JEE Advanced 2025 Paper 1

Let ℝ denote the set of all real numbers. Let 𝑎𝑖,𝑏𝑖∈ℝ for 𝑖∈{1,2,3}. Define the functions 𝑓:ℝ→ℝ,𝑔:ℝ→ℝ, and ℎ:ℝ→ℝ by 𝑓(𝑥)=𝑎1+10𝑥+ 𝑎2𝑥2+𝑎3𝑥3+𝑥4, 𝑔(𝑥)=𝑏1+3𝑥+ 𝑏2𝑥2+𝑏3𝑥3+𝑥4, ℎ(𝑥)=𝑓(𝑥+1)−𝑔(𝑥+2). If 𝑓(𝑥)≠𝑔(𝑥) for every 𝑥∈ ℝ, then the coefficient of 𝑥3 in ℎ(𝑥) is

1. 8
2. 2
3. −4
4. −6

Three students 𝑆1,𝑆2, and 𝑆3 are given a problem to solve. Consider the following events : 𝑈: At least one of 𝑆1,𝑆2, and 𝑆3 can solve the problem, 𝑉: 𝑆1 can solve the problem, given that neither 𝑆2 nor 𝑆3 can solve the problem, 𝑊: 𝑆2 can solve the problem and 𝑆3 cannot solve the problem , 𝑇: 𝑆3 can solve the problem . For any event 𝐸, let 𝑃(𝐸) denote the probability of 𝐸. If 𝑃(𝑈)=1 2 ,𝑃(𝑉)=1 10 ,and 𝑃(𝑊)=1 12 , then 𝑃(𝑇) is equal to

1. 13 36
2. 1 3
3. 19 60
4. 1 4

Let ℝ denote the set of all real numbers. Define the function 𝑓:ℝ→ℝ by 𝑓(𝑥)={2−2𝑥2−𝑥2sin1 𝑥 if 𝑥≠0, 2 if 𝑥=0 . Then which one of the following statements is TRUE?

1. The function 𝑓 is NOT differentiable at 𝑥=0
2. There is a positive real number 𝛿, such that 𝑓 is a decreasing function on the interval (0,𝛿)
3. For any positive real number 𝛿, the function 𝑓 is NOT an increasing function on the interval (−𝛿,0)
4. 𝑥=0 is a point of local minima of 𝑓

Consider the matrix 𝑃=( 200 020 003) . Let the transpose of a matrix 𝑋 be denoted by 𝑋𝑇. Then the number of 3×3 invertible matrices 𝑄 with integer entries , such that 𝑄−1=𝑄𝑇 and 𝑃𝑄=𝑄𝑃 , is

1. 32
2. 8
3. 16
4. 24 • 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 𝐿1 be the line of intersection of the planes given by the equations 2𝑥+3𝑦+𝑧=4 and 𝑥+2𝑦+𝑧=5 . Let 𝐿2 be the line passing through the point 𝑃(2,−1,3) and parallel to 𝐿1. Let 𝑀 denote the plane given by the equation 2𝑥+𝑦−2𝑧=6 . Suppose that the line 𝐿2 meets the plane 𝑀 at the poin t 𝑄. Let 𝑅 be the foot of the perpendicular drawn from 𝑃 to the plane 𝑀 . Then which of the following statements is (are) TRUE?

1. The length of the line segment 𝑃𝑄 is 9√3
2. The length of the line segment 𝑄𝑅 is 15
3. The area of Δ𝑃𝑄𝑅 is 3 2√234
4. The acute angle between the line segment s 𝑃𝑄 and 𝑃𝑅 is cos⁻¹( 1 2√3 )

Let ℕ denote the set of all natural numbers, and ℤ denote the set of all integers . Consider the functions 𝑓:ℕ→ℤ and 𝑔:ℤ→ℕ defined by 𝑓(𝑛)={(𝑛+1)/2 if 𝑛 is odd , (4−𝑛)/2 if 𝑛 is even , and 𝑔(𝑛)={3+2𝑛 if 𝑛 ≥ 0 , −2𝑛 if 𝑛 < 0 . Define (𝑔∘𝑓)(𝑛)=𝑔(𝑓(𝑛)) for all 𝑛∈ℕ, and (𝑓∘𝑔)(𝑛)=𝑓(𝑔(𝑛)) for all 𝑛∈ℤ. Then which of the following statements is (are) TRUE?

