JEE Advanced 2024 Paper 1

Let ()fxbe a continuously differentiable function on the interval (0, )such that (1) 2f= and 10 1099() ( )lim 1txtf x xf ttx→−=− for each 0.x Then, for all 0,x ()fx is equal to

1. 1031 911 11xx−
2. 1091 311 11xx+
3. 1093 111 11xx−+
4. 1013 911 11xx+

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 1.2Also assume that the probability of the answer for a question being guessed, given that the student’s answer is correct, is 1.6 Then the probability that the student knows the answer of a randomly chosen question is

1. 112
2. 17
3. 57
4. 512

Let 2x be such that 5cot .11x−= Then ()()11 11sin sin 6 cos6 cos sin 6 cos622xxxx xx −+ +   is equal to

1. 11 123−
2. 11 123+
3. 11 132+
4. 11 132−

Consider the ellipse 221.94xy+= Let (,)Sp qbe a point in the first quadrant such that 221.94pq+ Two tangents are drawn from Sto the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let Rbe the vertex of the ellipse with positive x-coordinate and Obe the center of the ellipse. If the area of the triangle ORTis 3,2 then which of the following options is correct?

1. 2, 3 3qp==
2. 2, 4 3qp==
3. 1, 5 3qp==
4. 1, 6 3qp== • 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
8. will get +2 marks; choosing ONLY (B ) and ( D) will get +2 marks; choosing ONLY (A) will get +1 mark; choosing ONLY
9. will get +1 mark; choosing ONLY
10. 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 2 : , ,Sa b a b=+  ()112 : nTn=− +  , and ()212 : .nTn=+  Then which of the following statements is (are) TRUE?

1. 12TT S
2. 110,2024T= , where  denotes the empty set.
3. ()22024,T
4. For any given , ,ab ()()()()cos 2 sin 2ab i ab++ + if and only if 0,b= where 1i=−.

Let 2 denote . Let 22 2( , , ) : , , and 2 0 for all ( , ) (0,0) .Sa b c a b c a xb x y c y x y= + +   − Then which of the following statements is (are) TRUE?

1. 72, , 62S
2. If 13, , ,12bS then |2 |b< 1.
3. For any given (),, ,abc S the system of linear equations 1 1ax bybx cy+=+= − has a unique solution.
4. For any given (),, ,abc S the system of linear equations ( 1) 0 (1 ) 0a x bybx c y++=++ = has a unique solution.

Let 3 denote the three-dimensional space. Take two points (1, 2, 3)P= and (4,2,7).Q= Let (,)dist X Y denote the distance between two points Xand Yin 3. Let ()()223 : ( , ) ( , ) 5 0SX d i s t X P d i s t X Q= − = and ()()223 : ( , ) ( , ) 5 0 .TY d i s t Y Q d i s t Y P= − = Then which of the following statements is (are) TRUE?

1. There is a triangle whose area is 1 and all of whose vertices are from .S
2. There are two distinct points L and M in Tsuch that each point on the line segment LMis also in .T
3. There are infinitely many rectangles of perimeter 48, two of whose vertices are from Sand the other two vertices are from .T
4. There is a square of perimeter 48, two of whose vertices are from Sand the other two vertices are from .T

Let 32a=and 1/6156b=. If ,xy are such that ()5432 l o g 1 8axy+= and ()2l o g 1 0 8 0 ,bxy−= then 45xy+ is equal to ________.

Let 432()fx x a x b x c=+ + + be a polynomial with real coefficients such that(1) 9.f=− Suppose that 3i is a root of the equation 3243 2 0 ,xa xb x++ = where 1i=−. If 123 4,,, a n d  are all the roots of the equation () 0 ,fx= then 22221234+++is equal to ______.

