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JEE Main 2 April 2026 Shift 1 Question Paper with Answers

2 April 2026 · April session · 73 questions

73 of the 75 questions from the JEE Main 2 April 2026 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

2 questions are held back from this paper while we re-check the transcription or the answer key. We would rather show you nothing than show you an answer we are not confident is right.

Physics
24
Chemistry
25
Mathematics
24

Physics — JEE Main 2 April 2026 Shift 1

Q1·PhysicsSingle correct
The dimensional formula of 12ϵ0E2\frac{1}{2}\epsilon_{0}E^{2}21​ϵ0​E2 (ϵ0\epsilon_{0}ϵ0​ = permittivity of vacuum and EEE = electric field) is MaLbTcM^{a}L^{b}T^{c}MaLbTc. The value of 2a−b+c2a - b + c2a−b+c = ______.
  1. (A)0
  2. (B)1
  3. (C)−1
  4. (D)2

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is α×109\alpha \times 10^{9}α×109 N/m2^{2}2. The value of α\alphaα is ______. (Ignore the contribution of the load to Young's modulus error calculation)
  1. (A)1.3
  2. (B)1.65
  3. (C)0.13
  4. (D)0.25

Correct answer: (B)

Step-by-step solution →
Q3·PhysicsSingle correct
The velocity of a particle is given as v⃗=−xi^+2yj^−zk^\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}v=−xi^+2yj^​−zk^ m/s. The magnitude of acceleration at point (1,2,4)(1, 2, 4)(1,2,4) is ______ m/s2^{2}2.
  1. (A)6\sqrt{6}6​
  2. (B)9
  3. (C)33\sqrt{33}33​
  4. (D)0

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
The position of an object having mass 0.1 kg as a function of time ttt is given as r⃗=(10t2i^+5t3j^)\vec{r} = \left(10t^{2}\hat{i} + 5t^{3}\hat{j}\right)r=(10t2i^+5t3j^​) m. At t=1t = 1t=1 s, which of the following statements are correct? A. The linear momentum p⃗=(2i^+1.5j^)\vec{p} = \left(2\hat{i} + 1.5\hat{j}\right)p​=(2i^+1.5j^​) kg·m/s. B. The force acting on the object F⃗=(2i^+3j^)\vec{F} = \left(2\hat{i} + 3\hat{j}\right)F=(2i^+3j^​) N. C. The angular momentum of the object about its origin L⃗=15k^\vec{L} = 15\hat{k}L=15k^ J·s. D. The torque acting on the object about its origin τ⃗=20k^\vec{\tau} = 20\hat{k}τ=20k^ N·m. Choose the correct answer from the options given below :
  1. (A)A, B and C only
  2. (B)B, C and D only
  3. (C)A, C and D only
  4. (D)A, B and D only

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
A planet (P1)(P_{1})(P1​) is moving around the star of mass 2M2M2M in the orbit of radius RRR. Another planet (P2)(P_{2})(P2​) is moving around another star of mass 4M4M4M in a orbit of radius 2R2R2R. Ratio of time periods of revolution of P2P_{2}P2​ and P1P_{1}P1​ is ______.
  1. (A)12\frac{1}{2}21​
  2. (B)2
  3. (C)4
  4. (D)14\frac{1}{4}41​

Correct answer: (B)

Step-by-step solution →
Q6·PhysicsSingle correct
A particle is rotating in a circular path and at any instant its motion can be described as θ=5t440−t33\theta = \frac{5t^{4}}{40} - \frac{t^{3}}{3}θ=405t4​−3t3​. The angular acceleration of the particle after 10 seconds is ______ rad/s2^{2}2.
  1. (A)150
  2. (B)120
  3. (C)130
  4. (D)170

Correct answer: (C)

Step-by-step solution →
Q7·PhysicsSingle correct
A parallel plate air capacitor has a capacitance CCC. When it is half filled as show in figure with a dielectric constant K=5K = 5K=5, the percentage increase in the capacitance is ______.
  1. (A)33.34
  2. (B)66.67
  3. (C)200
  4. (D)400

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
Heat is supplied to a diatomic gas at constant pressure. Then the ratio of ΔQ:ΔU:ΔW\Delta Q : \Delta U : \Delta WΔQ:ΔU:ΔW is ______.
  1. (A)2 : 3 : 5
  2. (B)5 : 3 : 2
  3. (C)2 : 5 : 7
  4. (D)7 : 5 : 2

Correct answer: (D)

Step-by-step solution →
Q9·PhysicsSingle correct
Two charged conducting spheres S1S_{1}S1​ and S2S_{2}S2​ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1S_{1}S1​ and S2S_{2}S2​ spheres are ES1E_{S_{1}}ES1​​ and ES2E_{S_{2}}ES2​​ respectively. The value of ES1ES2\frac{E_{S_{1}}}{E_{S_{2}}}ES2​​ES1​​​ is ______.
  1. (A)32\frac{3}{2}23​
  2. (B)23\frac{2}{3}32​
  3. (C)49\frac{4}{9}94​
  4. (D)94\frac{9}{4}49​

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
The equation of a plane progressive wave is given by y=5cos⁡π(200t−x150)y = 5\cos\pi\left(200t - \frac{x}{150}\right)y=5cosπ(200t−150x​) where xxx and yyy are in cm and ttt is in second. The velocity of the wave is ______ m/s.
  1. (A)120
  2. (B)150
  3. (C)200
  4. (D)300

Correct answer: (D)

Step-by-step solution →
Q11·PhysicsSingle correct
Two short electric dipoles AAA and BBB having dipole moment p1p_{1}p1​ and p2p_{2}p2​ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point xxx is making an angle of 60° with the line joining points OOO and xxx. The ratio of the dipole moments p2/p1p_{2}/p_{1}p2​/p1​ is ______.
  1. (A)32\frac{\sqrt{3}}{2}23​​
  2. (B)232\sqrt{3}23​
  3. (C)13\frac{1}{\sqrt{3}}3​1​
  4. (D)3\sqrt{3}3​

