A sample of MgCO₃ is dissolved in dil. HCl and the solution is neutralized with ammonia and buffered with NH₄Cl / NH₄OH. Disodium hydrogen phosphate reagent is added to the resulting solution. A white precipitate is formed. What is the formula of the precipitate?

XeF₂, NO₂, HCN, ClO₂, CO₂.

Identify the non-linear molecule-pair from the above mentioned molecules.

The number of atoms in body centred and face centred cubic unit cell respectively are

The number of unpaired electron in Mn²⁺ ion is

The average speed of H₂ at T₁K is equal to that of O₂ at T₂K. The ratio T₁ : T₂ is

Sodium nitroprusside is :

Choose the correct statement for the [Ni(CN)₄]^2$$-$$ complex ion (Atomic no. of Ni = 28)

The boiling point of the water is higher than liquid HF. The reason is that

The metal-pair that can produce nascent hydrogen in alkaline medium is :

The correct bond order of B-F bond in BF₃ molecule is :

Which of the following is radioactive?

The correct order of acidity of the following hydra acids is

To a solution of colourless sodium salt, a solution of lead nitrate was added to have a white precipitate which dissolves in warm water and reprecipitates on cooling. Which of the following acid radical is present in the salt?

Oxidation states of Cr in K₂Cr₂O₇ and CrO₅ are respectively

The correct order of relative stability for the given free radicals is :

Hybridisation of the negative carbons in (1) and (2) are

The correct relationship between molecules I and II is

The enol form in which ethyle-3-oxobutanoate exists is

How many monobriminated product(s) (including stereoisomers) would form in the free radical bromination of n-butane?

What is the correct order of acidity of salicylic acid, 4-hydroxybenzoic acid, and 2, 6-dihydroxybenzoic acid ?

How much solid oxalic acid (Molecular weight 126) has to be weighed to prepare 100 ml. exactly 0.1 (N) oxalic acid solution in water?

The major product of the following reaction is

$${F_3}C - CH = C{H_2} + HBr \to $$

The correct order of relative stability of the given conformers of n-butane is

$${C_6}{H_6}(liq) + {{15} \over 2}{O_2}(g) \to 6C{O_2}(g) + 3{H_2}O(liq)$$

Benzene burns in oxygen according to the above equation. What is the volume of oxygen (at STP) needed for complete combustion of 39 gram of liquid benzene?

Avogadro's law is valid for

A metal (M) forms two oxides. The ratio M:O (by weight) in the two oxides are 25:4 and 25:6. The minimum value of atomic mass of M is

The de-Broglie wavelength ($$\lambda$$) for electron (e), proton (p) and He²⁺ ion ($$\alpha$$) are in the following order. Speed of e, p and $$\alpha$$ are the same

1 mL of water has 25 drops. Let N₀ be the Avogadro number. What is the number of molecules present in 1 drop of water ? (Density of water = 1 g/mL)

In Bohr model of atom, radius of hydrogen atom in ground state is r₁ and radius of He⁺ ion in ground state is r₂. Which of the following is correct?

Which one of the following is the correct set of four quantum numbers (n, 1, m, s) ?

Let (C_rms)_H2 is the r.m.s. speed of H₂ at 150 K. At what temperature, the most probable speed of helium [C_mp)_He] will be half of (C_rms)_H2 ?

The correct pair of electron affinity order is

The product of the following reaction is :

The product of the following hydrogenation reaction is:

Pick the correct statement.

During the preparation of NH₃ in Haber's process, the promoter(s) used is/are -

The correct statement(s) about B₂H₆ is /are :

Which of the following would produce enantiomeric products when reacted with methyl magnesium iodide?

The above conversion can be carried out by,

Which of the statements are incorrect?

