JEE Advanced 2025 Paper 2

Let 𝑥0 be the real number such that 𝑒𝑥0+𝑥0=0 . For a given real number 𝛼, define 𝑔(𝑥)=3𝑥𝑒𝑥+3𝑥−𝛼𝑒𝑥−𝛼𝑥 3(𝑒𝑥+1) for all real numbers 𝑥. Then which one of the following statements is TRUE?

1. For 𝛼=2 , lim 𝑥→𝑥0| 𝑔(𝑥)+ 𝑒𝑥0 𝑥−𝑥0 |=0
2. For 𝛼=2 , lim 𝑥→𝑥0| 𝑔(𝑥)+ 𝑒𝑥0 𝑥−𝑥0 |=1
3. For 𝛼=3 , lim 𝑥→𝑥0| 𝑔(𝑥)+ 𝑒𝑥0 𝑥−𝑥0 |=0
4. For 𝛼=3 , lim 𝑥→𝑥0| 𝑔(𝑥)+ 𝑒𝑥0 𝑥−𝑥0 |=2 3

Let ℝ denote the set of all real numbers. The n the area of the region {(𝑥,𝑦)∈ℝ×ℝ∶𝑥>0,𝑦>1 𝑥 ,5𝑥−4𝑦−1>0,4𝑥+4𝑦−17<0 } is

1. 17 16−log𝑒4
2. 33 8−log𝑒4
3. 57 8−log𝑒4
4. 17 2−log𝑒4

The total number of real solution s of the equation 𝜃=tan−1(2tan𝜃)−1 2sin−1(6tan𝜃 9+tan2𝜃) is (Here, the inverse trig onometric functions sin−1𝑥 and tan−1𝑥 assume values in [−𝜋 2,𝜋 2] and (−𝜋 2,𝜋 2), respectively.)

1. 1
2. 2
3. 3
4. 5

Let 𝑆 denote the locus of the point of intersection of the pair of lines 4𝑥−3𝑦=12𝛼 , 4𝛼𝑥+3𝛼𝑦=12 , where 𝛼 varies over the set of non -zero real numbers. Let 𝑇 be the tangent to 𝑆 passing through the points (𝑝,0) and (0,𝑞),𝑞>0, and parallel to the line 4 𝑥−3 √2 𝑦=0 . Then the value of 𝑝𝑞 is

1. −6√2
2. −3√2
3. −9√2
4. −12√2 • For example, in a question, if (A), (B ) and
5. are the ONLY three options corresponding to correct answers , then choosing ONLY (A),
6. and
7. will get +4 marks; choosing ONLY (A) and ( B) will get +2 marks; choosing ONLY (A) and ( D) will get +2 marks; choosing ONLY (B ) and ( D) will get +2 marks; choosing ONLY (A) will get +1 mark; choosing ONLY
8. will get +1 mark; choosing ONLY
9. will get +1 mark; choosing no option (i.e. the question is unanswered) will get 0 marks; and choosing any other combination of options will get −2 mark s.

Let 𝐼= (10 01) and 𝑃=(20 03). Let 𝑄=(𝑥𝑦 𝑧4) for some non -zero real numbers 𝑥,𝑦, and 𝑧, for which there is a 2×2 matrix 𝑅 with all entries being non-zero real numbers , such that 𝑄𝑅=𝑅𝑃 . Then which of the following statements is (are) TRUE?

1. The determinant of 𝑄−2𝐼 is zero
2. The determinant of 𝑄−6𝐼 is 12
3. The determinant of 𝑄−3𝐼 is 15
4. 𝑦𝑧=2

Let 𝑆 denote the locus of the mid -point s of those chords of the parabola 𝑦2=𝑥 , such that the area of the region enclosed between the parabola and the chord is 4 3 . Let ℛ denote the region lying in the first quadrant, enclosed by the parabola 𝑦2=𝑥 ,the curve 𝑆, and the lines 𝑥=1 and 𝑥=4 . Then which of the following statements is (are) TRUE?