Let 𝑆={𝐴= (01𝑐 1𝑎𝑑 1𝑏𝑒)∶ 𝑎,𝑏,𝑐,𝑑,𝑒∈{0,1} and |𝐴|∈ {−1,1}}, where |𝐴| denotes the determinant of 𝐴. Then the number of elements in 𝑆 is _______.

Numerical answer type

A group of 9students, 12 9,, ,,ss s is to be divided to form three teams , , and XY Z of sizes 2,3, and 4,respectively. Suppose that 1s cannot be selected for the team ,X and 2s cannot be selected for the team .Y Then the number of ways to form such teams, is _______.

Numerical answer type

Let 11ˆˆˆˆ ˆ ˆ, OP i j k OQ i j k−−=+ += ++ and 1ˆˆˆ2OR i j k=++ be three vectors, where ,0− and O denotes the origin. If ()0OP OQ OR = and the point (, , 2 ) lies on the plane 33 0 ,xy z l+− + =then the value of l is ________.

Numerical answer type

Let Xbe a random variable, and let ()PX x= denote the probability that X takes the value .xSuppose that the points (),( )xPX x=, 0,1, 2,3, 4,x=lie on a fixed straight line in the xy-plane, and () 0PX x==for all 0,1,2,3,4 .x− If the mean of Xis 52, and the variance of Xis ,then the value of 24is ______.

Numerical answer type

Let and  be the distinct roots of the equation 21 0.xx+−= Consider the set 1, , .T= For a 33matrix ()33,ijMa= define 123ii i iRa a a=++ and 123jjjjCaa a=++ for 1, 2, 3i=and1,2,3.j= Match each entry in List-I to the correct entry in List-II. List-I List-II (P) The number of matrices ()33ijMa=with all entries in Tsuch that 0ijRC== for all , ,ij is (1) 1 (Q) The number of symmetric matrices ()33ijMa= with all entries in Tsuch that 0 for all ,jCj= is (2) 12 (R) Let ()33ijMa= be a skew symmetric matrix such that ijaTfor ij. Then the number of elements in the set 1223 : , , , 0xx ayx y z M yzz a    =    −   is (3) infinite (S) Let ()33ijMa= be a matrix with all entries in Tsuch that 0 foriR=all .i Then the absolute value of the determinant of M is (4) 6 (5) 0 The correct option is

1. (P) (4) (Q) (2) (R) (5) (S) (1)→→→ →
2. (P) (2) (Q) (4) (R) (1) (S) (5)→→→ →
3. (P) (2) (Q) (4) (R) (3) (S) (5)→→→ →
4. (P) (1) (Q) (5) (R) (3) (S) (4)→→→ →

Let the straight line 2yx= touch a circle with center (0, ), > 0, and radius r at a point 1.A Let 1Bbe the point on the circle such that the line segment 11ABis a diameter of the circle. Let 5 5.r+=+ Match each entry in List-I to the correct entry in List-II. List-I List-II (P)  equals (1) (2 , 4 )− (Q) r equals (2) 5 (R) 1A equals (3) (2 , 6 )− (S) 1B equals (4) 5 (5) (2,4) The correct option is

1. (P) (4) (Q) (2) (R) (1) (S) (3)→→→ →
2. (P) (2) (Q) (4) (R) (1) (S) (3)→→→ →
3. (P) (4) (Q) (2) (R) (5) (S) (3)→→→ →
4. (P) (2) (Q) (4) (R) (3) (S) (5)→→→ →

Let  be such that the lines 111 21 29:123xyzL+++== and 216 11 4:32xyzL+++== intersect. Let 1R be the point of intersection of 1L and 2.L Let (0,0,0),O= and ˆn denote a unit normal vector to the plane containing both the lines 1Land 2.L Match each entry in List-I to the correct entry in List-II. List-I List-II (P) equals (1) ˆˆˆij k−−+ (Q) A possible choice for ˆnis (2) 32 (R) 1OR equals (3) 1 (S) A possible value of 1ˆOR n is (4) 121ˆˆˆ66 6ij k−+ (5) 23 The correct option is

