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JEE Main 11 April 2023 Shift 2 Question Paper with Answers

11 April 2023 · April session · 90 questions

The complete JEE Main 11 April 2023 Shift 2 paper — all 90 questions with the correct answer for each, tagged to the chapter it tests. Free to read, no account needed.

Physics
30
Chemistry
30
Mathematics
30

Physics — JEE Main 11 April 2023 Shift 2

Q1·PhysicsSingle correct
Eight equal drops of water are falling through air with a steady speed of 101010 cm/s. If the drops coalesce, the new velocity is:
  1. (A)101010 cm/s
  2. (B)404040 cm/s
  3. (C)161616 cm/s
  4. (D)555 cm/s

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
A car P travelling at 202020 ms−1^{-1}−1 sounds its horn at a frequency of 400400400 Hz. Another car Q is travelling behind the first car in the same direction with a velocity 404040 ms−1^{-1}−1. The frequency heard by the passenger of car Q is approximately [Take velocity of sound =360=360=360 ms−1^{-1}−1]
  1. (A)514514514 Hz
  2. (B)421421421 Hz
  3. (C)485485485 Hz
  4. (D)471471471 Hz

Correct answer: (B)

Step-by-step solution →
Q3·PhysicsSingle correct
A plane electromagnetic wave of frequency 202020 MHz propagates in free space along the x-direction. At a particular space and time, E⃗=6.6 j^\vec{E}=6.6\,\hat{j}E=6.6j^​ V/m. What is B⃗\vec{B}B at this point?
  1. (A)−2.2×10−8 i^-2.2\times10^{-8}\,\hat{i}−2.2×10−8i^ T
  2. (B)2.2×10−8 k^2.2\times10^{-8}\,\hat{k}2.2×10−8k^ T
  3. (C)−2.2×10−8 k^-2.2\times10^{-8}\,\hat{k}−2.2×10−8k^ T
  4. (D)2.2×10−8 i^2.2\times10^{-8}\,\hat{i}2.2×10−8i^ T

Correct answer: (B)

Step-by-step solution →
Q4·Physics·Capacitors and DielectricsSingle correct
A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:
  1. (A)CV2ε0\dfrac{CV}{2\varepsilon_0}2ε0​CV​
  2. (B)2CVε0\dfrac{2CV}{\varepsilon_0}ε0​2CV​
  3. (C)CVε0\dfrac{CV}{\varepsilon_0}ε0​CV​
  4. (D)Zero

Correct answer: (C)

Step-by-step solution →
Q5·PhysicsSingle correct
If force (F), velocity (V) and time (T) are considered as fundamental physical quantities, then the dimensional formula of density will be:
  1. (A)FV−2T2FV^{-2}T^{2}FV−2T2
  2. (B)FV−4T−2FV^{-4}T^{-2}FV−4T−2
  3. (C)FV4T−6FV^{4}T^{-6}FV4T−6
  4. (D)F2V−2T6F^{2}V^{-2}T^{6}F2V−2T6

Correct answer: (B)

Step-by-step solution →
Q6·PhysicsSingle correct
In satellite communication, the uplink frequency band used is:
  1. (A)3.7−4.23.7-4.23.7−4.2 GHz
  2. (B)5.925−6.4255.925-6.4255.925−6.425 GHz
  3. (C)76−8876-8876−88 MHz
  4. (D)420−890420-890420−890 MHz

Correct answer: (B)

Step-by-step solution →
Q7·PhysicsSingle correct
If V is the gravitational potential due to a sphere of uniform density on its surface, then its value at the centre of the sphere will be:
  1. (A)3V2\dfrac{3V}{2}23V​
  2. (B)VVV
  3. (C)43V\dfrac{4}{3}V34​V
  4. (D)V2\dfrac{V}{2}2V​

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
A body of mass 500500500 g moves along the x-axis such that its velocity varies with displacement x according to the relation v=10xv=10\sqrt{x}v=10x​ m/s. The force acting on the body is:
  1. (A)166166166 N
  2. (B)252525 N
  3. (C)125125125 N
  4. (D)555 N

Correct answer: (B)

Step-by-step solution →
Q9·PhysicsSingle correct
A projectile is projected at 30∘30^\circ30∘ from the horizontal with initial velocity 404040 ms−1^{-1}−1. The velocity of the projectile at t=2t=2t=2 s from the start will be: (Given g=10g=10g=10 m/s2^22)
  1. (A)20320\sqrt{3}203​ ms−1^{-1}−1
  2. (B)40340\sqrt{3}403​ ms−1^{-1}−1
  3. (C)202020 ms−1^{-1}−1
  4. (D)Zero

Correct answer: (A)