Correct answer: (B)

Step-by-step solution →
Q12·PhysicsSingle correct
When a coil is placed in a time dependent magnetic field the power dissipated in it is PPP. The number of turns, area of the coil and radius of the coil wire are NNN, AAA and rrr respectively. For a second coils number of turns, area of the coil and radius of the coil wire are 2N2N2N, 2A2A2A and 3r3r3r respectively. When the first coil is replaced with second coil the power dissipated in it is 2 αP\sqrt{2}\,\alpha P2​αP. The value of α\alphaα is ______.
  1. (A)36
  2. (B)1282128\sqrt{2}1282​
  3. (C)16
  4. (D)64

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B1B_{1}B1​ and B2B_{2}B2​ respectively, then the ratio B1B2\frac{B_{1}}{B_{2}}B2​B1​​ is ________.
  1. (A)2+π1+π\frac{2+\pi}{1+\pi}1+π2+π​
  2. (B)1+π1−π\frac{1+\pi}{1-\pi}1−π1+π​
  3. (C)2+π1−π\frac{2+\pi}{1-\pi}1−π2+π​
  4. (D)1+π2−π\frac{1+\pi}{2-\pi}2−π1+π​

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be ________.
  1. (A)3 : 4
  2. (B)3 : 2
  3. (C)2 : 1
  4. (D)1 : 2

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
Refer the figure given below. μ1\mu_{1}μ1​ and μ2\mu_{2}μ2​ are refractive indices of air and lens material. The height of image will be ________ cm.
  1. (A)1
  2. (B)0.5
  3. (C)1.2
  4. (D)0.25

Correct answer: (A)

Step-by-step solution →
Q16·PhysicsSingle correct
For a certain metal, when monochromatic light of wavelength λ is incident, the stopping potential for photoelectrons is 3V03V_{0}3V0​. When the same metal is illuminated by light of wavelength 2λ, then the stopping potential becomes V0V_{0}V0​. The threshold wavelength for photoelectric emission for the given metal is αλ. The value of α is ________.
  1. (A)1
  2. (B)4
  3. (C)2
  4. (D)3

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
An electromagnetic wave travelling in xxx-direction is described by field equation Ey=300sin⁡ω(t−xc)E_{y} = 300 \sin \omega \left( t - \frac{x}{c} \right)Ey​=300sinω(t−cx​). If the electron is restricted to move in yyy-direction only with speed of 1.5×1061.5 \times 10^{6}1.5×106 m/s then ratio of maximum electric and magnetic forces acting on the electron is ________.
  1. (A)200
  2. (B)150
  3. (C)400
  4. (D)300

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
Angular momentum of an electron in a hydrogen atom is 3hπ\frac{3h}{\pi}π3h​, then the energy of the electron is ________ eV.
  1. (A)−1.51
  2. (B)−0.85
  3. (C)−0.38
  4. (D)−0.28

Correct answer: (C)

Step-by-step solution →
Q19·PhysicsSingle correct
A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is α×10−6\alpha \times 10^{-6}α×10−6 J. The value of α is ________. (Take surface tension of liquid = 0.08 N/m)
  1. (A)10
  2. (B)7
  3. (C)8
  4. (D)11

Correct answer: (B)

Step-by-step solution →
Q20·PhysicsNumerical
In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is α×10−2\alpha \times 10^{-2}α×10−2 degrees. The value of α is ________.

Correct answer: 36

Step-by-step solution →
Q21·PhysicsNumerical
A vessel contains 0.150.150.15 m3^{3}3 of a gas at pressure 8 bar and temperature 140 °C with cp=3Rc_{p} = 3Rcp​=3R and cv=2Rc_{v} = 2Rcv​=2R. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. (RRR is gas constant)

Correct answer: 120

Step-by-step solution →
Q22·Physics·Magnetic Field of CurrentNumerical
1 μC charge moving with velocity v⃗=(i^−2j^+3k^)\vec{v} = \left( \hat{i} - 2\hat{j} + 3\hat{k} \right)v=(i^−2j^​+3k^) m/s in the region of magnetic field B⃗=(2i^+3j^−5k^)\vec{B} = \left( 2\hat{i} + 3\hat{j} - 5\hat{k} \right)B=(2i^+3j^​−5k^) T. The magnitude of force acting on it is α×10−6\sqrt{\alpha} \times 10^{-6}α​×10−6 N. The value of α is ________.

Correct answer: 171

Step-by-step solution →
Q23·PhysicsNumerical
A uniform wire of length lll of weight www is suspended from the roof with a weight of WWW at the other end. The stress in the wire at l3\frac{l}{3}3l​ distance from the top is (WA+2γwA)\left( \frac{W}{A} + \frac{2}{\gamma} \frac{w}{A} \right)(AW​+γ2​Aw​), where, AAA is the cross sectional area of the wire. The value of γ is ________.

Correct answer: 3

Step-by-step solution →
Q24·PhysicsNumerical
A tub is filled with water and a wooden cube 10 cm × 10 cm × 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is ________ gram. (Take water density as 1 g/cm3^{3}3 and density of wood as 0.4 g/cm3^{3}3)

Correct answer: 387

Step-by-step solution →

Chemistry — JEE Main 2 April 2026 Shift 1

Q25·ChemistrySingle correct
The mass of iron converted into Fe3O4\mathrm{Fe_{3}O_{4}}Fe3​O4​ by the action of 18 g of steam is : (Given : Molar mass of H, O and Fe are 1, 16 and 56 g mol−1\mathrm{mol^{-1}}mol−1 respectively) Assume iron is present in excess :
  1. (A)2.1 g
  2. (B)4.2 g
  3. (C)21 g
  4. (D)42 g

Correct answer: (D)