1. (P) (3) (Q) (4) (R) (1) (S) (2)→→→ →
2. (P) (5) (Q) (4) (R) (1) (S) (2)→→→ →
3. (P) (3) (Q) (4) (R) (1) (S) (5)→→→ →
4. (P) (3) (Q) (1) (R) (4) (S) (5)→→→→

Let :f→ and :g→ be functions defined by 1| | sin , 0, ()0, 0,xx xfxxx== and 112 , 0 , ()20, otherwise .xxgx− = Let ,,, .abcd Define the function :h→ by () 1() () () () () , .2hx af x b gx g x c x gx d gx x=+ + − + − +  Match each entry in List-I to the correct entry in List-II. List-I List-II (P) If 0, 1, 0, and 0,ab c d=== = then (1) his one-one. (Q) If 1, 0, 0, and 0,ab c d=== = then (2) his onto. (R) If 0, 0, 1, and 0,abc d=== = then (3) his differentiable on . (S) If 0, 0, 0, and 1,abc d=== = then (4) the range of his 0,1 . (5) the range of his 0,1 . The correct option is

1. (P) (4) (Q) (3) (R) (1) (S) (2)→→→ →
2. (P) (5) (Q) (2) (R) (4) (S) (3)→→→→
3. (P) (5) (Q) (3) (R) (2) (S) (4)→→→→
4. (P) (4) (Q) (2) (R) (1) (S) (3)→→→ →

A dimensionless quantity is constructed in terms of electronic charge 𝑒, permittivity of free space 𝜀0, Planck’s constant ℎ, and speed of light 𝑐. If the dimensionless quantity is written as 𝑒𝛼𝜀0𝛽ℎ𝛾𝑐𝛿 and 𝑛 is a non -zero integer, then (𝛼,𝛽,𝛾,𝛿) is given by

1. (2𝑛,−𝑛,−𝑛,−𝑛)
2. (𝑛,−𝑛,−2𝑛,−𝑛)
3. (𝑛,−𝑛,−𝑛,−2𝑛)
4. (2𝑛,−𝑛,−2𝑛,−2𝑛)

An infinitely long wire , located on the 𝑧-axis, carries a current 𝐼 along the +𝑧-direction and produces the magnetic field 𝐵⃗ . The magnitude of the line integral ∫𝐵⃗ ⋅𝑑𝑙⃗⃗⃗ along a straight line from the point (−√3𝑎,𝑎,0) to (𝑎,𝑎,0) is given by [𝜇0 is the magnetic permeability of free space. ]

1. 7𝜇0𝐼/24
2. 7𝜇0𝐼/12
3. 𝜇0𝐼/8
4. 𝜇0𝐼/6

Two beads, each with charge 𝑞 and mass 𝑚, are on a horizontal , frictionless , non-conducting , circular h oop of radius 𝑅. One of the beads is glued to the hoop at some point , while the other one performs small oscillations about its equilibrium position along the hoop . The square of the angular frequency of the small oscillations is given by [𝜀0 is the permittivity of free space. ]

1. 𝑞2/(4𝜋𝜀0𝑅3𝑚)
2. 𝑞2/(32𝜋𝜀0𝑅3𝑚)
3. 𝑞2/(8𝜋𝜀0𝑅3𝑚)
4. 𝑞2/(16𝜋𝜀0𝑅3𝑚)

A block of mass 5 kg moves along the x-direction subject to the force 𝐹=(−20𝑥+10) N, with the value of 𝑥 in m etre. At time 𝑡=0 s, it is at rest at position 𝑥=1 m. The position and momentum of the block at 𝑡=(𝜋/4) s are