Step-by-step solution →
Q10·PhysicsSingle correct
A ray of light is reflected from a plane mirror with 30∘30^\circ30∘ angle of reflection. The angle of deviation of the ray after reflection is:
  1. (A)60∘60^\circ60∘
  2. (B)120∘120^\circ120∘
  3. (C)110∘110^\circ110∘
  4. (D)130∘130^\circ130∘

Correct answer: (B)

Step-by-step solution →
Q11·PhysicsSingle correct
A spaceship of mass 2×1042\times10^{4}2×104 kg is launched into a circular orbit close to the earth's surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if g=10g=10g=10 m/s2^22 and radius of earth =6400=6400=6400 km)
  1. (A)11.2(2−1)11.2\left(\sqrt{2}-1\right)11.2(2​−1) km/s
  2. (B)7.9(2−1)7.9\left(\sqrt{2}-1\right)7.9(2​−1) km/s
  3. (C)8(2−1)8\left(\sqrt{2}-1\right)8(2​−1) km/s
  4. (D)4(2−1)4\left(\sqrt{2}-1\right)4(2​−1) km/s

Correct answer: (C)

Step-by-step solution →
Q12·PhysicsSingle correct
The ratio of the de-Broglie wavelengths of a proton and an electron having the same kinetic energy is: (Assume mp=me×1849m_p=m_e\times1849mp​=me​×1849)
  1. (A)1:431:431:43
  2. (B)1:301:301:30
  3. (C)1:621:621:62
  4. (D)2:432:432:43

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
The thermodynamic process in which the internal energy of the system remains constant is:
  1. (A)Isochoric
  2. (B)Isothermal
  3. (C)Adiabatic
  4. (D)Isobaric

Correct answer: (B)

Step-by-step solution →
Q14·PhysicsSingle correct
The energy of the He+^++ ion in the first excited state is (the ground state energy for the hydrogen atom is −13.6-13.6−13.6 eV):
  1. (A)−3.4-3.4−3.4 eV
  2. (B)−54.4-54.4−54.4 eV
  3. (C)−13.6-13.6−13.6 eV
  4. (D)−27.2-27.2−27.2 eV

Correct answer: (C)

Step-by-step solution →
Q15·PhysicsSingle correct
The logic operation performed by the given digital circuit is equivalent to:
  1. (A)AND
  2. (B)NOR
  3. (C)OR
  4. (D)NAND

Correct answer: (A)

Step-by-step solution →
Q16·PhysicsSingle correct
The root mean square speed of molecules of nitrogen gas at 27∘27^\circ27∘C is: (Given mass of a nitrogen molecule =4.6×10−26=4.6\times10^{-26}=4.6×10−26 kg and take Boltzmann constant kB=1.4×10−23k_B=1.4\times10^{-23}kB​=1.4×10−23 JK−1^{-1}−1)
  1. (A)523523523 m/s
  2. (B)126012601260 m/s
  3. (C)919191 m/s
  4. (D)27.427.427.4 m/s

Correct answer: (A)

Step-by-step solution →
Q17·PhysicsSingle correct
In the given circuit, the current flowing through R2R_2R2​ is:
  1. (A)23\dfrac{2}{3}32​ A
  2. (B)14\dfrac{1}{4}41​ A
  3. (C)32\dfrac{3}{2}23​ A
  4. (D)13\dfrac{1}{3}31​ A

Correct answer: (D)

Step-by-step solution →
Q18·PhysicsSingle correct
When the vector A⃗=2i^+3j^+2k^\vec{A}=2\hat{i}+3\hat{j}+2\hat{k}A=2i^+3j^​+2k^ is subtracted from vector B⃗\vec{B}B, it gives a vector equal to 2j^2\hat{j}2j^​. Then the magnitude of vector B⃗\vec{B}B will be:
  1. (A)13\sqrt{13}13​
  2. (B)333
  3. (C)6\sqrt{6}6​
  4. (D)5\sqrt{5}5​

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with the same geometry and mass. Reason R: For the magnetic bar, eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below.
  1. (A)Both A and R are true but R is NOT the correct explanation of A
  2. (B)A is true but R is false
  3. (C)Both A and R are true and R is the correct explanation of A
  4. (D)A is false but R is true

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
An electron is allowed to move with constant velocity along the axis of a current carrying straight solenoid. A. The electron will experience magnetic force along the axis of the solenoid. B. The electron will not experience magnetic force. C. The electron will continue to move along the axis of the solenoid. D. The electron will be accelerated along the axis of the solenoid. E. The electron will follow a parabolic path inside the solenoid. Choose the correct answer from the options given below:
  1. (A)B, C and D only
  2. (B)B and C only
  3. (C)A and D only
  4. (D)B and E only

Correct answer: (B)

Step-by-step solution →
Q21·Physics·Capacitors and DielectricsNumerical
In the given circuit, C1=2 μC_1=2\ \muC1​=2 μF, C2=0.2 μC_2=0.2\ \muC2​=0.2 μF, C3=2 μC_3=2\ \muC3​=2 μF, C4=4 μC_4=4\ \muC4​=4 μF, C5=2 μC_5=2\ \muC5​=2 μF, C6=2 μC_6=2\ \muC6​=2 μF. The charge stored on capacitor C4C_4C4​ is ____ μ\muμC.