1. 𝑔∘𝑓 is NOT one-one and 𝑔∘𝑓 is NOT onto
2. 𝑓∘𝑔 is NOT one-one but 𝑓∘𝑔 is onto
3. 𝑔 is one -one and 𝑔 is onto
4. 𝑓 is NOT one-one but 𝑓 is onto

Let ℝ denote the set of all real numbers. Let 𝑧1=1+2𝑖 and 𝑧2=3𝑖 be two complex numbers, where 𝑖=√−1 . Let 𝑆={(𝑥,𝑦)∈ℝ×ℝ∶ |𝑥+𝑖𝑦−𝑧1|=2|𝑥+𝑖𝑦−𝑧2| }. Then which of the following statements is (are) TRUE?

1. 𝑆 is a circle with centre (−1 3,10 3)
2. 𝑆 is a circle with centre (1 3,8 3)
3. 𝑆 is a circle with radius √2 3
4. 𝑆 is a circle with radius 2√2 3

Let the set of all relations 𝑅 on the set {𝑎,𝑏,𝑐,𝑑,𝑒,𝑓}, such that 𝑅 is reflexive and symmetric, and 𝑅 contains exactly 10 elements , be denoted by 𝒮. Then the number of elements in 𝒮 is _________________.

Numerical answer type

For any two points 𝑀 and 𝑁 in the 𝑋𝑌-plane , let 𝑀𝑁⃗⃗⃗⃗⃗⃗⃗ denote the vector from 𝑀 to 𝑁, and 0⃗ denote the zero vector . Let 𝑃,𝑄 and 𝑅 be three distinct points in the 𝑋𝑌-plane. Let 𝑆 be a point inside the triangle Δ𝑃𝑄𝑅 such that 𝑆𝑃⃗⃗⃗⃗ +5 𝑆𝑄⃗⃗⃗⃗⃗ +6 𝑆𝑅⃗⃗⃗⃗⃗ =0⃗ . Let 𝐸 and 𝐹 be the mid -points of the sides 𝑃𝑅 and 𝑄𝑅, respectively. Then the value of length of the line segment 𝐸𝐹 length of the line segment 𝐸𝑆 is _______________ .

Numerical answer type

Let 𝑆 be the set of all seven -digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in 𝑆, but 0210222 is NOT in 𝑆. Then the number of elements 𝑥 in 𝑆 such that at least one of the digits 0 and 1 appears exactly twice in 𝑥, is equal to ____________.

Let 𝛼 and 𝛽 be the real numbers such that lim 𝑥→0 1 𝑥3(𝛼 2∫1 1−𝑡2𝑑𝑡+𝛽𝑥cos𝑥 𝑥 0)=2 . Then the value of 𝛼+𝛽 is __________ .

Numerical answer type

Let ℝ denote the set of all real numbers. Let 𝑓:ℝ→ℝ be a function such that 𝑓(𝑥)>0 for all 𝑥∈ℝ , and 𝑓(𝑥+𝑦)=𝑓(𝑥)𝑓(𝑦) for all 𝑥,𝑦∈ℝ. Let the real numbers 𝑎1,𝑎2,…,𝑎50 be in an arithmetic progression . If 𝑓(𝑎31)=64𝑓(𝑎25), and ∑𝑓(𝑎𝑖)=3(225+1)50 𝑖=1 , then the value of ∑𝑓(𝑎𝑖)30 𝑖=6 is _________________ .