1. −0.5 m, 5 kg m/s
2. 0.5 m, 0 kg m/s
3. 0.5 m, −5 kg m/s
4. −1 m, 5 kg m/s • 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 particle of mass 𝑚 is moving i n a circular orbit und er the influence of the central force 𝐹(𝑟)=−𝑘𝑟, corresponding to the potential energy 𝑉(𝑟)=𝑘𝑟2/2, where 𝑘 is a positive force constant and 𝑟 is the radial distance from the origin. Ac cording to the Bohr’s quantization rule, the angular momentum of the particle is given by 𝐿=𝑛ℏ, where ℏ=ℎ/(2𝜋), ℎ is the Planck’s constant, and 𝑛 a positive integer. If 𝑣 and 𝐸 are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

1. 𝑟2=𝑛ℏ√1 𝑚𝑘
2. 𝑣2=𝑛ℏ√𝑘 𝑚3
3. 𝐿 𝑚𝑟2=√𝑘 𝑚
4. 𝐸=𝑛ℏ 2√𝑘 𝑚

Two uniform strings of mass per unit length 𝜇 and 4 𝜇, and lengt h 𝐿 and 2𝐿, respectively, are joined at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension 𝑇. If we define the frequency 𝜈0=1 2𝐿√𝑇 𝜇 , which of the following statement(s) is(are) correct ?

1. With a node at O , the minimum frequency of vibration of the composite string is 𝜈0.
2. With an antinode at O , the minimum frequency of vibration of the composite string is 2𝜈0.
3. When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes.
4. No vibrational mode with an antinode at O is possible for the composite string.

A glass beaker has a solid, plano -convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index 𝑛 up to the level QPR. If the image of a point object O at a height of ℎ (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?

1. For 𝑛 = 1.42, ℎ=50 cm.
2. For 𝑛 = 1.35, ℎ = 36 cm.
3. For 𝑛 = 1.45, ℎ=65 cm.
4. For 𝑛 = 1.48,ℎ =85 cm.

The specific heat capacity of a substance is temperature dependent and is given by the formula 𝐶 = 𝑘𝑇, where 𝑘 is a constant of suitable dimensions in SI units , and 𝑇 is the absol ute temperature . If the heat required to raise the temperature of 1 kg of the substance from −73 °C to 27 °C is 𝑛𝑘, the value of 𝑛 is _____. [Given: 0 K = −273 °C.]

Numerical answer type

A disc of mass 𝑀 and radius 𝑅 is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference . Another disc of the same mass 𝑀 and radius 𝑅/2 is fixed to the motor’s thin s haft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotate s at a uniform angular speed 𝜔. If the angular sp eed at which the large disc rotate s is 𝜔/𝑛, then the value of 𝑛 is _____.

Numerical answer type

A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio 𝑟=𝐼𝐴/𝐼𝐵 of the intensities of li ght is 2 . If a set of two polar oids having 45° angle between their pass -axes is placed just before point B, then the new value of 𝑟 will be _____.

A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed 𝑣 with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and the source move away from each other at the same speed 𝑣 with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be 𝑛 Hz. The value of 𝑛 is _____.

Numerical answer type

Two large, identical water tanks, 1 and 2, kept on the top of a building of height 𝐻, are filled with water up to height ℎ in each tank. Both the tanks contain an identical hole of small radius on the ir sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are 𝑡1 and 𝑡2, respectively . If 𝐻=(16 9)ℎ, then the ratio 𝑡1/𝑡2 is _____.

Numerical answer type

A thin uniform rod of length 𝐿 and certain mass is kept on a frictionless horizontal table with a massless string of length 𝐿 fixed to one end (top view is shown in the figure) . The other end of the string is pivoted to a point O. If a horizontal impulse 𝑃 is imparted to the rod at a distance 𝑥=𝐿/𝑛 from the mid-point of the rod (see figure) , then the rod and string revolve together around the point O, with the rod remaining aligned with the string . In such a case, the value of 𝑛 is _____.