1. (4,√3 )∈𝑆
2. (5,√2 )∈𝑆
3. Area of ℛ is 14 3−2 √3
4. Area of ℛ is 14 3−√3

Let 𝑃(𝑥1,𝑦1) and 𝑄(𝑥2,𝑦2) be two distinct points on the ellipse 𝑥2 9 +𝑦2 4=1 such that 𝑦1>0,and 𝑦2>0 . Let 𝐶 denote the circle 𝑥2+𝑦2=9 , and 𝑀 be the point (3,0). Suppose the line 𝑥=𝑥1 intersect s 𝐶 at 𝑅,and the line 𝑥=𝑥2 intersects C at 𝑆, such that the 𝑦-coordinates of 𝑅 and 𝑆 are positive. Let ∠𝑅𝑂𝑀=𝜋 6 and ∠𝑆𝑂𝑀=𝜋 3 , where 𝑂 denotes the origin (0,0). Let |𝑋𝑌| denote the length of the line seg ment 𝑋𝑌 . Then which of the following statements is (are) TRUE?

1. The equation of the line joining 𝑃 and 𝑄 is 2𝑥+3𝑦=3 (1+√3 )
2. The equation of the line joining 𝑃 and 𝑄 is 2𝑥+𝑦=3 (1+√3 )
3. If 𝑁2=(𝑥2,0), then 3 |𝑁2𝑄|=2 |𝑁2𝑆|
4. If 𝑁1=(𝑥1,0), then 9 |𝑁1𝑃|=4 |𝑁1𝑅|

Let ℝ denote the set of all real numbers. Let 𝑓:ℝ→ℝ be defined by 𝑓(𝑥)={ 6𝑥+sin𝑥 2𝑥+sin𝑥 if 𝑥≠0, 7 3 if 𝑥=0 . Then which of the following statements is (are) TRUE?

1. The point 𝑥=0 is a point of local maxima of 𝑓
2. The point 𝑥=0 is a point of local minima of 𝑓
3. Number of points of local maxima of 𝑓 in the interval [𝜋,6𝜋] is 3
4. Number of points of local minima of 𝑓 in the interval [2𝜋,4𝜋] is 1

Let 𝑦(𝑥) be the solution of the differential equation 𝑥2𝑑𝑦 𝑑𝑥+𝑥𝑦=𝑥2+𝑦2, 𝑥>1 𝑒 , satisfying 𝑦(1)=0 . Then the value of 2(𝑦(𝑒))2 𝑦(𝑒2) is ___________.

Numerical answer type

Let 𝑎0,𝑎1,…,𝑎23 be real numbers such that (1+2 5𝑥)23 = ∑𝑎𝑖𝑥𝑖 23 𝑖=0 for every real number 𝑥. Let 𝑎𝑟 be the largest among the numbers 𝑎𝑗 for 0≤𝑗≤23. Then the value of 𝑟 is ___________.

Numerical answer type

A factory has a total of three manufacturing units, 𝑀1,𝑀2,and 𝑀3, which produce bulbs independent of each other. The units 𝑀1,𝑀2,and 𝑀3 produce bulbs in the proportions of 2:2:1, respectively. It is known that 20% of the bulbs produced in the factory are defective. It is also known that, of all the bulbs produced by 𝑀1, 15% are defective. Suppose that, if a randomly chosen bulb produced in the factory is found to be defective, the probability that it was produced by 𝑀2 is 2 5 . If a bulb is chosen randomly from the bulbs produc ed by 𝑀3, then the probability that it is defective is ___________.

Numerical answer type

Consider the vectors 𝑥⃗=𝑖̂+2𝑗̂+3𝑘̂ ,𝑦⃗=2𝑖̂+3𝑗̂+𝑘̂ ,and 𝑧⃗=3𝑖̂+𝑗̂+2𝑘̂ . For two distinct positive real numbers 𝛼 and 𝛽, define 𝑋⃗=𝛼𝑥⃗+𝛽𝑦⃗−𝑧⃗ ,𝑌⃗⃗=𝛼𝑦⃗+𝛽𝑧⃗−𝑥⃗,and 𝑍⃗=𝛼𝑧⃗+𝛽𝑥⃗−𝑦⃗ . If the vectors 𝑋⃗,𝑌⃗⃗, and 𝑍⃗ lie in a plane, then the value of 𝛼+𝛽−3 is_____________.

Numerical answer type

For a non -zero complex number 𝑧, let arg(𝑧) denote the principal argument of 𝑧, with −𝜋<arg(𝑧)≤𝜋. Let 𝜔 be the cube root of unity for which 0<arg(𝜔)<π. Let 𝛼=arg( ∑(−𝜔)𝑛2025 𝑛=1) . Then the value of 3𝛼 𝜋 is ________________ .