Numerical answer type

For all 𝑥>0, let 𝑦1(𝑥),𝑦2(𝑥), and 𝑦3(𝑥) be the functions satisfying 𝑑𝑦1 𝑑𝑥−(sin𝑥)2𝑦1=0, 𝑦1(1)=5 , 𝑑𝑦2 𝑑𝑥−(cos𝑥)2𝑦2=0,𝑦2(1)=1 3 , 𝑑𝑦3 𝑑𝑥−(2−𝑥3 𝑥3)𝑦3=0, 𝑦3(1)=3 5𝑒 , respectively. Then lim 𝑥→0+𝑦1(𝑥)𝑦2(𝑥)𝑦3(𝑥)+2𝑥 𝑒3𝑥sin𝑥 is equal to ______________.

Consider the following frequency distribution : Value 4 5 8 9 6 12 11 Frequency 5 𝑓1 𝑓2 2 1 1 3 Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For th e given frequency distribution, let 𝛼 denote the mean deviation about the mean, 𝛽 denote the mean deviation about the median, and 𝜎2 denote the variance. Match each entry in List -I to the correct entr y in List -II and choose the correct option. List-I List-II (P) 7𝑓1+9𝑓2 is equal to (1) 146 (Q) 19𝛼 is equal to (2) 47 (R) 19𝛽 is equal to (3) 48 (S) 19𝜎2 is equal to (4) 145 (5) 55

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

Let ℝ denote the set of all real numbers. For a real number 𝑥, let [𝑥] denote the greatest integer less than or equal to 𝑥. Let 𝑛 denote a natural number. Match each entry in List -I to the correct entry in List -II and choose the correct option. List-I List-II (P) The minimum value of 𝑛 for which the function 𝑓(𝑥)=[10𝑥3−45𝑥2+60𝑥+35 𝑛] is continuous on the interval [1,2], is (1) 8 (Q) The minimum value of 𝑛 for which 𝑔(𝑥)=(2𝑛2−13𝑛−15)(𝑥3+3𝑥), 𝑥∈ℝ, is an increasing function on ℝ, is (2) 9 (R) The smallest natural number 𝑛 which is greater than 5, such that 𝑥=3 is a point of local minima of ℎ(𝑥)=(𝑥2−9)𝑛(𝑥2+2𝑥+3), is (3) 5 (S) Number of 𝑥0∈ℝ such that 𝑙(𝑥)=∑(sin|𝑥−𝑘|+cos|𝑥−𝑘+1 2|)4 𝑘=0, (4) 6 𝑥∈ℝ , is NOT differentiable at 𝑥0, is (5) 10

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

Let 𝑤⃗⃗ =𝑖̂+𝑗̂−2𝑘̂, and 𝑢⃗ and 𝑣 be two vectors , such that 𝑢⃗ ×𝑣 = 𝑤⃗⃗ and 𝑣 ×𝑤⃗⃗ =𝑢⃗ . Let 𝛼,𝛽,𝛾, and 𝑡 be real numbers such that 𝑢⃗ =𝛼𝑖̂+𝛽𝑗̂+𝛾𝑘̂, −𝑡 𝛼+𝛽+𝛾=0, 𝛼−𝑡 𝛽+𝛾=0, and 𝛼+𝛽−𝑡 𝛾=0. Match each entry in List -I to the correct entry in List -II and choose the correct option. List-I List-II (P) |𝑣 |2 is equal to (1) 0 (Q) If 𝛼=√3 , then 𝛾2 is equal to (2) 1 (R) If 𝛼=√3 , then (𝛽+𝛾)2 is equal to (3) 2 (S) If 𝛼=√2 , then 𝑡+3 is equal to (4) 3 (5) 5

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

The center of a disk of radius 𝑟 and mass 𝑚 is attached to a spring of spring constant 𝑘, inside a ring of radius 𝑅>𝑟 as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping . The spring can only b e stretched or compressed along the periphery of the ring , following the Hooke’s law . In equilibrium , the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as 𝑇=2𝜋 𝜔. The correct expression for 𝜔 is (𝑔 is the acceleration due to gravity):