Step-by-step solution →
Q26·ChemistrySingle correct
What is the energy (in J atom−1\mathrm{atom^{-1}}atom−1) required for the following process? Li2+(g)→Li3+(g)+e−\mathrm{Li^{2+}(g)} \rightarrow \mathrm{Li^{3+}(g)} + e^{-}Li2+(g)→Li3+(g)+e− (Take the ionization energy for the H atom in the ground state as 2.18×10−182.18 \times 10^{-18}2.18×10−18 J atom−1\mathrm{atom^{-1}}atom−1)
  1. (A)8.72×10−188.72 \times 10^{-18}8.72×10−18
  2. (B)1.962×10−181.962 \times 10^{-18}1.962×10−18
  3. (C)1.962×10−171.962 \times 10^{-17}1.962×10−17
  4. (D)6.54×10−176.54 \times 10^{-17}6.54×10−17

Correct answer: (C)

Step-by-step solution →
Q27·ChemistrySingle correct
Given below are two statements : Statement (I) : The correct sequence of bond lengths in the following species is : O2+<O2<O2−<O22−\mathrm{O_{2}^{+}} < \mathrm{O_{2}} < \mathrm{O_{2}^{-}} < \mathrm{O_{2}^{2-}}O2+​<O2​<O2−​<O22−​ Statement (II) : The correct sequence of number of unpaired electrons in the following species is : O2>O2+>O2−>O22−\mathrm{O_{2}} > \mathrm{O_{2}^{+}} > \mathrm{O_{2}^{-}} > \mathrm{O_{2}^{2-}}O2​>O2+​>O2−​>O22−​ In the light of the above statements, choose the correct answer from the options given below :
  1. (A)Both Statement I and Statement II are true
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is true but Statement II is false
  4. (D)Statement I is false but Statement II is true

Correct answer: (C)

Step-by-step solution →
Q28·ChemistrySingle correct
Consider the following data. (i) 2Al(s)+6HCl(aq)→Al2Cl6(aq)+3H2(g)+12002\mathrm{Al}(s) + 6\mathrm{HCl}(aq) \rightarrow \mathrm{Al_{2}Cl_{6}}(aq) + 3\mathrm{H_{2}}(g) + 12002Al(s)+6HCl(aq)→Al2​Cl6​(aq)+3H2​(g)+1200 kJ/mol (ii) H2(g)+Cl2(g)→2HCl(g)+164\mathrm{H_{2}}(g) + \mathrm{Cl_{2}}(g) \rightarrow 2\mathrm{HCl}(g) + 164H2​(g)+Cl2​(g)→2HCl(g)+164 kJ/mol (iii) HCl(g)+aq→HCl(aq)+83\mathrm{HCl}(g) + aq \rightarrow \mathrm{HCl}(aq) + 83HCl(g)+aq→HCl(aq)+83 kJ/mol (iv) Al2Cl6(s)+aq→Al2Cl6(aq)+663\mathrm{Al_{2}Cl_{6}}(s) + aq \rightarrow \mathrm{Al_{2}Cl_{6}}(aq) + 663Al2​Cl6​(s)+aq→Al2​Cl6​(aq)+663 kJ/mol The enthalpy of formation of anhydrous solid Al2Cl6\mathrm{Al_{2}Cl_{6}}Al2​Cl6​ is :
  1. (A)−648 kJ mol−1\mathrm{mol^{-1}}mol−1
  2. (B)−1350 kJ mol−1\mathrm{mol^{-1}}mol−1
  3. (C)−2002 kJ mol−1\mathrm{mol^{-1}}mol−1
  4. (D)−1527 kJ mol−1\mathrm{mol^{-1}}mol−1

Correct answer: (D)

Step-by-step solution →
Q29·ChemistrySingle correct
19.5 g of fluoro acetic acid (molar mass = 78 g mol−1\mathrm{mol^{-1}}mol−1) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1 °C. What is KaK_{a}Ka​ of fluoro acetic acid? (For water, Kf=1.86K_{f} = 1.86Kf​=1.86 K kg mol−1\mathrm{mol^{-1}}mol−1). Assume molarity and molality to have same values.
  1. (A)10−610^{-6}10−6
  2. (B)4×10−44 \times 10^{-4}4×10−4
  3. (C)3×10−53 \times 10^{-5}3×10−5
  4. (D)3×10−33 \times 10^{-3}3×10−3

Correct answer: (D)

Step-by-step solution →
Q30·ChemistrySingle correct
The solubility product constants of Ag2CrO4\mathrm{Ag_{2}CrO_{4}}Ag2​CrO4​ and AgBr\mathrm{AgBr}AgBr are 32x32x32x and 4y4y4y respectively at 298 K. The value of (molarity of Ag2CrO4molarity of AgBr)\left(\frac{\text{molarity of } \mathrm{Ag_{2}CrO_{4}}}{\text{molarity of } \mathrm{AgBr}}\right)(molarity of AgBrmolarity of Ag2​CrO4​​) can be expressed as :
  1. (A)2x3y\frac{2\sqrt[3]{x}}{y}y23x​​
  2. (B)2xy2\sqrt{\frac{x}{y}}2yx​​
  3. (C)xy\sqrt{\frac{x}{y}}yx​​
  4. (D)x3y\frac{\sqrt[3]{x}}{\sqrt{y}}y​3x​​

Correct answer: (D)