Numerical answer type

Let ℝ denote the set of all real numbers. Let 𝑓:ℝ→ℝ and 𝑔:ℝ→(0,4) be functions defined by 𝑓(𝑥)=log𝑒(𝑥2+2𝑥+4) , and 𝑔(𝑥)=4 1+𝑒−2𝑥 . Define the composite function 𝑓∘𝑔−1 by (𝑓∘𝑔−1) (𝑥)=𝑓(𝑔−1(𝑥)), where 𝑔−1 is the inverse of the function 𝑔. Then the value of the derivative of the composite function 𝑓∘𝑔−1 at 𝑥=2 is ______________.

Numerical answer type

Let α=1 sin60∘ sin61∘ + 1 sin62∘ sin63∘ + ⋯ +1 sin118∘ sin119∘ . Then the value of ( cosec1∘ α)2 is ______________.

Numerical answer type

If 𝛼=∫tan−1𝑥 2𝑥2−3𝑥+22 1 2 𝑑𝑥 , then the value of √7tan(2𝛼 √7 𝜋) is _____________. (Here, the inverse trigonometric function tan−1𝑥 assumes values in (−𝜋 2,𝜋 2) .)

Numerical answer type

A temperature difference can generate e.m.f. in some materials. Let 𝑆 be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical conductivity and 𝜅 the thermal conductivity of the material of the wire. Taking 𝑀,𝐿,𝑇,𝐼 and 𝐾 as dimensions of mass, length, time, current and temperature, respectively , the dimension al formula of the quantity 𝑍=𝑆2σ 𝜅 is:

1. [𝑀0𝐿0𝑇0𝐼0𝐾0]
2. [𝑀0𝐿0𝑇0𝐼0𝐾−1]
3. [𝑀1𝐿2𝑇−2𝐼−1𝐾−1]
4. [𝑀1𝐿2𝑇−4𝐼−1𝐾−1]

Two co -axial conducting cylinders of same length ℓ with radii √2𝑅 and 2𝑅 are kept, as shown in Fig. 1 . The charge on the inner cylinder is 𝑄 and the outer cylinder is grounded . The annular region between the cylinders is filled with a material of dielectric constant 𝜅=5. Consider an imaginary plane of the same length ℓ at a d istance 𝑅 from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross -sectional view of this arrangement is shown in Fig. 2 . Ignoring edge effects, the flux of the electric field through the plane is (𝜖0 is the p ermittivity of free space) :

1. 𝑄 30𝜖0
2. 𝑄 15𝜖0
3. 𝑄 60𝜖0
4. 𝑄 120𝜖0

As shown in the figures, a uniform rod 𝑂𝑂′ of length 𝑙 is hinged at the point 𝑂 and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top -end ( 𝑂′) of the rod , as shown in Fig. 1 and the rod is made to oscillate by a small angular displacement . The frequency of oscillation of the rod is 𝑓1. On the other hand, if both the springs are connected at the midpoint of the rod , as shown in Fig. 2 and the rod is made to oscillate by a small angular displacement , then the frequency of oscillation is 𝑓2. Ignoring gravity and a ssuming motion only in the plane of the diagram, t he value of 𝑓1 𝑓2 is:

1. 2
2. √2
3. √5 2
4. √2 5

Consider a star of mass 𝑚2 kg revolving in a circular orbit around another star of mass 𝑚1 kg with 𝑚1≫𝑚2. The heavier star slowly acquire s mass from the lighter star at a constant rate of 𝛾 kg/s. In this transfer process, there is no other loss of mass . If the separation between the center s of the stars is 𝑟, then its relative rate of change 1 𝑟𝑑𝑟 𝑑𝑡 (in s⁻¹) is given by :

1. −3𝛾 2𝑚2
2. −2𝛾 𝑚2
3. −2𝛾 𝑚1
4. −3𝛾 2𝑚1  For example, in a question, if (A), (B ) and
5. are the ONLY three options corresponding to correct answers , then choosing ONLY (A),
6. and
7. will get +4 marks; choosing ONLY (A) and ( B) will get +2 marks; choosing ONLY (A) and ( D) will get +2 marks; choosing ONLY (B ) and ( D) will get +2 marks; choosing ONLY (A) will get +1 mark; choosing ONLY
8. will get +1 mark; choosing ONLY
9. will get +1 mark; choosing no option (i.e. the question is unanswered) will get 0 marks; and choosing any other combination of options will get −2 mark s.