The values of a, b, c for which the function $$f(x) = \left\{ \matrix{ {{\sin (a + 1)x + \sin x} \over x},x < 0 \hfill \cr c,x = 0 \hfill \cr {{{{(x + b{x^2})}^{{1 \over 2}}} - {x^{{1 \over 2}}}} \over {b{x^{{1 \over 2}}}}},x > 0 \hfill \cr} \right.$$ is continuous at x = 0, are

Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is

Let $$f(x) = {a_0} + {a_1}|x| + {a_2}|x{|^2} + {a_3}|x{|^3}$$, where $${a_0},{a_1},{a_2},{a_3}$$ are real constants. Then f(x) is differentiable at x = 0

If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then

$$\mathop {\lim }\limits_{x \to 0} \left( {{1 \over x}\ln \sqrt {{{1 + x} \over {1 - x}}} } \right)$$ is

Let f : [a, b] $$\to$$ R be continuous in [a, b], differentiable in (a, b) and f(a) = 0 = f(b). Then

$$I = \int {\cos (\ln x)dx} $$. Then I =

Let f be derivable in [0, 1], then

Let $$\int {{{{x^{{1 \over 2}}}} \over {\sqrt {1 - {x^3}} }}dx = {2 \over 3}g(f(x)) + c} $$ ; then

(c denotes constant of integration)

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

Let $$\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x} \over x} - 1,\left( {0 < x < {\pi \over 4}} \right)} $$. Then a and b are given by

Let $$f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt} $$. Then $$f'\left( {{\pi \over 4}} \right)$$ equals

If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to

A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes is bisected at the point of contact. The equation of the curve is

The solution of

$$\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}$$ is $$f(x) + {e^{ - \sin y}} = C$$ (C is arbitrary real constant) where f(x) is equal to

The point of contact of the tangent to the parabola y² = 9x which passes through the point (4, 10) and makes an angle $$\theta$$ with the positive side of the axis of the parabola where tan$$\theta$$ > 2, is

Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then

If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c $$ is unit vector perpendicular to $$\overrightarrow a $$ and coplanar with $$\overrightarrow a $$ and $$\overrightarrow b $$, then unit vector $$\overrightarrow d $$ perpendicular to both $$\overrightarrow a $$ and $$\overrightarrow c $$ is

If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is

A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k are positive constants. The maximum velocity attained by the particle is

If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the lengths of the sides of a triangle which is

Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then

The number of zeros at the end of $$\left| \!{\underline {\, {100} \,}} \right. $$ is

If $$|z - 25i| \le 15$$, then Maximum arg(z) $$-$$ Minimum arg(z) is equal to

(arg z is the principal value of argument of z)

If z = x $$-$$ iy and $${z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)$$, then $${{\left( {{x \over p} + {y \over q}} \right)} \over {({p^2} + {q^2})}}$$ is equal to

If a, b are odd integers, then the roots of the equation $$2a{x^2} + (2a + b)x + b = 0$$, $$a \ne 0$$ are

There are n white and n black balls marked 1, 2, 3, ...... n. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is

Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then

A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P $$\cap$$ Q = $$\varphi $$ is

Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{ 1 & 2 & 4 \cr 2 & 1 & 2 \cr 1 & 2 & {(a - 4)} \cr } } \right)\left( {\matrix{ x \cr y \cr z \cr } } \right) = \left( {\matrix{ 6 \cr 4 \cr a \cr } } \right)$$ possesses(possess) unique solution ?

If $$\Delta (x) = \left| {\matrix{ {x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr {x - 1} & {{x^2}} & {{{(x + 1)}^3}} \cr x & {{{(x + 1)}^2}} & {{{(x + 2)}^3}} \cr } } \right|$$, then coefficient of x in $$\Delta$$x is

If $$p = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$ is the adjoint of the $$3 \times 3$$ matrix A and det A = 4, then $$\alpha$$ is equal to

If $$A = \left( {\matrix{ 1 & 1 \cr 0 & i \cr } } \right)$$ and $${A^{2018}} = \left( {\matrix{ a & b \cr c & d \cr } } \right)$$, then $$(a + d)$$ equals

Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defined. Let g . f be injective mapping. Then

For the mapping $$f:R - \{ 1\} \to R - \{ 2\} $$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is correct?