Step-by-step solution →
Q31·ChemistrySingle correct
An electrochemical cell is constructed using half cells in the direction of spontaneous change Fe(OH)2(s)+2e−→Fe(s)+2OH−(aq)\mathrm{Fe(OH)_{2}}(s) + 2e^{-} \rightarrow \mathrm{Fe}(s) + 2\mathrm{OH^{-}}(aq)Fe(OH)2​(s)+2e−→Fe(s)+2OH−(aq) Eθ=−0.88E^{\theta} = -0.88Eθ=−0.88 V and AgBr(s)+e−→Ag(s)+Br−(aq)\mathrm{AgBr}(s) + e^{-} \rightarrow \mathrm{Ag}(s) + \mathrm{Br^{-}}(aq)AgBr(s)+e−→Ag(s)+Br−(aq) Eθ=+0.07E^{\theta} = +0.07Eθ=+0.07 V Which of the following option is correct?
  1. (A)Overall reaction Fe(s)+2OH−(aq)+2AgBr(s)⇌Fe(OH)2(s)+2Ag(s)+2Br−(aq)\mathrm{Fe}(s) + 2\mathrm{OH^{-}}(aq) + 2\mathrm{AgBr}(s) \rightleftharpoons \mathrm{Fe(OH)_{2}}(s) + 2\mathrm{Ag}(s) + 2\mathrm{Br^{-}}(aq)Fe(s)+2OH−(aq)+2AgBr(s)⇌Fe(OH)2​(s)+2Ag(s)+2Br−(aq)
  2. (B)Ecellθ=−0.95E^{\theta}_{cell} = -0.95Ecellθ​=−0.95 V
  3. (C)Fe is reduced in the electrochemical cell
  4. (D)EcellθE^{\theta}_{cell}Ecellθ​ is an extensive property

Correct answer: (A)

Step-by-step solution →
Q32·ChemistrySingle correct
t100%t_{100\%}t100%​ is the time required for the 100% completion of the reaction while t1/2t_{1/2}t1/2​ is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between t100%t_{100\%}t100%​ and t1/2t_{1/2}t1/2​ for zero and first order reactions respectively?
  1. (A)t100%=(t1/2)2t_{100\%} = (t_{1/2})^{2}t100%​=(t1/2​)2 and t100%=(t1/2)−∞t_{100\%} = (t_{1/2})^{-\infty}t100%​=(t1/2​)−∞
  2. (B)t100%=2t1/2t_{100\%} = 2t_{1/2}t100%​=2t1/2​ and t100%=(t1/2)∞t_{100\%} = (t_{1/2})^{\infty}t100%​=(t1/2​)∞
  3. (C)t100%=2t1/2t_{100\%} = 2t_{1/2}t100%​=2t1/2​ and t100%=(2t1/2)2t_{100\%} = (2t_{1/2})^{2}t100%​=(2t1/2​)2
  4. (D)t100%=(t1/2)∞t_{100\%} = (t_{1/2})^{\infty}t100%​=(t1/2​)∞ and t100%=2t1/2t_{100\%} = 2t_{1/2}t100%​=2t1/2​

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
Given below are two statements : Statement (I) : The first ionisation enthalpy of the elements Na, Mg, Cl and Ar follows the order Na > Mg > Cl > Ar. Statement (II) : Among Ca, Al, Fe and B, the third ionisation enthalpy is very high for Ca. In the light of the above statements, choose the correct answer from the options given below :
  1. (A)Both Statement I and Statement II are true
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is true but Statement II is false
  4. (D)Statement I is false but Statement II is true

Correct answer: (D)

Step-by-step solution →
Q34·ChemistrySingle correct
Given below are two statements : Statement (I) : Oxidising power of halogens decreases in the order F2>Cl2>Br2>I2\mathrm{F_{2}} > \mathrm{Cl_{2}} > \mathrm{Br_{2}} > \mathrm{I_{2}}F2​>Cl2​>Br2​>I2​, which is the basis of "Layer test". Statement (II) : "Layer test" to identify Br2\mathrm{Br_{2}}Br2​ and I2\mathrm{I_{2}}I2​ in aqueous solution involves the oxidation of bromide or iodide into Br2\mathrm{Br_{2}}Br2​ or I2\mathrm{I_{2}}I2​ respectively with Cl2\mathrm{Cl_{2}}Cl2​, which is a type of displacement redox reaction. In the light of the above statements, choose the correct answer from the options given below :
  1. (A)Both Statement I and Statement II are true
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is true but Statement II is false
  4. (D)Statement I is false but Statement II is true

Correct answer: (A)

Step-by-step solution →
Q35·ChemistrySingle correct
Which of the following sets includes all the species that will change the orange colour of K2Cr2O7\mathrm{K_{2}Cr_{2}O_{7}}K2​Cr2​O7​ in acidic medium?
  1. (A)Fe2+,Sn2+,I−,S2−\mathrm{Fe^{2+}}, \mathrm{Sn^{2+}}, \mathrm{I^{-}}, \mathrm{S^{2-}}Fe2+,Sn2+,I−,S2−
  2. (B)S2−,Fe3+,I−,C2O42−\mathrm{S^{2-}}, \mathrm{Fe^{3+}}, \mathrm{I^{-}}, \mathrm{C_{2}O_{4}^{2-}}S2−,Fe3+,I−,C2​O42−​
  3. (C)Fe2+,NO2−,SO2,Sn4+\mathrm{Fe^{2+}}, \mathrm{NO_{2}^{-}}, \mathrm{SO_{2}}, \mathrm{Sn^{4+}}Fe2+,NO2−​,SO2​,Sn4+
  4. (D)Fe3+,SO42−,S2−,Sn4+\mathrm{Fe^{3+}}, \mathrm{SO_{4}^{2-}}, \mathrm{S^{2-}}, \mathrm{Sn^{4+}}Fe3+,SO42−​,S2−,Sn4+

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
Match List - I (Chromium (III) Complexes) with List - II (Δ0\Delta_{0}Δ0​ / cm−1\mathrm{cm^{-1}}cm−1). Choose the correct answer from the options given below :
List - I (Chromium (III) Complexes, en = ethylene diamine)List - II ($\Delta_{0}$ / $\mathrm{cm^{-1}}$)
A.[Cr(CN)6]3−[\mathrm{Cr(CN)_{6}}]^{3-}[Cr(CN)6​]3−I.15,060
B.[CrF6]3−[\mathrm{CrF_{6}}]^{3-}[CrF6​]3−II.17,400
C.[Cr(H2O)6]3+[\mathrm{Cr(H_{2}O)_{6}}]^{3+}[Cr(H2​O)6​]3+III.22,300
D.[Cr(en)3]3+[\mathrm{Cr(en)_{3}}]^{3+}[Cr(en)3​]3+IV.26,600
  1. (A)A-I, B-II, C-III, D-IV
  2. (B)A-II, B-III, C-IV, D-I
  3. (C)A-III, B-IV, C-I, D-II
  4. (D)A-IV, B-I, C-II, D-III