A positive point charge of 10ି଼ C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm . The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of 10 cm further away from the center of the sphere along the radial direction. Tak ing ଵ ସగఢబ=9×10ଽ Nmଶ/Cଶ (where 𝜖଴ is the permittivity of free space), which of the following statements is/are correct :

1. Before the grounding, t he electrostatic potential of the sphere is 450 V .
2. Charge flowing from the sphere to the ground because of grounding is 5×10ିଽ C.
3. After the grounding is removed, the charge on the sphere is −5×10ିଽ C.
4. The final electrostatic potential of the sphere is 300 V.

Two identical concave mirrors each of focal length 𝑓 are facing each other as shown in the schematic diagram . The focal length 𝑓 is much larger than the size of the mirror s. A glass slab of thickness 𝑡 and refractive index 𝑛଴ is kept equidistant from the mirrors and perpendicular to the ir common principal axis . A monochromatic point light source 𝑆 is embedded at the center of the slab on the principal axis , as shown in the schematic diagram . For the image to be formed on 𝑆 itself, which of the following distance s between the two mirror s is/are correct :

1. 4𝑓+൬1−1 𝑛଴൰𝑡
2. 2𝑓+൬1−1 𝑛଴൰𝑡
3. 4𝑓+(𝑛଴−1)𝑡
4. 2𝑓+(𝑛଴−1)𝑡

Six infinitely large and thin non-conducting sheets are fixed in configurations I and II . As shown in the figure , the sheets carry uniform surface charge densit ies which are indicated in terms of 𝜎଴. The separation between any two consecutive sheets is 1 𝜇m. The various regions between the sheets are denoted as 1, 2, 3, 4 and 5. If 𝜎଴=9 𝜇C/m², then which of the following statements is/are correct : (Take permittivity of free space 𝜖଴ = 9×10ିଵଶ F/m)

1. In region 4 of the configuration I, the magnitude of the electric fi eld is zero.
2. In region 3 of the configuration II, the magnitude of the electric field is ఙబ ఢబ.
3. Potential difference between the first and the last sheet s of the configuration I is 5 V.
4. Potential difference between the first and the last sheet s of the configuration II is zero.

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir . The work extracted from this engine is being fully used to run a heat pump which has a coeffici ent of performance 10. The hot reservoir of the heat pump is at a temperature of 300 K. Which of the following statements is/are correct :

1. Work extracted from the Carnot engine in one cycle is 60 J.
2. Temperature of the cold reservoir of the Carnot engine is 600 K.
3. Temperature of t he cold reservoir of the heat pump is 270 K.
4. Heat supplied to the hot reservoir of the heat pum p in one cycle is 540 J.

A conducting solid sphere of radius 𝑅 and mass 𝑀 carries a charge 𝑄. The sphere is rotating about an axis passing through its center with a uniform angular speed ω. The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as 𝛼ொ ଶெ. The value of 𝛼 is ___

Numerical answer type

A hydrogen atom , initially at rest in its ground state , absorbs a photon of frequency νଵ and ejects the electron with a kinetic energy of 10 eV. The electron then combines with a positron at rest to form a positronium atom in its ground state and simultaneously emits a photon of frequency νଶ. The center of mass of the resulting positronium atom moves with a kinetic energy of 5 eV. It is given that positron has the same mass as that of electron and the positronium atom can be considered as a Bohr atom , in which the electron and the positron orbit around their center of mass . Cons idering no other energy loss during the whole process, the difference between the two photon energies (in eV) is ___

Numerical answer type

An ideal monatomic gas of 𝑛 moles is taken through a cycle 𝑊𝑋𝑌𝑍𝑊 consisting of consecutive adiabatic and isobaric quasi -static processes, as shown in the schematic 𝑉-𝑇 diagram. The volume of the gas at 𝑊,𝑋 and 𝑌 points are, 64 cmଷ, 125 cmଷ and 250 cmଷ, respectively. If the absolute temperature of the gas 𝑇ௐ at the point 𝑊 is such that 𝑛𝑅𝑇ௐ=1 J (𝑅 is the universal gas constant), then the amount of heat absorbed (in J) by the gas along the path 𝑋𝑌 is ___