Numerical answer type

One mole of a monatomic ideal gas undergoes the cyclic process J→ K→ L→ M→ J, as shown in the P -T diagram . Match t he quantities mentioned in List -I with their values in L ist-II and choose the correct option. [ℛ is the gas constant.] List-I List-II (P) Work done in the complete cyclic process (1) ℛ𝑇0−4ℛ𝑇0ln2 (Q) Change in the internal energy of the gas in the process JK (2) 0 (R) Heat given to the gas in the process KL (3) 3ℛ𝑇0 (S) Change in the internal energy of the gas in the process MJ (4) −2ℛ𝑇0ln2 (5) −3ℛ𝑇0ln2

1. P → 1; Q → 3; R → 5; S → 4
2. P → 4; Q → 3; R → 5; S → 2
3. P → 4; Q → 1; R → 2; S → 2
4. P → 2; Q → 5; R → 3; S → 4

Four identical thin, square metal sheets, 𝑆1, 𝑆2, 𝑆3 and 𝑆4, each of side 𝑎 are ke pt parallel to each other with equal distance 𝑑 (≪𝑎) between them , as shown in the figure . Let 𝐶0=𝜀0𝑎2/𝑑, where 𝜀0 is the permittivity of free spa ce. Match t he quantities mentioned in List -I with their values in L ist-II and choose the correct option. List-I List-II (P) The capacitance between 𝑆1 and 𝑆4, with 𝑆2 and 𝑆3 not connected, is (1) 3𝐶0 (Q) The capacitance between 𝑆1 and 𝑆4, with 𝑆2 shorted to 𝑆3, is (2) 𝐶0/2 (R) The capacitance between 𝑆1 and 𝑆3, with 𝑆2 shorted to 𝑆4, is (3) 𝐶0/3 (S) The capacitance between 𝑆1 and 𝑆2, with 𝑆3 shorted to 𝑆1, and 𝑆2 shorted to 𝑆4, is (4) 2𝐶0/3 (5) 2𝐶0

1. P → 3; Q → 2; R → 4; S → 5
2. P → 2; Q → 3; R → 2; S → 1
3. P → 3; Q → 2; R → 4; S → 1
4. P → 3; Q → 2; R → 2; S → 5

A light ray is incident on the surface of a sphere of refractive index 𝑛 at an angle of incidence 𝜃0. The ray partially refracts into the sphere with angle of refraction 𝜙0 and then partly reflect s from the back surface . The reflected ray then emerges out of the sphere after a partial refraction . The total angle of deviation of the emergent ray with respect to the incident ray is 𝛼. Match t he quantities mentioned in List -I with their values in L ist-II and choose the correct option. List-I List-II (P) If 𝑛=2 and 𝛼=180°, then all the possible value s of 𝜃0 will be (1) 30° and 0° (Q) If 𝑛=√3 and 𝛼=180°, then all the possible value s of 𝜃0 will be (2) 60° and 0° (R) If 𝑛=√3 and 𝛼=180°, then all the possible value s of 𝜙0 will be (3) 45° and 0° (S) If 𝑛=√2 and 𝜃0=45°, then all the possible value s of 𝛼 will be (4) 150° (5) 0°

1. P → 5; Q → 2; R→ 1; S→ 4
2. P → 5; Q → 1; R→ 2; S→ 4
3. P → 3; Q → 2; R→ 1; S→ 4
4. P → 3; Q → 1; R→ 2; S→ 5

The circuit shown in the figure contains an i nductor 𝐿, a capacitor 𝐶0, a resistor 𝑅0 and an ideal battery. The circuit also contains two keys K 1 and K 2. Initially, both the keys are open and there is no charge on the capacitor. At an instant , key K 1 is closed and immediately after this the current in 𝑅0 is found to be 𝐼1. After a long time, the current attains a steady state value 𝐼2. Thereafter, K2 is closed and simultaneously K 1 is opened and the voltage across 𝐶0 oscillate s with amplitude 𝑉0 and angular frequency 𝜔0. Match the quantities mentioned in List -I with their values in List -II and choose the correct option. List-I List-II (P) The value of 𝐼1 in Ampere is (1) 0 (Q) The value of 𝐼2 in Ampere is (2) 2 (R) The value of 𝜔0 in kilo -radians/s is (3) 4 (S) The value of 𝑉0 in Volt is (4) 20 (5) 200