Correct answer: (D)

Step-by-step solution →
Q37·ChemistrySingle correct
Given below are two statements : Statement (I) : 1,2,3-Trihydroxypropane can be separated from water by simple distillation. Statement (II) : An azeotropic mixture cannot be separated by fractional distillation. In the light of the above statements, choose the correct answer from the options given below :
  1. (A)Both Statement I and Statement II are true
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is true but Statement II is false
  4. (D)Statement I is false but Statement II is true

Correct answer: (D)

Step-by-step solution →
Q38·ChemistrySingle correct
Given below are two statements : Statement (I) : Benzyl chloride reacts faster in SN1S_{N}1SN​1 mechanism than ethyl chloride. Statement (II) : Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance. In the light of the above statements, choose the correct answer from the options given below :
  1. (A)Both Statement I and Statement II are true
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is true but Statement II is false
  4. (D)Statement I is false but Statement II is true

Correct answer: (A)

Step-by-step solution →
Q39·Chemistry·IUPAC NomenclatureSingle correct
In IUPAC nomenclature, the correct order of decreasing priority of functional group is :
  1. (A)−CONH2, >C=O, −CHO, −NH2, −C≡C−-\mathrm{CONH_{2}},\ >\mathrm{C}=\mathrm{O},\ -\mathrm{CHO},\ -\mathrm{NH_{2}},\ -\mathrm{C}\equiv\mathrm{C}-−CONH2​, >C=O, −CHO, −NH2​, −C≡C−
  2. (B)−CONH2, −COOCH3, −CHO, −NH2, −OH-\mathrm{CONH_{2}},\ -\mathrm{COOCH_{3}},\ -\mathrm{CHO},\ -\mathrm{NH_{2}},\ -\mathrm{OH}−CONH2​, −COOCH3​, −CHO, −NH2​, −OH
  3. (C)−CONH2, −CHO, >C=O, −NH2, −C≡C−-\mathrm{CONH_{2}},\ -\mathrm{CHO},\ >\mathrm{C}=\mathrm{O},\ -\mathrm{NH_{2}},\ -\mathrm{C}\equiv\mathrm{C}-−CONH2​, −CHO, >C=O, −NH2​, −C≡C−
  4. (D)−CONH2, −CHO, −CN, −NH2, −C≡C−-\mathrm{CONH_{2}},\ -\mathrm{CHO},\ -\mathrm{CN},\ -\mathrm{NH_{2}},\ -\mathrm{C}\equiv\mathrm{C}-−CONH2​, −CHO, −CN, −NH2​, −C≡C−

Correct answer: (C)

Step-by-step solution →
Q40·Chemistry·Electronic Effects and StabilitySingle correct
For the given molecule, "xxx", the preferred site for the attack of the electrophile is :
  1. (A)Predominantly at "r"
  2. (B)"r" and "u"
  3. (C)"p" and "s"
  4. (D)Predominantly at "u"

Correct answer: (D)

Step-by-step solution →
Q41·ChemistrySingle correct
Match List - I (Mixture of Compounds) with List - II (Reagent used to distinguish). Choose the correct answer from the options given below :
List - I (Mixture of Compounds)List - II (Reagent used to distinguish)
A.Diethyl amine + Ethyl amineI.Bromine water
B.Acetaldehyde + AcetoneII.CHCl3+KOH\mathrm{CHCl_{3}} + \mathrm{KOH}CHCl3​+KOH, Δ\DeltaΔ
C.Ethanol + PhenolIII.Neutral FeCl3\mathrm{FeCl_{3}}FeCl3​
D.Benzoic acid + Cinnamic acidIV.Ammonical silver nitrate
  1. (A)A-IV, B-II, C-I, D-III
  2. (B)A-IV, B-II, C-III, D-I
  3. (C)A-II, B-IV, C-I, D-III
  4. (D)A-II, B-IV, C-III, D-I

Correct answer: (D)

Step-by-step solution →
Q42·ChemistrySingle correct
Consider the three aromatic molecules (P, Q and R) whose structures have been given below : The correct order regarding the reactivity of these compounds with Ph−N≡NCl(+)(−)Ph-N\equiv NCl^{(-)}_{(+)}Ph−N≡NCl(+)(−)​ under optimum but slightly acidic medium is :
  1. (A)P>Q>RP>Q>RP>Q>R
  2. (B)R>P>QR>P>QR>P>Q
  3. (C)R>Q>PR>Q>PR>Q>P
  4. (D)P>R>QP>R>QP>R>Q

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
Match List - I (Vitamin) with List - II (Name). Choose the correct answer from the options given below :
List - I (Vitamin)List - II (Name)
A.Vitamin B1B_{1}B1​I.Pyridoxine
B.Vitamin B2B_{2}B2​II.Ascorbic acid
C.Vitamin B6B_{6}B6​III.Thiamine
D.Vitamin CIV.Riboflavin
  1. (A)A-II, B-I, C-III, D-IV
  2. (B)A-IV, B-III, C-II, D-I
  3. (C)A-III, B-IV, C-I, D-II
  4. (D)A-I, B-III, C-II, D-IV

Correct answer: (C)