A, B, C are mutually exclusive events such that $$P(A) = {{3x + 1} \over 3}$$, $$P(B) = {{1 - x} \over 4}$$ and $$P(C) = {{1 - 2x} \over 2}$$. Then the set of possible values of x are in

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is

If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 < {\alpha _1},{\alpha _2},....\,{\alpha _n} < \pi /2$$, then the maximum value of $$(\cos {\alpha _1})(\cos {\alpha _2}).....(\cos {\alpha _n})$$ is given by

If the algebraic sum of the distances from the points (2, 0), (0, 2) and (1, 1) to a variable straight line be zero, then the line passes through the fixed point

The side AB of $$\Delta$$ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical angle is always constant and is $$\alpha$$. Let x-axis be along AB and the origin be at A. Then the locus of the vertex is

If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is

A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the positive direction of x-axis. If this line meets the curve $${x^2} = 4y - 9$$ at A and B, then |AB| is equal to

Two circles $${S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0$$ and $${S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0$$ have a common chord PQ. The equation of PQ is

Let $$P(3\sec \theta ,2\tan \theta )$$ and $$Q(3\sec \phi ,2\tan \phi )$$ be two points on $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ such that $$\theta + \phi = {\pi \over 2},0 < \theta ,\phi < {\pi \over 2}$$. Then the ordinate of the point of intersection of the normals at P and Q is

Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)² = 2(x $$-$$ 4). Then the locus of mid-point of PQ is

AB is a chord of a parabola y² = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right angle at the origin O, then $${1 \over {O{A^2}}} + {1 \over {O{B^2}}}$$ equals to

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y $$-$$ z + 4 = 0 and parallel to the x-axis is

The line $$x - 2y + 4z + 4 = 0$$, $$x + y + z - 8 = 0$$ intersect the plane $$x - y + 2z + 1 = 0$$ at the point

If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} $$, $${I_2} = \int\limits_0^1 {{e^{ - {x^2}}}{{\cos }^2}x\,dx} $$, $${I_3} = \int\limits_0^1 {{e^{ - {x^2}}}dx} $$, $${I_4} = \int\limits_0^1 {{e^{ - {x^2}/2}}dx} $$, then

$$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + 1} \over {x + 1}} - ax - b} \right),(a,b \in R)$$ = 0. Then

If the transformation $$z = \log \tan {x \over 2}$$ reduces the differential equation

$${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$ into the form $${{{d^2}y} \over {d{z^2}}} + ky = 0$$ then k is equal to

From the point ($$-$$1, $$-$$6), two tangents are drawn to y² = 4x. Then the angle between the two tangents is

If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow \gamma = \widehat i + \widehat k$$ then the maximum value of $$\left[ {\overrightarrow \alpha \overrightarrow \beta \overrightarrow \gamma } \right]$$ is

The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is

A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

Let the tangent and normal at any point P(at², 2at), (a > 0), on the parabola y² = 4ax meet the axis of the parabola at T and G respectively. Then the radius of the circle through P, T and G is

The value of a for which the sum of the squares of the roots of the equation $${x^2} - (a - 2)x - a - 1 = 0$$ assumes the least value is

If x satisfies the inequality $${\log _{25}}{x^2} + {({\log _5}x)^2} < 2$$, then x belongs to

The solution of $$\det (A - \lambda {I_2}) = 0$$ be 4 and 8 and $$A = \left( {\matrix{ 2 & 2 \cr x & y \cr } } \right)$$. Then

(I₂ is identity matrix of order 2)

If P₁P₂ and P₃P₄ are two focal chords of the parabola y² = 4ax then the chords P₁P₃ and P₂P₄ intersect on the

$$f:X \to R,X = \{ x|0 < x < 1\} $$ is defined as $$f(x) = {{2x - 1} \over {1 - |2x - 1|}}$$. Then

Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int\limits_0^x {f(t)dt} } $$ and f (0) = 0. Then

PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OPQ$$ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon above the ground when the stone reaches the ground after 4 sec is [g = 32 ft/sec²]

Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then

Let z₁ and z₂ be two non-zero complex numbers. Then

Let $$\Delta = \left| {\matrix{ {\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr {\cos \theta \cos \phi } & {\cos \theta \sin \phi } & { - \sin \theta } \cr { - \sin \theta \sin \phi } & {\sin \theta \cos \phi } & 0 \cr } } \right|$$. Then

Let R and S be two equivalence relations on a non-void set A. Then

Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

Consider the equation $$y - {y_1} = m(x - {x_1})$$. If m and x₁ are fixed and different lines are drawn for different values of y₁, then

Let p(x) be a polynomial with real co-efficient, p(0) = 1 and p'(x) > 0 for all x $$\in$$ R. Then

Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed be greatest?