Correct answer: 4

Step-by-step solution →
Q22·PhysicsNumerical
A circular plate is rotating in a horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity ω\omegaω. A person sits at the centre having two dumbbells in his hands. When he stretches out his hands the moment of inertia of the system becomes triple. If E is the initial kinetic energy of the system, then the final kinetic energy will be Ex\dfrac{E}{x}xE​. The value of x is ____.

Correct answer: 3

Step-by-step solution →
Q23·PhysicsNumerical
A nucleus disintegrates into two nuclear parts, in such a way that the ratio of their nuclear sizes is 1:21/31:2^{1/3}1:21/3. Their respective speeds have a ratio of n:1n:1n:1. The value of n is ____.

Correct answer: 2

Step-by-step solution →
Q24·PhysicsNumerical
Two identical cells each of emf 1.51.51.5 V are connected in series across a 10 Ω10\ \Omega10 Ω resistance. An ideal voltmeter connected across the 10 Ω10\ \Omega10 Ω resistance reads 1.51.51.5 V. The internal resistance of each cell is ____ Ω\OmegaΩ.

Correct answer: 5

Step-by-step solution →
Q25·PhysicsNumerical
A block of mass 555 kg starting from rest is pulled up on a smooth inclined plane making an angle of 30∘30^\circ30∘ with the horizontal with an effective acceleration of 111 ms−2^{-2}−2. The power delivered by the pulling force at t=10t=10t=10 s from the start is ____ W. [Use g=10g=10g=10 ms−2^{-2}−2] (calculate the nearest integer value)

Correct answer: 300

Step-by-step solution →
Q26·PhysicsNumerical
A coil has an inductance of 222 H and resistance of 4 Ω4\ \Omega4 Ω. A 101010 V supply is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ____ ×10−3\times10^{-3}×10−3 J.

Correct answer: 625

Step-by-step solution →
Q27·PhysicsNumerical
A metallic cube of side 151515 cm is moving along the y-axis at a uniform velocity of 222 ms−1^{-1}−1 in a region of uniform magnetic field of magnitude 0.50.50.5 T directed along the z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be ____ mV.

Correct answer: 150

Step-by-step solution →
Q28·PhysicsNumerical
A wire of density 8×1038\times10^{3}8×103 kg/m3^33 is stretched between two clamps 0.50.50.5 m apart. The extension developed in the wire is 3.2×10−43.2\times10^{-4}3.2×10−4 m. If Y=8×1010Y=8\times10^{10}Y=8×1010 N/m2^22, the fundamental frequency of vibration in the wire will be ____ Hz.

Correct answer: 80

Step-by-step solution →
Q29·PhysicsNumerical
The surface tension of soap solution is 3.5×10−23.5\times10^{-2}3.5×10−2 Nm−1^{-1}−1. The amount of work done required to increase the radius of the soap bubble from 101010 cm to 202020 cm is ____ ×10−4\times10^{-4}×10−4 J.

Correct answer: 264

Step-by-step solution →
Q30·PhysicsNumerical
As shown in the figure, a plane mirror is fixed at a height of 505050 cm from the bottom of a tank containing water (μ=43)\left(\mu=\dfrac{4}{3}\right)(μ=34​). The height of water in the tank is 888 cm. A small bulb is placed at the bottom of the water tank. The distance of the image of the bulb formed by the mirror from the bottom of the tank is ____ cm.

Correct answer: 98

Step-by-step solution →

Chemistry — JEE Main 11 April 2023 Shift 2

Q31·ChemistrySingle correct
Which hydride among the following is less stable?
  1. (A)BeH2BeH_2BeH2​
  2. (B)NH3NH_3NH3​
  3. (C)HFHFHF
  4. (D)LiHLiHLiH

Correct answer: (A)

Step-by-step solution →
Q32·Chemistry·Aldehydes and KetonesSingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Methyl cyclohexyl ketone can be subjected to Wolff-Kishner reduction to give ethylcyclohexane. Reason R: Wolff-Kishner reduction is used to convert an acyl chloride (R–COClR\text{--}COClR–COCl) into a methyl group (R–CH3R\text{--}CH_3R–CH3​). In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both A and R are true but R is NOT the correct explanation of A
  2. (B)A is true but R is false
  3. (C)A is false but R is true
  4. (D)Both A and R are true and R is the correct explanation of A