1. √2 3(𝑔 𝑅−𝑟+𝑘 𝑚)
2. √2𝑔 3(𝑅−𝑟)+𝑘 𝑚
3. √1 6(𝑔 𝑅−𝑟+𝑘 𝑚)
4. √1 4(𝑔 𝑅−𝑟+𝑘 𝑚)

In a scattering experiment, a particle of mass 2𝑚 collides with another particle of mass 𝑚, which is initially at rest . Assuming the collision to be perfectly elastic , the maximum angular deviation 𝜃 of the heavier particle , as shown in the figure , in radian s is:

1. 𝜋
2. tan−1(1 2)
3. 𝜋 3
4. 𝜋 6

A conducting square loop initially lies in the 𝑋𝑍 plane with its lower edge hinged along the 𝑋-axis. Only i n the region 𝑦≥0, there is a time dependent magnetic field pointing along the 𝑍-direction, 𝐵⃗ (𝑡)=𝐵0(cos𝜔𝑡)𝑘̂, where 𝐵0 is a constant . The magnet ic field is zero everywhere else. At time 𝑡=0, the loop starts rotating with constant angular speed 𝜔 about the 𝑋 axis in the clockwise direction as viewed from the +𝑋 axis (as shown in the figure ). Ignoring self -inductance of the loop and gravity , which of the following plots correctly represent s the induced e.m.f. (𝑉) in the loop as a function of time :

Figure 1 show s the configuration of main scale and Vernier scale before measurement . Fig. 2 shows the configuration corresponding to the measurement of diameter 𝐷 of a tube. The measured value of 𝐷 is:

1. 0.12 cm
2. 0.11 cm
3. 0.13 cm
4. 0.14 cm • 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 conducting square loop of side 𝐿, mass 𝑀 and resistance 𝑅 is moving in the 𝑋𝑌 plane with its edges parallel to the 𝑋 and 𝑌 axes. The region 𝑦≥0 has a uniform magnetic field, 𝐵⃗ =𝐵0𝑘̂. The magnetic field is zero everywhere else . At time 𝑡=0, the loop starts to enter the magnetic field with an initial velocity 𝑣0𝑗̂ m/s, as shown in the figure . Consider ing the quantity 𝐾=𝐵02𝐿2 𝑅𝑀 in appropriate unit s, ignoring self-inductance of the loop and gravity , which of the following statements is/are correct :

1. If 𝑣0=1.5𝐾𝐿, the loop will stop before it enters completely in side the region of magnetic field.
2. When the complete loop is inside the region of magnetic field, the net force acting on the loop is zero .
3. If 𝑣0=𝐾𝐿 10, the loop comes to rest at 𝑡=(1 𝐾)ln(5 2).
4. If 𝑣0=3𝐾𝐿, the complete loop enters inside the region of magnetic field at time 𝑡=(1 𝐾)ln(3 2).

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm, 0.05 mm, and 6.0 𝜇m, respectively . Which of the following option(s) give(s) the volume of the strip in cm³ with correct significant figures :

1. 3.2×10−5
2. 32.0×10−6
3. 3.0×10−5
4. 3×10−5

Consider a system of three connected strings, 𝑆1,𝑆2 and 𝑆3 with uniform linear mass densities 𝜇 kg/m, 4𝜇 kg/m and 16𝜇 kg/m, respectively, as shown in the figure . 𝑆1 and 𝑆2 are connected at the point 𝑃, whereas 𝑆2 and 𝑆3 are connected at the point 𝑄, and the other end of 𝑆3 is connected to a wall. A wave generator O is connected to the free end of 𝑆1. The wave from th e generator is represented by 𝑦=𝑦0cos(𝜔𝑡−𝑘𝑥) cm, where 𝑦0, 𝜔 and 𝑘 are constants of appropriate dimensions. Which of the following statements is/are correct:

1. When the wave r eflects from 𝑃 for the first time , the reflected wave is represented by 𝑦=𝛼1y0 cos(𝜔𝑡+𝑘𝑥+𝜋) cm, where 𝛼1 is a positive constant.
2. When the wave transmits through 𝑃 for the first time , the transmitted wave is represented by 𝑦=𝛼2y0 cos(𝜔𝑡−𝑘𝑥) cm, where 𝛼2 is a positive constant.
3. When the wave reflects from 𝑄 for the first time , the reflected wave is represented by 𝑦=𝛼3y0 cos(𝜔𝑡−𝑘𝑥+𝜋) cm, where 𝛼3 is a positive constant.
4. When the wave transmits through 𝑄 for the first time , the transmitted wave is represented by 𝑦=𝛼4y0 cos(𝜔𝑡−4𝑘𝑥) cm, where 𝛼4 is a positive constant.

A person sitting inside a n elevator performs a weighing experiment with an object of mass 50 kg. Suppose that t he variation of the height 𝑦 (in m) of the elevator , from the ground , with time 𝑡 (in s) is given by 𝑦=8[1+sin(2𝜋𝑡 𝑇)], where 𝑇=40𝜋 s. Taking acceleration due to gravity, 𝑔= 10 m/s2, the maximum variation of the object’s weight (in N) as observed in the experiment is ____

Numerical answer type

A cube of unit volume contains 35×107 photons of frequency 1015 Hz. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume , then the amplitude of the magnetic field is 𝛼×10−9 T. Taking permeability of free space 𝜇0=4𝜋×10⁻⁷ Tm/A , Planck’s constant ℎ=6×10⁻³4Js and 𝜋=22 7, the value of 𝛼 is____

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures TP and TQ, respectively, with TQ<TP, as shown in Fig. 1 . The radiated power transferred per unit area from P to Q is 𝑊0. Subsequently, two more plates , identical to P and Q , are introduced between P and Q , as shown in Fig. 2 . Assum e that heat transfer takes place only between adjacent plates . If the power trans ferred per unit area in the direction from P to Q (Fig. 2) in the steady state is 𝑊𝑆, then the ratio 𝑊0 𝑊𝑆 is ___

Numerical answer type

A solid glass sphere of refractive index 𝑛=√3 and radius 𝑅 contains a spherical air cavity of radius 𝑅 2, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index 𝑛=1) remains inside the glass sphere. An unpolarized , unidirectional and monochromatic light source 𝑆 emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere . If the light is reflected from the point O and is fully polarized , then the angle of incidence at the inner surface of the glass sphere is 𝜃. The value of sin𝜃 is ____

Numerical answer type

A single slit diffraction experiment is performed to determine the slit width using the equation , 𝑏𝑑 𝐷= 𝑚λ, where 𝑏 is the slit width, 𝐷 the shortest distance between the slit and the screen , 𝑑 the distance between the 𝑚th diffraction maxim um and the central maximum , and λ is the wavelength . 𝐷 and 𝑑 are measured with scales of least count of 1 cm and 1 mm, respectively. The value s of λ and 𝑚 are known precisely to be 600 nm and 3, respectively . The absolute error (in 𝜇m) in the value of 𝑏 estimated using the diffraction maxim um that occurs for 𝑚=3 with 𝑑= 5 mm and 𝐷=1 m is ___

Numerical answer type

Consider an electron in the 𝑛=3 orbit of a hydrogen -like atom with atomic number 𝑍. At absolute temperature 𝑇, a neutron having thermal energy 𝑘B𝑇 has the same de Broglie wavelength as that of this electron . If this temperature is given by 𝑇=𝑍2ℎ2 𝛼𝜋2𝑎02𝑚N𝑘B , (where ℎ is the Planck’s constant, 𝑘𝐵 is the Boltzmann constant, 𝑚N is the mass of the neutron and 𝑎0 is the first Bohr radius of hydrogen atom) then the value of 𝛼 is ___

