^ \wedge } \right){{Wb} \over {{m^2}}}$$

The associated electric field will be :-

In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :-

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 midpoint P, at angle q = 45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant ?
(d is much larger than the dimensions of the dipole)

Let $$\left| {\mathop {{A_1}}\limits^ \to } \right| = 3$$, $$\left| {\mathop {{A_2}}\limits^ \to } \right| = 5$$ and $$\left| {\mathop {{A_1}}\limits^ \to + \mathop {{A_2}}\limits^ \to } \right| = 5$$. The value of $$\left( {2\mathop {{A_1}}\limits^ \to + 3\mathop {{A_2}}\limits^ \to } \right)\left( {3\mathop {{A_1}}\limits^ \to - \mathop {2{A_2}}\limits^ \to } \right)$$ is :-

A nucleus A, with a finite de-broglie wavelength $$\lambda $$_A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths $$\lambda $$_B and $$\lambda $$_C of B and C are respectively :

A body of mass m₁ moving with an unknown velocity of $${v_1}\mathop i\limits^ \wedge $$, undergoes a collinear collision with a body of mass m₂ moving with a velocity $${v_2}\mathop i\limits^ \wedge $$ . After collision, m₁ and m₂ move with velocities of $${v_3}\mathop i\limits^ \wedge $$ and $${v_4}\mathop i\limits^ \wedge $$ , respectively. If m₂ = 0.5 m₁ and v₃ = 0.5 v₁, then v₁ is :-

In the figure shown, what is the current (in Ampere) drawn from the battery ?
You are given: R₁ = 15$$\Omega $$, R₂ = 10 $$\Omega $$, R₃ = 20 $$\Omega $$, R₄ = 5$$\Omega $$, R₅ = 25$$\Omega $$, R₆ = 30 $$\Omega $$, E = 15 V

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be :-

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

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to :
[Boltzmann Constant k_B = 1.38 × 10^–23 J/K Avogadro Number N_A = 6.02 × 10²⁶ /kg Radius of Earth : 6.4 × 10⁶ m Gravitational acceleration on Earth = 10ms^–2]

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

A parallel plate capacitor has 1μF capacitance. One of its two plates is given +2μC charge and the other plate, +4μC charge. The potential difference developed across the capacitor is:-

The electric field in a region is given by $$\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge $$ , where E is in NC^–1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V₁ and that at x = –5 is V₂, then V₁ – V₂ is :-

A positive point charge is released from rest at a distance r₀ from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :-

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by :-

A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights h_sph and h_cyl on the incline. The ratio h_sph/h_cyl is given by :-

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

The ratio of mass densities of nuclei of ⁴⁰Ca and ¹⁶O is close to :-

Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star :-