Correct answer: (C)

Step-by-step solution →
Q33·Chemistry·Aldehydes and KetonesSingle correct
The major product formed in the following reaction is: C6H5–CH(OH)–CH(CH3)–CH2–CHO→ΔZn(Hg)/HClC_6H_5\text{--}CH(OH)\text{--}CH(CH_3)\text{--}CH_2\text{--}CHO \xrightarrow[\Delta]{Zn(Hg)/HCl}C6​H5​–CH(OH)–CH(CH3​)–CH2​–CHOZn(Hg)/HClΔ​ Major Product. The possible products (A), (B), (C) and (D) are shown in the figure. Choose the correct answer from the options given below:
  1. (A)A only
  2. (B)B only
  3. (C)C only
  4. (D)D only

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
Which of the following compounds is an example of Freon?
  1. (A)C2Cl2F2C_2Cl_2F_2C2​Cl2​F2​
  2. (B)C2HF3C_2HF_3C2​HF3​
  3. (C)C2H2F2C_2H_2F_2C2​H2​F2​
  4. (D)C2F4C_2F_4C2​F4​

Correct answer: (A)

Step-by-step solution →
Q35·ChemistrySingle correct
For a chemical reaction A+B→A+B\rightarrowA+B→ Product, the order is 1 with respect to A and B. Given the rate data — Rate (mol L−1^{-1}−1s−1^{-1}−1)/[A] (mol L−1^{-1}−1)/[B] (mol L−1^{-1}−1): row 1 = 0.10, 20, 0.50.10,\ 20,\ 0.50.10, 20, 0.5; row 2 = 0.40, x, 0.50.40,\ x,\ 0.50.40, x, 0.5; row 3 = 0.80, 40, y0.80,\ 40,\ y0.80, 40, y. What are the values of x and y?
  1. (A)80 and 2
  2. (B)40 and 4
  3. (C)160 and 4
  4. (D)80 and 4

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: [CoCl(NH3)5]2+[CoCl(NH_3)_5]^{2+}[CoCl(NH3​)5​]2+ absorbs at lower wavelength of light with respect to [Co(NH3)5(H2O)]3+[Co(NH_3)_5(H_2O)]^{3+}[Co(NH3​)5​(H2​O)]3+. Reason R: It is because the wavelength of the light absorbed depends on the oxidation state of the metal ion. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)A is false but R is true
  2. (B)A is true but R is false
  3. (C)Both A and R are true and R is the correct explanation of A
  4. (D)Both A and R are true and R is NOT the correct explanation of A

Correct answer: (A)

Step-by-step solution →
Q37·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A solution of the product obtained by heating a mole of glycine with a mole of chlorine in presence of red phosphorus generates a chiral carbon atom. Reason R: A molecule with 2 chiral carbons is always optically active. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)A is false but R is true
  2. (B)A is true but R is false
  3. (C)Both A and R are true and R is the correct explanation of A
  4. (D)Both A and R are true and R is NOT the correct explanation of A

Correct answer: (B)

Step-by-step solution →
Q38·ChemistrySingle correct
H3C–CH2–CH(OH)–CH3→(i) NaI, H3PO4; (ii) Mg, Dry ether; (iii) D2OH_3C\text{--}CH_2\text{--}CH(OH)\text{--}CH_3 \xrightarrow{(i)\ NaI,\ H_3PO_4;\ (ii)\ Mg,\ Dry\ ether;\ (iii)\ D_2O}H3​C–CH2​–CH(OH)–CH3​(i) NaI, H3​PO4​; (ii) Mg, Dry ether; (iii) D2​O​ [X] Product. The product [X] formed in the above reaction is:
  1. (A)H3C–CH2–CHD–CH3H_3C\text{--}CH_2\text{--}CHD\text{--}CH_3H3​C–CH2​–CHD–CH3​
  2. (B)H3C–CH2–CH(CH3)DH_3C\text{--}CH_2\text{--}CH(CH_3)DH3​C–CH2​–CH(CH3​)D (deuterium on the added carbon)
  3. (C)H3C–CH2–CH=CH2H_3C\text{--}CH_2\text{--}CH=CH_2H3​C–CH2​–CH=CH2​
  4. (D)H3C–CH=CH–CH3H_3C\text{--}CH=CH\text{--}CH_3H3​C–CH=CH–CH3​

Correct answer: (A)

Step-by-step solution →
Q39·ChemistrySingle correct
Given below are two statements: Statement I: Ethene at 333 to 343 K and 6-7 atm pressure in the presence of AlEt3AlEt_3AlEt3​ and TiCl4TiCl_4TiCl4​ undergoes addition polymerization to give LDP. Statement II: Caprolactam at 533-543 K in H2OH_2OH2​O through step growth polymerizes to give Nylon 6. 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)Statement I is false but Statement II is true
  3. (C)Statement I is true but Statement II is false
  4. (D)Both Statement I and Statement II are false