Step-by-step solution →
Q44·ChemistrySingle correct
A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with K2CrO4\mathrm{K_{2}CrO_{4}}K2​CrO4​ to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. HNO3\mathrm{HNO_{3}}HNO3​ and ammonium molybdate, it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively,
  1. (A)Ca2+\mathrm{Ca}^{2+}Ca2+ and SO42−\mathrm{SO_{4}^{2-}}SO42−​
  2. (B)Ba2+\mathrm{Ba}^{2+}Ba2+ and PO43−\mathrm{PO_{4}^{3-}}PO43−​
  3. (C)Mn2+\mathrm{Mn}^{2+}Mn2+ and PO43−\mathrm{PO_{4}^{3-}}PO43−​
  4. (D)Ba2+\mathrm{Ba}^{2+}Ba2+ and SO42−\mathrm{SO_{4}^{2-}}SO42−​

Correct answer: (B)

Step-by-step solution →
Q45·ChemistryNumerical
5.33 g of CrCl3⋅6H2O\mathrm{CrCl_{3}\cdot 6H_{2}O}CrCl3​⋅6H2​O, which is a 1 : 3 electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with AgNO3\mathrm{AgNO_{3}}AgNO3​ results in 8.61 g of AgCl\mathrm{AgCl}AgCl. The ratio of moles of complex reacted and moles of AgCl\mathrm{AgCl}AgCl formed is ________ ×10−2\times 10^{-2}×10−2. (Nearest integer) [Molar mass in g mol−1\mathrm{mol^{-1}}mol−1 Cr : 52, Ag : 108, Cl : 35.5, H : 1, O : 16]

Correct answer: 33

Step-by-step solution →
Q46·ChemistryNumerical
Consider the isomers of hydrocarbon with molecular formula C5H10\mathrm{C_{5}H_{10}}C5​H10​. These isomers do not decolourise KMnO4\mathrm{KMnO_{4}}KMnO4​ solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is ________.

Correct answer: 14

Step-by-step solution →
Q47·ChemistryNumerical
One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is ________.

Correct answer: 17

Step-by-step solution →
Q48·ChemistryNumerical
For reaction A→PA\rightarrow PA→P, rate constant k=1.5×103 s−1k=1.5\times 10^{3}\ \mathrm{s^{-1}}k=1.5×103 s−1 at 27 ∘C27\,^{\circ}\mathrm{C}27∘C. If activation energy for the above reaction is 60 kJ mol−1\mathrm{mol^{-1}}mol−1, then the temperature (in °C) at which rate constant, k=4.5×103 s−1k=4.5\times 10^{3}\ \mathrm{s^{-1}}k=4.5×103 s−1 is ________. (Nearest integer) Given : log⁡2=0.30\log 2=0.30log2=0.30, log⁡3=0.48\log 3=0.48log3=0.48, R=8.3 J K−1 mol−1R=8.3\ \mathrm{J\,K^{-1}\,mol^{-1}}R=8.3 JK−1mol−1, ln⁡10=2.3\ln 10=2.3ln10=2.3

Correct answer: 41

Step-by-step solution →
Q49·ChemistryNumerical
At the transition temperature TTT, A⇌BA\rightleftharpoons BA⇌B and ΔG0=105−35log⁡T\Delta G^{0}=105-35\log TΔG0=105−35logT where AAA and BBB are two states of substance XXX. The transition temperature in °C when pressure is 1 atm is ________. (Nearest integer)

Correct answer: 727

Step-by-step solution →

Mathematics — JEE Main 2 April 2026 Shift 1

Q50·MathematicsSingle correct
Let α, α + 2, α ∈ ℤ, be the roots of the quadratic equation x(x+2)+(x+1)(x+3)+(x+2)(x+4)+…+(x+n−1)(x+n+1)=4nx(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots+(x+n-1)(x+n+1)=4nx(x+2)+(x+1)(x+3)+(x+2)(x+4)+…+(x+n−1)(x+n+1)=4n for some n ∈ ℕ. Then n + α is equal to :
  1. (A)0
  2. (B)1
  3. (C)2
  4. (D)3

Correct answer: (C)

Step-by-step solution →
Q51·MathematicsSingle correct
Let x and y be real numbers such that 50(2x1+3i−y1−2i)=31+17i50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i50(1+3i2x​−1−2iy​)=31+17i, i=−1i=\sqrt{-1}i=−1​. Then the value of 10(x−3y)10(x-3y)10(x−3y) is :
  1. (A)20
  2. (B)31
  3. (C)35
  4. (D)75

Correct answer: (D)

Step-by-step solution →
Q52·MathematicsSingle correct
Let α, β ∈ ℝ be such that the system of linear equations x+2y+z=5x+2y+z=5x+2y+z=5 2x+y+αz=52x+y+\alpha z=52x+y+αz=5 8x+4y+βz=188x+4y+\beta z=188x+4y+βz=18 has no solution. Then βα\frac{\beta}{\alpha}αβ​ is equal to :
  1. (A)−4
  2. (B)4
  3. (C)8
  4. (D)−8

Correct answer: (B)

Step-by-step solution →
Q53·MathematicsSingle correct
Let A=[121α]A=\begin{bmatrix}1 & 2\\ 1 & \alpha\end{bmatrix}A=[11​2α​] and B=[33β2]B=\begin{bmatrix}3 & 3\\ \beta & 2\end{bmatrix}B=[3β​32​]. If A2−4A+I=OA^{2}-4A+I=OA2−4A+I=O and B2−5B−6I=OB^{2}-5B-6I=OB2−5B−6I=O, then among the two statements : (S1): [(B−A)(B+A)]T=[1315710][(B-A)(B+A)]^{T}=\begin{bmatrix}13 & 15\\ 7 & 10\end{bmatrix}[(B−A)(B+A)]T=[137​1510​] and (S2): det⁡(adj⁡(A+B))=−5\det(\operatorname{adj}(A+B))=-5det(adj(A+B))=−5,
  1. (A)only (S1) is correct
  2. (B)only (S2) is correct
  3. (C)both (S1) and (S2) are correct
  4. (D)both (S1) and (S2) are wrong