Numerical answer type

A geostationary satellite above the equator is orbiting around the earth at a fixed distance 𝑟ଵ from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth’s rotation , at a distance 𝑟ଶ from the center of the earth , such that 𝑟ଵ=1.21 𝑟ଶ. The time period of the second satellite as measured from the geostationary satellite is ଶସ ௣ hours. The value of 𝑝 is ___

Numerical answer type

The l eft and right compartment s of a thermally isolated container of length 𝐿 are separated by a thermally conducting, movable piston of area 𝐴. The left and right compartments are filled with ଷ ଶ and 1 moles of an ideal gas , respectively . In the left compartment the piston is attached by a spring with spring constant 𝑘 and natu ral length ଶ௅ ହ. In thermodynamic equilibrium , the piston is at a distance ௅ ଶ from the left and right edges of the container as shown in the figure . Under the above conditions, if the pressure in the right compartment is 𝑃=௞௅ ஺𝛼, then the value of 𝛼 is ____

Numerical answer type

In a Young’s double slit experiment, a combination of two glass wedges 𝐴 and 𝐵, having refractive indices 1.7 and 1.5, respectively , are placed in front of the slits, as shown in the figure. The separation between the slits is 𝑑=2 mm and the shortest distance between the slits and the screen is 𝐷=2 m. Thickness of the combination of the wedges is 𝑡=12 𝜇m. The value of 𝑙 as shown in the figure is 1 mm. Neglect any refraction effect at the slanted interface of the wedge s. Due to the combination of the wedges , the central maximum shifts (in mm) with respect to O by ____

A projectile of mass 200 g is launched in a viscous medium at an angle 60° with the horizontal , with an initial velocity of 270 m/s. It experiences a viscous drag force 𝐹⃗=−𝑐𝑣⃗ where the drag coefficient 𝑐=0.1 kg/s and 𝑣⃗ is the instantaneous velocity of the projectile. The pro jectile hits a vertical wall after 2 s. Taking 𝑒=2.7, the horizontal distance of the wall from th e point of projection (in m ) is ____

Numerical answer type

An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless string s of length 8 m with their pivots well separated along the 𝑋 axis. They are pulled from the equilibrium position in opposite direction s along the 𝑋 axis by a small angular amplitude 𝜃଴=cosିଵ(0.9) and released simultane ously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 m/s, the maximum variation in the frequency (in Hz) as measured by the receiver (Take the acceleration due to gravity 𝑔=10 m/sଶ) is ___

Numerical answer type

During sodium nitroprusside test of sulphide ion in an aqueous solution, one of the ligand s coordinated to the metal ion is converted to

1. NOS
2. SCN
3. SNO
4. NCS

The c omplete h ydrolysis of ICl, ClF 3 and BrF 5, respectively, gives

1. IO, ClO 2 and BrO 3
2. IO3, ClO 2 and BrO 3
3. IO, ClO and BrO 2
4. IO3, ClO 4 and BrO 2

Monocyclic compounds P, Q, R and S are the major products formed in the reaction sequences given below. COOH(i)Br₂/Red phosphorus(ii) H2OP CHOQ+OHaq. NaOH, 293 K The product having the highest number of unsaturated carbon atom(s) is

1. P
2. Q
3. R
4. S

The correct reaction /reaction sequence that would produce a dicarboxylic acid as the major product is

1. HOCl(i) NaCN(ii) HO H₂O(iii) H3O
2. Br₂, H₂O(CHOH)4CH2OHCHO
3. Br(i) KOH, EtOH(ii) KMnO₄, H₂SO₄, 
4. H2CrO4OOH  For example, in a question, if (A), (B ) and
5. are the ONLY three options corresponding to correct answers , then choosing ONLY (A),
6. and
7. will get +4 marks; choosing ONLY (A) and ( B) will get +2 marks; choosing ONLY (A) and ( D) will get +2 marks; choosing ONLY (B ) and ( D) will get +2 marks; choosing ONLY (A) will get +1 mark; choosing ONLY
8. will get +1 mark; choosing ONLY
9. will get +1 mark; choosing no option (i.e. the question is unanswered) will get 0 marks; and choosing any other combination of options will get −2 mark s.