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
In the following reaction sequence, compound 'B' is (choose the correct structure from the options shown in the figure):
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
Which one of the following pairs is an example of polar molecular solids?
  1. (A)SO2(s), NH3(s)SO_2(s),\ NH_3(s)SO2​(s), NH3​(s)
  2. (B)SO2(s), CO2(s)SO_2(s),\ CO_2(s)SO2​(s), CO2​(s)
  3. (C)HCl(s), AlN(s)HCl(s),\ AlN(s)HCl(s), AlN(s)
  4. (D)MgO(s), SO2(s)MgO(s),\ SO_2(s)MgO(s), SO2​(s)

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
One mole of P4P_4P4​ reacts with 8 moles of SOCl2SOCl_2SOCl2​ to give 4 moles of A, x moles of SO2SO_2SO2​ and 2 moles of B. A, B and x respectively are
  1. (A)PCl3, S2Cl2PCl_3,\ S_2Cl_2PCl3​, S2​Cl2​ and 4
  2. (B)POCl3, S2Cl2POCl_3,\ S_2Cl_2POCl3​, S2​Cl2​ and 4
  3. (C)PCl3, S2Cl2PCl_3,\ S_2Cl_2PCl3​, S2​Cl2​ and 2
  4. (D)POCl3, S2Cl2POCl_3,\ S_2Cl_2POCl3​, S2​Cl2​ and 2

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
The compound from the following that will not produce a precipitate on reaction with AgNO3AgNO_3AgNO3​ is (choose from the structures shown in the figure):
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
A solution is prepared by adding 2 g of "X" to 1 mole of water. The mass percent of "X" in the solution is:
  1. (A)20%
  2. (B)5%
  3. (C)2%
  4. (D)10%

Correct answer: (D)

Step-by-step solution →
Q45·ChemistrySingle correct
Given below are two statements: Statement I: In the metallurgy process, sulphide ore is converted to oxide before reduction. Statement II: Oxide ores in general are easier to reduce. In the light of the above statements, choose the most appropriate answer from the options given below:
  1. (A)Both Statement I and Statement II are correct
  2. (B)Statement I is correct but Statement II is incorrect
  3. (C)Both Statement I and Statement II are incorrect
  4. (D)Statement I is incorrect but Statement II is correct

Correct answer: (A)

Step-by-step solution →
Q46·ChemistrySingle correct
The alkali metal from the following with the least melting point is:
  1. (A)Rb
  2. (B)K
  3. (C)Na
  4. (D)Cs

Correct answer: (D)

Step-by-step solution →
Q47·ChemistrySingle correct
What weight of glucose must be dissolved in 100 g of water to lower the vapour pressure by 0.20 mm Hg? (Assume a dilute solution is being formed.) Given: Vapour pressure of pure water is 54.2 mm Hg at room temperature; molar mass of glucose is 180 g mol−1^{-1}−1.
  1. (A)4.69 g
  2. (B)3.59 g
  3. (C)2.59 g
  4. (D)3.69 g

Correct answer: (D)

Step-by-step solution →
Q48·ChemistrySingle correct
The magnetic moment is measured in Bohr Magneton (BM). The spin-only magnetic moment of Fe in [Fe(H2O)6]3+[Fe(H_2O)_6]^{3+}[Fe(H2​O)6​]3+ and [Fe(CN)6]3−[Fe(CN)_6]^{3-}[Fe(CN)6​]3− complexes respectively is:
  1. (A)6.92 B.M. in both
  2. (B)4.89 B.M. and 6.92 B.M.
  3. (C)3.87 B.M. and 1.732 B.M.
  4. (D)5.92 B.M. and 1.732 B.M.

Correct answer: (D)

Step-by-step solution →
Q49·ChemistrySingle correct
Match List-I (Compound) with List-II (Colour). Choose the correct answer from the options given below:
List-I (Compound)List-II (Colour)
A.Mg(NH4)PO4Mg(NH_4)PO_4Mg(NH4​)PO4​I.Brown
B.K3[Co(NO2)6]K_3[Co(NO_2)_6]K3​[Co(NO2​)6​]II.White
C.MnO(OH)2MnO(OH)_2MnO(OH)2​III.Yellow
D.Fe4[Fe(CN)6]3Fe_4[Fe(CN)_6]_3Fe4​[Fe(CN)6​]3​IV.Blue
  1. (A)A-II, B-III, C-I, D-IV
  2. (B)A-III, B-IV, C-II, D-I
  3. (C)A-II, B-IV, C-I, D-III
  4. (D)A-II, B-III, C-IV, D-I