The line y = x + 5 touches

Two infinite line-charges parallel to each other are moving with a constant velocity v in the same direction as shown in the figure. The separation between two line-charges is d. The magnetic attraction balances the electric repulsion when, [ c = speed of light in free space ]

The electric potential for an electric field directed parallel to X-axis is shown in the figure. Choose the correct plot of electric field strength.

An electron revolves around the nucleus in a circular path with angular momentum $$\overrightarrow L $$. A uniform magnetic field $$\overrightarrow B $$ is applied perpendicular to the plane of its orbit. If the electron experiences a torque $$\overrightarrow T $$, then

A straight wire is placed in a magnetic field that varies with distance x from origin as $$\overrightarrow B = {B_0}\left( {2 - {x \over a}} \right)\widehat k$$. Ends of wire are at (a, 0) and (2a, 0) and it carries a current I. If force on wire is $$\overrightarrow F = I{B_0}\left( {{{ka} \over 2}} \right)\widehat j$$, then value of k is

In a closed circuit there is only a coil of inductance L and resistance 100 $$\Omega$$. The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by 5 Weber. What amount of charge will flow in the circuit as a result?

When an AC source of emf E with frequency $$\omega$$ = 100 Hz is connected across a circuit, the phase difference between E and current I in the circuit is observed to be $${\pi \over 4}$$ as shown in the figure. If the circuit consist of only RC or RL in series, then

A battery of emf E and internal resistance r is connected with an external resistance R as shown in the figure. The battery will act as a constant voltage source if

If the kinetic energies of an electron, an alpha particle and a proton having same de-Broglie wavelength are $${\varepsilon _1},{\varepsilon _2}$$ and $${\varepsilon _3}$$ respectively, then

In a Young's double slit experiment, the intensity of light at a point on the screen where the path difference between the interfering waves is $$\lambda$$, ($$\lambda$$ being the wavelength of light used) is I. The intensity at a point where the path difference is $${\lambda \over 4}$$ will be (assume two waves have same amplitude)

In Young's double slit experiment with a monochromatic light, maximum intensity is 4 times the minimum intensity in the interference pattern. What is the ratio of the intensities of the two interfering waves?

The human eye has an approximate angular resolution of $$\theta$$ = 5.8 $$\times$$ 10^$$-$$4 rad and typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance d should a printed page be held so that one does not see the individual dots?

Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of $${h \over {2\pi }}$$. The largest possible wavelength emitted by hydrogen atoms in visible range in a world according to Bohr's model will be,

(Consider hc = 1242 Mev-fm)

A Zener diode having break down voltage Vz = 6V is used in a voltage regulator circuit as shown in the figure. The minimum current required to pass through the Zener to act as a voltage regulator is 10 mA and maximum allowed current through Zener is 40 mA. The maximum value of R_s for Zener to act as a voltage regulator is

The expression $$\overline A (A + B) + (B + AA)(A + \overline B )$$ simplifies to

Given : The percentage error in the measurements of A, B, C and D are respectively, 4%, 2%, 3% and 1%. The relative error in $$Z = {{{A^4}{B^{{1 \over 3}}}} \over {C{D^{{3 \over 2}}}}}$$ is

The Entropy (S) of a black hole can be written as $$S = \beta {k_B}A$$, where k_B is the Boltzmann constant and A is the area of the black hole. The $$\beta$$ has dimension of

The kinetic energy (E_k) of a particle moving along X-axis varies with its position (X) as shown in the figure. The force acting on the particle at X = 10 m is

A particle is moving in an elliptical orbit as shown in figure. If $$\overrightarrow p $$, $$\overrightarrow L $$ and $$\overrightarrow r $$ denote the linear momentum, angular momentum and position vector of the particle (from focus O) respectively at a point A, then the direction of $$\overrightarrow \alpha $$ = $$\overrightarrow p $$ $$\times$$ $$\overrightarrow L $$ is along.