The correct statement(s) about intermolecular forces is(are)

1. The potential energy between two point charges approaches zero more rapidly than the potential energy between a point dipole and a point charge as the distance between them approaches infinity.
2. The average potential energy of two rotating polar molecules that are separated by a distance r has 1/ r3 dependence.
3. The dipole -induced dipole average intera ction energy is independent of temperature.
4. Nonpolar molecules attract one another even though neither has a permanent dipole moment.

The compound(s) with P H bond(s) is(are)

1. H3PO 4
2. H3PO 3
3. H4P2O7
4. H3PO 2

For the reaction sequence given below, the correct statement(s) is(are)

1. Both X and Y are oxygen containing compounds .
2. Y on heating with CHCl 3/KOH forms isocyanide .
3. Z reacts with Hinsberg’s reagent .
4. Z is an aromatic primary amine .

For the reaction sequence given below, the correct statement(s) is(are) OPhOPRQNaOH and CaO, LiAlH4CrO3-H2SO4H₂SO₄, 443 KS

1. P is optically active .
2. S gives Bayer’s test.
3. Q gives effervescence with aq. NaHCO 3.
4. R is an alkyn e.

The density (in g cmିଷ) of the metal which forms a cubic close packed (ccp) lattice with an axi al distance (edge length) equal to 400 pm is ______ . Use: Atomic mass of metal =105.6 amu and Avogadro’s constant =6×10ଶଷ molିଵ

Numerical answer type

The solubility of barium iodate in an aqueous solution prepared by mixing 200 mL of 0.010 M barium nitrate with 100 mL of 0.10 M sodium iodate is 𝑿×10ି଺ mol dmିଷ. The value of 𝑿 is ______ . Use: Solubility product constant ( Ksp) of barium iodate =1.58 ×10ିଽ

Numerical answer type

Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from 10 mg gିଵ and 16 mg gିଵ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be 4 mg gିଵ and 10 mg gିଵ, respectively. At this temperature, the concentration (in mg gିଵ) of adsorbed phenol from 20 mg gିଵ aqueous solution of phenol will be ______ . Use: logଵ଴ 2 =0.3

Consider a reaction 𝐴+𝑅 ⟶𝑃𝑟𝑜𝑑𝑢𝑐𝑡. The rate of this reaction is measured to be k[A][R]. At the start of the reaction, the concentration of 𝑅, [𝑅]଴, is 10 -times the concentration of 𝐴, [𝐴]଴. The reaction c an be considered to be a pseudo first order reaction with assumption that k[R] = k′ is constant . Due to this assumption, the relative error (in %) in the ra te when this reaction is 40 % complete , is ______ . [k and k′ represent corresponding rate constants]

Numerical answer type

At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density =1.00 g cmିଷ) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is 2.00 g dmିଷ, the molar mass of the macromolecule is calculated to be 𝑿×10ସ g molିଵ. The value of 𝑿 is ______ . Use: Universal gas constant (R) =8.3 J Kିଵ molିଵ and acceleration due to gravity (g) =10 m sିଶ

Numerical answer type

An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is 𝑿 ி×103 volts , where F is the Faraday constant . The value of X is ______ . Use: Standard Gibbs energies of formation at 298 K are: ∆௙𝐺େ୓మ௢= −394 kJ molିଵ; ∆௙𝐺୵ୟ୲ୣ୰௢= −237 kJ molିଵ; ∆௙𝐺ୠ୳୲ୟ୬ୣ௢= −18 kJ molିଵ

Numerical answer type

The sum of the spin only magnetic moment values (in B.M.) of [Mn(Br) 6]3 and [Mn(CN) 6]3 is _____ .

Numerical answer type

A linear octasaccharide (molar mass =1024 g mol1) on complete hydrolysis produces three monosaccharides: ribose, 2 -deoxyribose and glucose. The amount of 2 -deoxyribose formed is 58.26 % (w/w) of the total amount of the monosaccharides produced in the hydrolyzed products. The number of ribose unit(s) pr esent in one molecule of octasaccharide is ______ . Use: Molar mass (in g mol1): ribose =150, 2-deoxyribose =134, glucose =180; Atomic mass (in amu ): H = 1, O = 16

Numerical answer type