Correct answer: (A)

Step-by-step solution →
Q50·ChemistrySingle correct
If Ni2+Ni^{2+}Ni2+ is replaced by Pt2+Pt^{2+}Pt2+ in the complex [NiCl2Br2]2−[NiCl_2Br_2]^{2-}[NiCl2​Br2​]2−, which of the following properties are expected to get changed? A. Geometry B. Geometrical isomerism C. Optical isomerism D. Magnetic properties.
  1. (A)A, B and C
  2. (B)A, B and D
  3. (C)A and D
  4. (D)B and C

Correct answer: (B)

Step-by-step solution →
Q51·ChemistryNumerical
The number of compounds from the following which will not produce an orange-red precipitate with Benedict's solution is ____. Glucose, maltose, sucrose, ribose, 2-deoxyribose, amylose, lactose.

Correct answer: 3

Step-by-step solution →
Q52·ChemistryNumerical
4.5 moles each of hydrogen and iodine are heated in a sealed ten litre vessel. At equilibrium, 3 moles of HI were found. The equilibrium constant for H2(g)+I2(g)⇌2HI(g)H_2(g)+I_2(g)\rightleftharpoons 2HI(g)H2​(g)+I2​(g)⇌2HI(g) is ____.

Correct answer: 1

Step-by-step solution →
Q53·ChemistryNumerical
The number of correct statements about the modern adsorption theory of heterogeneous catalysis from the following is ____. A. The catalyst is diffused over the surface of reactants. B. Reactants are adsorbed on the surface of the catalyst. C. Occurrence of chemical reaction on the catalyst's surface through formation of an intermediate. D. It is a combination of intermediate compound formation theory and the old adsorption theory. E. It explains the action of the catalyst as well as those of catalytic promoters and poisons.

Correct answer: 3

Step-by-step solution →
Q54·ChemistryNumerical
The number of correct statements from the following is ____. A. For 1s orbital, the probability density is maximum at the nucleus. B. For 2s orbital, the probability density first increases to a maximum and then decreases sharply to zero. C. Boundary surface diagrams of the orbitals enclose a region of 100% probability of finding the electron. D. p and d-orbitals have 1 and 2 angular nodes respectively. E. Probability density of a p-orbital is zero at the nucleus.

Correct answer: 3

Step-by-step solution →
Q55·ChemistryNumerical
The number of possible isomeric products formed when 3-chloro-1-butene reacts with HCl through carbocation formation is ____.

Correct answer: 4

Step-by-step solution →
Q56·ChemistryNumerical
Mg(NO3)2⋅XH2OMg(NO_3)_2\cdot XH_2OMg(NO3​)2​⋅XH2​O and Ba(NO3)2⋅YH2OBa(NO_3)_2\cdot YH_2OBa(NO3​)2​⋅YH2​O represent the formula of the crystalline forms of nitrate salts. The sum of X and Y is ____.

Correct answer: 6

Step-by-step solution →
Q57·ChemistryNumerical
The total number of intensive properties from the following is ____. Volume, Molar heat capacity, Molarity, EcellE_{cell}Ecell​, Gibbs free energy change, Molar mass, Mole.

Correct answer: 4

Step-by-step solution →
Q58·ChemistryNumerical
The maximum number of lone pairs of electrons on the central atom from the following species is ____. ClO3−, XeF4, SF4ClO_3^-,\ XeF_4,\ SF_4ClO3−​, XeF4​, SF4​ and I3−I_3^-I3−​.

Correct answer: 3

Step-by-step solution →
Q59·ChemistryNumerical
The volume of hydrogen liberated at STP by treating 2.4 g of magnesium with excess of hydrochloric acid is ____ ×10−2\times10^{-2}×10−2 L. Given: Molar volume of gas is 22.4 L at STP; molar mass of magnesium is 24 g mol−1^{-1}−1.

Correct answer: 224

Step-by-step solution →
Q60·ChemistryNumerical
The number of correct statements from the following is ____. A. EcellE_{cell}Ecell​ is an intensive parameter. B. A negative E∘E^\circE∘ means that the redox couple is a stronger reducing agent than the H+/H2H^+/H_2H+/H2​ couple. C. The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode reaction. D. The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte.