Numerical answer type

List-I shows four configurations, each consisting of a pair of ideal electric dipole s. Each dipole has a dipole moment of magnitude 𝑝, oriented as marked by arrows in the figures . In all the configurations the dipoles are fixed such that they are at a distance 2 𝑟 apart along the 𝑥 direction. The midpoint of the line joining the two dipoles is 𝑋. The possible resultant electric field s 𝐸⃗ at 𝑋 are given in List-II. Choose the option that describes the correct match between the entries in List -I to those in List -II. List-I List-II (P) (1) 𝐸⃗ = 0 (Q) (2) 𝐸⃗ =−𝑝 2𝜋𝜖0𝑟3𝑗̂ (R) (3) 𝐸⃗ =−𝑝 4𝜋𝜖0𝑟3(𝑖̂−𝑗̂) (S) (4) 𝐸⃗ =𝑝 4𝜋𝜖0𝑟3(2𝑖̂−𝑗̂) (5) 𝐸⃗ =𝑝 𝜋𝜖0𝑟3𝑖̂

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

A circuit with a n electrical load having impedance 𝑍 is connected with an AC source as shown in the diagram. The source voltage varies in time as 𝑉(𝑡)=300sin(400𝑡) V, where 𝑡 is time in s. List-I shows various options for the load . The possible current s 𝑖(𝑡) in the circuit as a function of time are given in List -II. Choose the option that describes the correct match between the entries in List -I to those in List - II. List-I List-II (P) (1) (Q) (2) (R) (3) (S) (4) (5)

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

List-I shows various functional dependenc ies of energy (𝐸) on the atomic number (𝑍). Energies associated with certain phenomena are given in List -II. Choose the option that describes the correct match between the entries in List -I to those in List - II. List-I List-II (P) 𝐸∝𝑍2 (1) energy of characteristic x -rays (Q) 𝐸∝(𝑍−1)2 (2) electrostatic part of the nuclear binding energy for stable nuclei with mass number s in the range 30 to 170 (R) 𝐸∝𝑍(𝑍−1) (3) energy of continuous x -rays (S) 𝐸 is practically independent of 𝑍 (4) average nuc lear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170 (5) energy of radiation due to electronic transition s from hydrogen -like atoms

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

The h eating of NH 4NO 2 at 60−70 C and NH 4NO 3 at 200−250 C is associated with the formation of nitrogen containing compounds X and Y, respectively. X and Y, respectively , are

1. N₂ and N 2O
2. NH 3 and NO 2
3. NO and N 2O
4. N₂ and NH 3

The correct order of the wavelength maxima of the absorption band in the u ltraviolet -visible region for the given complexes is

1. [Co(CN) 6]3− < [Co(NH 3)6]3+ < [Co(NH 3)5(H₂O)]3+ < [Co(NH 3)5(Cl)]2+
2. [Co(NH 3)5(Cl)]2+ < [Co(NH 3)5(H₂O)]3+ < [Co(NH 3)6]3+ < [Co(CN) 6]3−
3. [Co(CN) 6]3− < [Co(NH 3)5(Cl)]2+ < [Co(NH 3)5(H₂O)]3+ < [Co(NH 3)6]3+
4. [Co(NH 3)6]3+ < [Co(CN) 6]3− < [Co(NH 3)5(Cl)]2+ < [Co(NH 3)5(H₂O)]3+

One of the products formed from t he reaction of permanganate ion with iodide ion in neutral aqueous medium is

1. I₂
2. IO3−
3. IO4−
4. IO2−

Consider the depicted hydrogen (H) in the hydrocarbons given below . The most acidic hydrogen (H) is

1. H
2. H
3. H
4. H • 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.

Regarding the molecular orbital (MO) energy level s for homonuclear diatomic molecules, the INCORRECT statement(s) is(are)

1. Bond order of Ne2 is zero.
2. The highest occupied molecular orbital (HOMO) of F2 is σ-type.
3. Bond energy of O₂+ is smaller than the bond energy of O₂.
4. Bond length of Li2 is larger than the bond length of B2.