1. P → 1; Q → 3; R → 2; S → 5
2. P → 1; Q → 2; R → 3; S → 5
3. P → 1; Q → 3; R → 2; S → 4
4. P → 2; Q → 5; R → 3; S → 4

A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is

1. 2√2∶√3
2. 2√2∶1
3. 1∶2
4. 2∶1

At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid (HNO 2) gives the species

1. H 3O+, NO 3− and NO
2. H 3O+, NO 3− and NO 2
3. H 3O+, NO− and NO 2
4. H 3O+, NO 3− and N 2O

Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is Structures of phenylalanine and aspartic acid are given below.

Among the following options , select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each othe r. [en = H 2NCH 2CH 2NH 2]

1. Set-I: [Ni(CO) 4] and [PdCl 2(PPh 3)2] Set-II: [Co(NH 3)5Cl]SO 4 and [Co(NH 3)5(SO 4)]Cl
2. Set-I: [Co(en)(NH 3)2Cl₂] and [PdCl 2(PPh 3)2] Set-II: [Co(NH 3)6][Cr(CN) 6] and [Cr(NH 3)6][Co(CN) 6]
3. Set-I: [Co(NH 3)3(NO 2)3] and [Co(en) 2Cl₂] Set-II: [Co(NH 3)5Cl]SO 4 and [Co(NH 3)5(SO 4)]Cl
4. Set-I: [Cr(NH 3)5Cl]Cl 2 and [Co(en)(NH 3)2Cl₂] Set-II: [Cr(H 2O)6]Cl 3 and [Cr(H 2O)5Cl]Cl 2∙H₂O • 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.

Among the following, the correct statement(s) for electrons in an atom is(are)

1. Uncertainty principle rules out the existence of definite paths for electrons.
2. The energy of an electron in 2s orbital of an atom is lower than the energy of a n electron that is infinitely far away from the nucleus .
3. According to Bohr’s model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit.
4. According to Bohr’s model, the magnitude of velocity of electrons increases with increase in values of n.

Reaction of iso-propylbenzene with O 2 followed by the treatment with H 3O+ forms phenol and a by-product P. Reaction of P with 3 equivalents of Cl 2 gives compound Q. Treatment of Q with Ca(OH) 2 produces compound R and calcium salt S. The correct statement(s) regarding P, Q, R and S is(are)

1. Reaction of P with R in the presence of KOH followed by acidification gives
2. Reaction of R with O 2 in the presence of light gives phosgene gas
3. Q reacts with aqueous NaOH to produce Cl 3CCH 2OH and Cl 3CCOONa
4. S on heating gives P

The option(s) in which at least three molecules follow Octet Rule is(are)

1. CO 2, C₂H₄, NO and HCl
2. NO 2, O 3, HCl and H 2SO 4
3. BCl 3, NO, NO 2 and H 2SO 4
4. CO 2, BCl 3, O 3 and C 2H4

Consider the following volume −temperature (V −T) diagram for the expansion of 5 moles of an ideal monoatomic gas. Considering only P -V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X→Y→Z is ____ __. [Use the g iven data: Molar heat capacity of the gas for the given temperature range , CV, m = 12 J K⁻¹ mol⁻¹ and gas constant, R = 8.3 J K⁻¹ mol⁻¹]

Numerical answer type

Consider the following reaction, ()()()()22 22H g + 2NO g N g + 2H g O→ which follows the mechanism given below: ()()()11222NO g N O g fast equlibriumkk− ()()()()()222 2 2 2NO g + H g NOg + HOg s l o w r e a ctionk→ ()()()()()322 2 2NOg + H g N g + HOg f a s t reactionk→ The order of the reaction is ______.