A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motion, the phase difference ($$\delta$$) between the two motion is

A body of mass m is thrown with velocity u from the origin of a co-ordinate axes at an angle $$\theta$$ with the horizon. The magnitude of the angular momentum of the particle about the origin at time t when it is at the maximum height of the trajectory is proportional to

Three particles, each of mass 'm' grams situated at the vertices of an equilateral $$\Delta$$ABC of side 'a' cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC in g-cm² units will be

A body of mass m is thrown vertically upward with speed $$\sqrt3$$ v_e, where v_e is the escape velocity of a body from earth surface. The final velocity of the body is

If a string, suspended from the ceiling is given a downward force F₁, its length becomes L₁. Its length is L₂, if the downward force is F₂. What is its actual length?

27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

Certain amount of an ideal gas is taken from its initial state 1 to final state 4 through the paths 1 $$\to$$ 2 $$\to$$ 3 $$\to$$ 4 as shown in figure. AB, CD, EF are all isotherms. If v_p is the most probable speed of the molecules, then

Consider a thermodynamic process where integral energy $$U = A{P^2}V$$ (A = constant). If the process is performed adiabatically, then

One mole of a diatomic ideal gas undergoes a process shown in P-V diagram. The total heat given to the gas (ln 2 = 0.7) is

Two charges, each equal to $$-$$q are kept at ($$-$$a, 0) and (a, 0). A charge q is placed at the origin. If q is given a small displacement along y direction, the force acting on q is proportional to

A neutral conducting solid sphere of radius R has two spherical cavities of radius a and b as shown in the figure. Centre to centre distance between two cavities is c. q_a and q_b charges are placed at the centres of cavities respectively. The force between q_a and q_b is

Consider two concentric conducting sphere of radii R and 2R respectively. The inner sphere is given a charge +Q. The other sphere is grounded. The potential at $$r = {{3R} \over 2}$$ is

A horizontal semi-circular wire of radius r is connected to a battery through two similar springs X and Y to an electric cell, which sends current I through it. A vertically downward uniform magnetic field B is applied on the wire, as shown in the figure. What is the force acting on each spring?

Find the equivalent capacitance between A and B of the following arrangement :

A golf ball of mass 50 gm placed on a tee, is struck by a golf-club. The speed of the golf ball as it leaves the tee is 100 m/s, the time of contact on the ball is 0.02 s. If the force decreases to zero linearly with time, then the force at the beginning of the contact is

Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities +$$\sigma$$, $$-$$$$\sigma$$ and +$$\sigma$$ respectively. The potential of shell B is

One mole of an ideal monoatomic gas expands along the polytrope PV³ = constant from V₁ to V₂ at a constant pressure P₁. The temperature during the process is such that molar specific heat $${C_V} = {{3R} \over 2}$$. The total heat absorbed during the process can be expressed as

As shown in figure, a rectangular loop of length 'a' and width 'b' and made of a conducting material of uniform cross-section is kept in a horizontal plane where a uniform magnetic field of intensity B is acting vertically downward. Resistance per unit length of the loop is $$\lambda$$ $$\Omega$$/m. If the loop is pulled with uniform velocity 'v' in horizontal direction, which of the following statement is/are true?

A sample of hydrogen atom in its ground state is radiated with photons of 10.2 eV energies. The radiation from the sample is absorbed by excited ionized He⁺. Thenwhich of the following statement/s is/are true?

A particle is moving in x-y plane according to $$\overrightarrow r = b\cos \omega t\widehat i + b\sin \omega t\widehat j$$, where $$\omega$$ is constant. Which of the following statement(s) is/are true?

Two wires A and B of same length are made of same material. Load (F) vs. elongation (x) graph for these two wires is shown in the figure. Then which of the following statement(s) is/are true?

A hemisphere of radius R is placed in a uniform electric field E so that its axis is parallel to the field. Which of the following statement(s) is/are true?