Correct answer: (B)

Step-by-step solution →
Q54·MathematicsSingle correct
Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A ∩ B, which are divisible by 3, is :
  1. (A)4
  2. (B)5
  3. (C)6
  4. (D)7

Correct answer: (B)

Step-by-step solution →
Q55·MathematicsSingle correct
The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :
  1. (A)15400
  2. (B)17800
  3. (C)16800
  4. (D)29400

Correct answer: (C)

Step-by-step solution →
Q56·MathematicsSingle correct
The number of elements in the set S={(r,k):k∈Z and 36Cr+1=6(35Cr)(k2−3)}S=\left\{(r,k):k\in\mathbb{Z}\ \text{and}\ {}^{36}C_{r+1}=\frac{6\left({}^{35}C_{r}\right)}{(k^{2}-3)}\right\}S={(r,k):k∈Z and 36Cr+1​=(k2−3)6(35Cr​)​}, is :
  1. (A)2
  2. (B)4
  3. (C)8
  4. (D)16

Correct answer: (B)

Step-by-step solution →
Q57·MathematicsSingle correct
If the mean of the data is 21, then kkk is one of the roots of the equation :
Class5 − 1010 − 1515 − 2020 − 2525 − 3030 − 35
Frequency2kkk2854k+1k+1k+15
  1. (A)2x2−23x−10=02x^{2}-23x-10=02x2−23x−10=0
  2. (B)4x2−35x+24=04x^{2}-35x+24=04x2−35x+24=0
  3. (C)2x2−19x−10=02x^{2}-19x-10=02x2−19x−10=0
  4. (D)2x2−35x+98=02x^{2}-35x+98=02x2−35x+98=0

Correct answer: (C)

Step-by-step solution →
Q58·MathematicsSingle correct
Let the mid points of the sides of a triangle ABC be (52,7)\left(\frac{5}{2},7\right)(25​,7), (52,3)\left(\frac{5}{2},3\right)(25​,3) and (4,5)(4,5)(4,5). If its incentre is (h,k)(h,k)(h,k), then 3h+k3h+k3h+k is equal to :
  1. (A)11
  2. (B)12
  3. (C)13
  4. (D)14

Correct answer: (C)

Step-by-step solution →
Q59·MathematicsSingle correct
Let an ellipse x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1a2x2​+b2y2​=1, a<ba<ba<b, pass through the point (4,3)(4,3)(4,3) and have eccentricity 53\frac{\sqrt{5}}{3}35​​. Then the length of its latus rectum is :
  1. (A)453\frac{4\sqrt{5}}{3}345​​
  2. (B)252\sqrt{5}25​
  3. (C)753\frac{7\sqrt{5}}{3}375​​
  4. (D)853\frac{8\sqrt{5}}{3}385​​

Correct answer: (D)

Step-by-step solution →
Q60·MathematicsSingle correct
If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=Ksin(18π​)sin(185π​)sin(187π​)=K, then the value of sin⁡(10Kπ3)\sin\left(\frac{10K\pi}{3}\right)sin(310Kπ​) is :
  1. (A)3+122\frac{\sqrt{3}+1}{2\sqrt{2}}22​3​+1​
  2. (B)3−12\frac{\sqrt{3}-1}{\sqrt{2}}2​3​−1​
  3. (C)32\frac{\sqrt{3}}{2}23​​
  4. (D)12\frac{1}{2}21​

Correct answer: (A)

Step-by-step solution →
Q61·MathematicsSingle correct
Let S={x∈[−π,π]:sin⁡x(sin⁡x+cos⁡x)=a,a∈Z}S=\{x\in[-\pi,\pi]:\sin x(\sin x+\cos x)=a,a\in\mathbb{Z}\}S={x∈[−π,π]:sinx(sinx+cosx)=a,a∈Z}. Then n(S)n(S)n(S) is equal to :
  1. (A)3
  2. (B)6
  3. (C)7
  4. (D)9

Correct answer: (D)

Step-by-step solution →
Q62·MathematicsSingle correct
If the point of intersection of the lines x+13=y+a5=z+b+17\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}3x+1​=5y+a​=7z+b+1​ and x−21=y−b4=z−2a7\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}1x−2​=4y−b​=7z−2a​ lies on xy-plane, then the value of a+ba+ba+b is :
  1. (A)2
  2. (B)5
  3. (C)7
  4. (D)9

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
If a⃗\vec{a}a and b⃗\vec{b}b are two vectors such that ∣a⃗∣=2|\vec{a}| = 2∣a∣=2 and ∣b⃗∣=3|\vec{b}| = 3∣b∣=3, then the maximum value of 3∣(3a⃗+2b⃗)∣+4∣(3a⃗−2b⃗)∣3\left|\left(3\vec{a} + 2\vec{b}\right)\right| + 4\left|\left(3\vec{a} - 2\vec{b}\right)\right|3​(3a+2b)​+4​(3a−2b)​ is :
  1. (A)30
  2. (B)36
  3. (C)60
  4. (D)72

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
Let a line LLL passing through the point (1,1,1)(1, 1, 1)(1,1,1) be perpendicular to both the vectors 2i^+2j^+k^2\hat{i} + 2\hat{j} + \hat{k}2i^+2j^​+k^ and i^+2j^+2k^\hat{i} + 2\hat{j} + 2\hat{k}i^+2j^​+2k^. If P(a,b,c)P(a, b, c)P(a,b,c) is the foot of perpendicular from the origin on the line LLL, then the value of 34(a+b+c)34(a + b + c)34(a+b+c) is :
  1. (A)50
  2. (B)80
  3. (C)100
  4. (D)120

Correct answer: (C)