Correct answer: 4

Step-by-step solution →

Mathematics — JEE Main 11 April 2023 Shift 2

Q61·Mathematics·Matrices and DeterminantsSingle correct
If ∣x+1xxxx+λxxxx+λ2∣=98(103x+81)\begin{vmatrix} x+1 & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda^2 \end{vmatrix}=\dfrac{9}{8}(103x+81)​x+1xx​xx+λx​xxx+λ2​​=89​(103x+81), then λ,λ3\lambda,\dfrac{\lambda}{3}λ,3λ​ are the roots of the equation
  1. (A)4λ2+24λ+27=04\lambda^2+24\lambda+27=04λ2+24λ+27=0
  2. (B)4λ2−24λ+27=04\lambda^2-24\lambda+27=04λ2−24λ+27=0
  3. (C)4λ2+24λ−27=04\lambda^2+24\lambda-27=04λ2+24λ−27=0
  4. (D)4λ2−24λ−27=04\lambda^2-24\lambda-27=04λ2−24λ−27=0

Correct answer: (B)

Step-by-step solution →
Q62·MathematicsSingle correct
Let the line passing through the points P(2,−1,2)P(2,-1,2)P(2,−1,2) and Q(5,3,4)Q(5,3,4)Q(5,3,4) meet the plane x−y+z=4x-y+z=4x−y+z=4 at the point RRR. Then the distance of the point RRR from the plane x+2y+3z+2=0x+2y+3z+2=0x+2y+3z+2=0 measured parallel to the line x−72=y+32=z−21\dfrac{x-7}{2}=\dfrac{y+3}{2}=\dfrac{z-2}{1}2x−7​=2y+3​=1z−2​ is equal to
  1. (A)31\sqrt{31}31​
  2. (B)189\sqrt{189}189​
  3. (C)61\sqrt{61}61​
  4. (D)333

Correct answer: (D)

Step-by-step solution →
Q63·MathematicsSingle correct
If the 1011th1011^{\text{th}}1011th term from the end in the binomial expansion of (4x5−52x)2022\left(\dfrac{4x}{5}-\dfrac{5}{2x}\right)^{2022}(54x​−2x5​)2022 is 102410241024 times the 1011th1011^{\text{th}}1011th term from the beginning, then ∣x∣|x|∣x∣ is equal to
  1. (A)121212
  2. (B)888
  3. (C)101010
  4. (D)151515

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
Let the function f:[0,2]→Rf:[0,2]\to\mathbb{R}f:[0,2]→R be defined as f(x)={emin⁡{x2, x−[x]},x∈[0,1)e[x−log⁡ex],x∈[1,2]f(x)=\begin{cases} e^{\min\{x^2,\,x-[x]\}}, & x\in[0,1) \\ e^{[x-\log_e x]}, & x\in[1,2] \end{cases}f(x)={emin{x2,x−[x]},e[x−loge​x],​x∈[0,1)x∈[1,2]​ where [t][t][t] denotes the greatest integer less than or equal to ttt. Then the value of the integral ∫02x f(x) dx\int_0^2 x\,f(x)\,dx∫02​xf(x)dx is
  1. (A)2e−12e-12e−1
  2. (B)2e+3e22e+\dfrac{3e}{2}2e+23e​
  3. (C)2e−122e-\dfrac{1}{2}2e−21​
  4. (D)(e−1)(e2+12)(e-1)\left(e^2+\dfrac{1}{2}\right)(e−1)(e2+21​)

Correct answer: (C)

Step-by-step solution →
Q65·MathematicsSingle correct
Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation dydx+5x(x5+1)y=(x5+1)2x7\dfrac{dy}{dx}+\dfrac{5}{x\left(x^5+1\right)}y=\dfrac{\left(x^5+1\right)^2}{x^7}dxdy​+x(x5+1)5​y=x7(x5+1)2​, x>0x>0x>0. If y(1)=2y(1)=2y(1)=2, then y(2)y(2)y(2) is equal to
  1. (A)637128\dfrac{637}{128}128637​
  2. (B)679128\dfrac{679}{128}128679​
  3. (C)693128\dfrac{693}{128}128693​
  4. (D)697128\dfrac{697}{128}128697​

Correct answer: (C)

Step-by-step solution →
Q66·MathematicsSingle correct
If four distinct points with position vectors a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c}a,b,c and d⃗\vec{d}d are coplanar, then [a⃗ b⃗ c⃗]\left[\vec{a}\,\vec{b}\,\vec{c}\right][abc] is equal to
  1. (A)[d⃗ c⃗ a⃗]+[b⃗ a⃗ d⃗]+[c⃗ d⃗ b⃗]\left[\vec{d}\,\vec{c}\,\vec{a}\right]+\left[\vec{b}\,\vec{a}\,\vec{d}\right]+\left[\vec{c}\,\vec{d}\,\vec{b}\right][dca]+[bad]+[cdb]
  2. (B)[d⃗ b⃗ a⃗]+[a⃗ c⃗ d⃗]+[d⃗ b⃗ c⃗]\left[\vec{d}\,\vec{b}\,\vec{a}\right]+\left[\vec{a}\,\vec{c}\,\vec{d}\right]+\left[\vec{d}\,\vec{b}\,\vec{c}\right][dba]+[acd]+[dbc]
  3. (C)[a⃗ d⃗ b⃗]+[d⃗ c⃗ a⃗]+[b⃗ d⃗ c⃗]\left[\vec{a}\,\vec{d}\,\vec{b}\right]+\left[\vec{d}\,\vec{c}\,\vec{a}\right]+\left[\vec{b}\,\vec{d}\,\vec{c}\right][adb]+[dca]+[bdc]
  4. (D)[b⃗ c⃗ d⃗]+[a⃗ b⃗ c⃗]+[d⃗ b⃗ a⃗]\left[\vec{b}\,\vec{c}\,\vec{d}\right]+\left[\vec{a}\,\vec{b}\,\vec{c}\right]+\left[\vec{d}\,\vec{b}\,\vec{a}\right][bcd]+[abc]+[dba]