The pair(s) of diamagnetic ions is (are)

1. La3+, Ce4+
2. Yb2+, Lu3+
3. La2+, Ce3+
4. Yb3+, Lu2+

For the reaction sequence given below, the correct statement(s) is(are) P QHBr Finkelstein reaction Swarts reaction R (In the options, X is any atom other than carbon and hydrogen , and it is different in P, Q and R)

1. C−X bond length in P, Q and R follows the order Q > R > P.
2. C−X bond enthalpy in P, Q and R follows the order R > P > Q.
3. Relative reactivity toward SN2 reaction in P, Q and R follows the order P > R > Q.
4. pKa value of the conjugate acids of the leaving group s in P, Q and R follows the order R > Q > P.

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to Cr³⁺. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of Cr³⁺ is ______ . Use: 1 Faraday =96500 °C mol⁻¹

Numerical answer type

At 25 ℃, the concentration of H+ ions in 1.00×10⁻³ M aqueous solution of a weak monobasic acid having acid dissociation constant (Ka) of 4.00 ×10⁻¹¹ is 𝑿×10⁻⁷ M. The value of 𝑿 is ______ . Use: Ionic product of water ( Kw) =1.00×10⁻¹⁴ at 25 ℃

Numerical answer type

Molar volume (Vm) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with Vm as the variable . The ratio (in mol dm−3) of the coefficient of 𝑉m² to the coefficient of Vm for a gas having van der Waals c onstants a = 6.0 dm6 atm mol−2 and b = 0.060 dm³ mol⁻¹ at 300 K and 300 atm is ______ . Use: Universal gas constant (R) =0.082 dm³ atm mol⁻¹ K⁻¹

Numerical answer type

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ______ . Use: Universal gas constant (R) =8.3 J K⁻¹ mol⁻¹; Atomic mass (in amu ): H = 1, O = 16

Numerical answer type

The monomer ( X) involved in the synthesis of Nylon 6,6 gives positive carbylamine test. If 10 moles of X are analyzed using Dumas method, the amount (in grams) of nitrogen gas evolved is ______ . Use: Atomic mass of N (in amu) = 14

Numerical answer type

The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parenthese s. The amount (in grams) of S produced is ______ . Use: Atomic mass (in amu ): H = 1, C = 12, O = 16, Br = 80

Numerical answer type

The correct m atch of the group reagents in List-I for precipitating the metal ion given in List-II from solution s, is List-I List-II (P) Passing H 2S in the presence of NH 4OH (1) Cu²⁺ (Q) (NH 4)2CO 3 in the presence of NH 4OH (2) Al³⁺ (R) NH 4OH in the presence of NH 4Cl (3) Mn²⁺ (S) Passing H 2S in the presence of dilute HCl (4) Ba²⁺ (5) Mg²⁺

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

The major products obtained from the reaction s in List-II are the reactants for the named reactions mentioned in List-I. Match each entry in List-I with the appropriate entry in List-II and c hoose the correct option . List-I List-II (P) Stephen reaction (1) (i) CrO2Cl₂/CS2 (ii) H3O+ Toluene (Q) Sandmeyer reaction (2) Benzoic acid(i) PCl₅ (ii) NH₃ (iii) P₄O₁₀,  (R) Hoffmann bromamide degradation reaction (3) (S) Cannizzaro reaction (4) (5) (i) (CH3CO)2O, Pyridine (ii) HNO₃, H₂SO₄, 288 K (iii) aq. NaOHAniline

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

Match the compounds in List-I with the appropriate observations in List-II and c hoose the correct option . List-I List-II (P) H NNH2 OOMeO HO (1) Reaction with phenyl diazonium salt gives yellow dye. (Q) H NNH OOMeO O (2) Reaction w ith ninhydrin gives purple colo r and it also reacts with FeCl 3 to give violet color. (R) NH₃+Cl− (3) Reaction with glucose will give corresponding hydrazo ne. (S) (4) Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous FeCl 3 gives blood red colo r. (5) After complete hydrolysis, it will give ninhydrin test and it DOES NOT give positive phthalein dye test.

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