Step-by-step solution →
Q65·MathematicsSingle correct
If lim⁡x→2sin⁡(x3−5x2+ax+b)(x−1−1)log⁡e(x−1)=m\lim_{x \to 2} \frac{\sin\left(x^{3} - 5x^{2} + ax + b\right)}{\left(\sqrt{x-1} - 1\right)\log_{e}(x-1)} = mlimx→2​(x−1​−1)loge​(x−1)sin(x3−5x2+ax+b)​=m, then a+b+ma + b + ma+b+m is equal to :
  1. (A)5
  2. (B)6
  3. (C)8
  4. (D)10

Correct answer: (B)

Step-by-step solution →
Q66·MathematicsSingle correct
The number of critical points of the function f(x)={∣sin⁡xx∣,x≠01,x=0f(x) = \begin{cases} \left|\frac{\sin x}{x}\right|, & x \neq 0 \\ 1, & x = 0 \end{cases}f(x)={​xsinx​​,1,​x=0x=0​ in the interval (−2π,2π)(-2\pi, 2\pi)(−2π,2π) is equal to :
  1. (A)1
  2. (B)3
  3. (C)5
  4. (D)7

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
Let [⋅][\cdot][⋅] denote the greatest integer function. Then the value of ∫03(ex+e−x[x]!)dx\int_{0}^{3}\left(\frac{e^{x} + e^{-x}}{[x]!}\right)dx∫03​([x]!ex+e−x​)dx is :
  1. (A)e2+e3−1e2−1e3e^{2} + e^{3} - \frac{1}{e^{2}} - \frac{1}{e^{3}}e2+e3−e21​−e31​
  2. (B)12(e2+e3−1e2−1e3)\frac{1}{2}\left(e^{2} + e^{3} - \frac{1}{e^{2}} - \frac{1}{e^{3}}\right)21​(e2+e3−e21​−e31​)
  3. (C)e2+e3−12e2−12e3e^{2} + e^{3} - \frac{1}{2e^{2}} - \frac{1}{2e^{3}}e2+e3−2e21​−2e31​
  4. (D)12(e2+e3)−1e2−1e3\frac{1}{2}\left(e^{2} + e^{3}\right) - \frac{1}{e^{2}} - \frac{1}{e^{3}}21​(e2+e3)−e21​−e31​

Correct answer: (B)

Step-by-step solution →
Q68·MathematicsSingle correct
Let y=y(x)y = y(x)y=y(x) be the solution curve of the differential equation (1+sin⁡x)dydx+(y+1)cos⁡x=0(1 + \sin x)\frac{dy}{dx} + (y + 1)\cos x = 0(1+sinx)dxdy​+(y+1)cosx=0, y(0)=0y(0) = 0y(0)=0. If the curve y=y(x)y = y(x)y=y(x) passes through the point (α,−12)\left(\alpha, \frac{-1}{2}\right)(α,2−1​), then a value of α\alphaα is :
  1. (A)π6\frac{\pi}{6}6π​
  2. (B)π4\frac{\pi}{4}4π​
  3. (C)π3\frac{\pi}{3}3π​
  4. (D)π2\frac{\pi}{2}2π​

Correct answer: (D)

Step-by-step solution →
Q69·MathematicsNumerical
If the domain of the function f(x)=log⁡(0.6)(∣2x−5x2−4∣)f(x) = \sqrt{\log_{(0.6)}\left(\left|\frac{2x - 5}{x^{2} - 4}\right|\right)}f(x)=log(0.6)​(​x2−42x−5​​)​ is (−∞,a]∪{b}∪[c,d)∪(e,∞)(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)(−∞,a]∪{b}∪[c,d)∪(e,∞), then the value of a+b+c+d+ea + b + c + d + ea+b+c+d+e is ________.

Correct answer: 4

Step-by-step solution →
Q70·MathematicsNumerical
If ∑k=1nak=6n3\sum_{k=1}^{n} a_{k} = 6n^{3}∑k=1n​ak​=6n3, then ∑k=16(ak+1−ak36)2\sum_{k=1}^{6}\left(\frac{a_{k+1} - a_{k}}{36}\right)^{2}∑k=16​(36ak+1​−ak​​)2 is equal to ________.

Correct answer: 91

Step-by-step solution →
Q71·MathematicsNumerical
Let a,b,c∈{1,2,3,4}a, b, c \in \{1, 2, 3, 4\}a,b,c∈{1,2,3,4}. If the probability, that ax2+22 bx+c>0ax^{2} + 2\sqrt{2}\,bx + c > 0ax2+22​bx+c>0 for all x∈Rx \in \mathbb{R}x∈R, is mn\frac{m}{n}nm​, gcd⁡(m,n)=1\gcd(m, n) = 1gcd(m,n)=1, then m+nm + nm+n is equal to ________.

Correct answer: 81

Step-by-step solution →
Q72·MathematicsNumerical
Let a circle CCC have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of CCC on the line x+y=1x + y = 1x+y=1 is 14\sqrt{14}14​, then the square of the radius of CCC is ________.

Correct answer: 8

Step-by-step solution →
Q73·MathematicsNumerical
If α=∫023log⁡2(x2+4)dx+∫242x−4 dx\alpha = \int_{0}^{2\sqrt{3}}\log_{2}\left(x^{2} + 4\right)dx + \int_{2}^{4}\sqrt{2^{x} - 4}\,dxα=∫023​​log2​(x2+4)dx+∫24​2x−4​dx, then α2\alpha^{2}α2 is equal to ________.

Correct answer: 192

Step-by-step solution →

Chapters tested in this paper

Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Chemical Bonding and Molecular Structure 151/186
  • Application of Derivatives 139/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Hydrocarbons 126/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • Quadratic Equations 148/186
  • Some Basic Concepts in Chemistry 129/186
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Statistics 118/186
  • Ellipse 103/186
  • Electronic Effects and Stability 74/186
  • Electric Potential 63/186
  • Principles of Qualitative Analysis 58/186
  • IUPAC Nomenclature 37/186
← 28 Jan Shift 2 2026All papers2 Apr Shift 2 2026 →

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