Numerical answer type

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH solution, gives P and Q. Compound P does not give Tollens’ test, whereas Q on acidification gives positive Tollens’ test. Treatment of P with excess cyclohexanone in the presence of catalytic amount of p-toluenesulfonic acid (PTSA) gives product R. Sum of the number of methylene groups ( -CH 2-) and oxygen atoms in R is ______.

Numerical answer type

Among V(CO)6, Cr(CO)5, Cu(CO)3, Mn(CO)5, Fe(CO)5, [Co(CO)3]3−, [Cr(CO)4]4−, and Ir(CO)3, the total number of species isoelectronic with Ni(CO)4 is ______. [Given, atomic number: V = 23, Cr = 24, Mn = 25, Fe = 26, Co = 27, Ni = 28, Cu = 29, Ir = 77]

Numerical answer type

In the following reaction sequence, the major product P is formed. Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of Q with excess NaOH followed by the treatment with CaCl2 yields Ca-soap R, quantitatively. Starting with one mole of Q, the amount of R produced in gram is ______. [Given, atomic weight: H = 1, C = 12, N = 14, O = 16, Na = 23, Cl = 35, Ca = 40]

Numerical answer type

Among the following complexes, the total number of diamagnetic species is ____ __. [Mn(NH 3)6]3+, [MnCl 6]3−, [FeF 6]3−, [CoF 6]3−, [Fe(NH 3)6]3+, and [Co(en) 3]3+ [Given, atomic number: Mn = 25, Fe = 26, Co = 27 ; en = H 2NCH 2CH 2NH 2]

Numerical answer type

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition . The limiting ionic conductivity ( Λ0) values (in mS m² mol⁻¹) for different ions in aqueous solutions are given below : Ions Ag+ K+ Na+ H+ NO3− Cl− SO₄²⁻− OH− CH3COO− Λ0 6.2 7.4 5.0 35.0 7.2 7.6 16.0 19.9 4.1 For different combinations of titrates and titrants given in List-I, the graphs of ‘conductance’ versus ‘volume of titrant’ are given in List-II. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. List-I List-II (P) Titrate: KCl Titrant: AgNO 3 (1) (Q) Titrate: AgNO 3 Titrant: KCl (2) (R) Titrate: NaOH Titrant: HCl (3) (S) Titrate: NaOH Titrant: CH 3COOH (4) (5)

1. P-4, Q-3, R-2, S-5
2. P-2, Q-4, R-3, S-1
3. P-3, Q-4, R-2, S-5
4. P-4, Q-3, R-2, S-1

Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option. List-I List-II (P) XeF 2 (1) Trigonal bipyramidal and two lone pair of electrons (Q) XeF 4 (2) Tetrahedral and one lone pair of electrons (R) XeO 3 (3) Octahedral and two lone pair of electrons (S) XeO 3F2 (4) Trigonal bipyramidal and no lone pair of electrons (5) Trigonal bipyramidal and three lone pair of electrons

1. P -5, Q-2, R-3, S-1
2. P -5, Q-3, R-2, S-4
3. P -4, Q-3, R-2, S-1
4. P -4, Q-2, R-5, S-3

List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. List-I List-II (P) (1) (Q) (2) (R) (3) (S) (4) (5)

1. P -3, Q-5, R-4, S-1
2. P -3, Q-2, R-4, S-1
3. P -3, Q-5, R-1, S-4
4. P -5, Q-2, R-4, S-1

List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. List-I List-II (P) (1) (Q) (2) (R) (3) (S) (4) (5)

1. P -2, Q-3, R-4, S-5
2. P -2, Q-3, R-5, S-1
3. P-3, Q-5, R-4, S-1
4. P -3, Q-2, R-5, S-4