Correct answer: (A)

Step-by-step solution →
Q67·MathematicsSingle correct
If f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R be a continuous function satisfying ∫0π/2f(sin⁡2x)sin⁡x dx+α∫0π/4f(cos⁡2x)cos⁡x dx=0\displaystyle\int_0^{\pi/2} f(\sin 2x)\sin x\,dx+\alpha\int_0^{\pi/4} f(\cos 2x)\cos x\,dx=0∫0π/2​f(sin2x)sinxdx+α∫0π/4​f(cos2x)cosxdx=0, then α\alphaα is equal to
  1. (A)−3-\sqrt{3}−3​
  2. (B)2\sqrt{2}2​
  3. (C)3\sqrt{3}3​
  4. (D)−2-\sqrt{2}−2​

Correct answer: (D)

Step-by-step solution →
Q68·Mathematics·Matrices and DeterminantsSingle correct
If the system of linear equations 7x+11y+αz=137x+11y+\alpha z=137x+11y+αz=13, 5x+4y+7z=β5x+4y+7z=\beta5x+4y+7z=β, 175x+194y+57z=361175x+194y+57z=361175x+194y+57z=361 has infinitely many solutions, then α+β+2\alpha+\beta+2α+β+2 is equal to
  1. (A)444
  2. (B)333
  3. (C)555
  4. (D)666

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
The domain of the function f(x)=1[x]2−3[x]−10f(x)=\dfrac{1}{\sqrt{[x]^2-3[x]-10}}f(x)=[x]2−3[x]−10​1​ is (where [x][x][x] denotes the greatest integer less than or equal to xxx)
  1. (A)(−∞,−3)∪(5,∞)(-\infty,-3)\cup(5,\infty)(−∞,−3)∪(5,∞)
  2. (B)(−∞,−2)∪(6,∞)(-\infty,-2)\cup(6,\infty)(−∞,−2)∪(6,∞)
  3. (C)(−∞,−3]∪(6,∞)(-\infty,-3]\cup(6,\infty)(−∞,−3]∪(6,∞)
  4. (D)(−∞,−3]∪[6,∞)(-\infty,-3]\cup[6,\infty)(−∞,−3]∪[6,∞)

Correct answer: (C)

Step-by-step solution →
Q70·MathematicsSingle correct
Let PPP be the plane passing through the points (5,3,0)(5,3,0)(5,3,0), (13,3,−2)(13,3,-2)(13,3,−2) and (1,6,2)(1,6,2)(1,6,2). For α∈N\alpha\in\mathbb{N}α∈N, if the distances of the points A(3,4,α)A(3,4,\alpha)A(3,4,α) and B(2,α,a)B(2,\alpha,a)B(2,α,a) from the plane PPP are 222 and 333 respectively, then the positive value of aaa is
  1. (A)666
  2. (B)444
  3. (C)333
  4. (D)555

Correct answer: (B)

Step-by-step solution →
Q71·MathematicsSingle correct
The converse of the statement ((∼p)∧q)⇒r((\sim p)\wedge q)\Rightarrow r((∼p)∧q)⇒r is
  1. (A)(∼r)⇒p∧q(\sim r)\Rightarrow p\wedge q(∼r)⇒p∧q
  2. (B)(∼r)⇒((∼p)∧q)(\sim r)\Rightarrow((\sim p)\wedge q)(∼r)⇒((∼p)∧q)
  3. (C)r⇒((∼p)∧q)r\Rightarrow((\sim p)\wedge q)r⇒((∼p)∧q)
  4. (D)(p∨(∼q))⇒(∼r)(p\vee(\sim q))\Rightarrow(\sim r)(p∨(∼q))⇒(∼r)

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
The angle of elevation of the top PPP of a tower from the feet of one person standing due South of the tower is 45∘45^\circ45∘ and from the feet of another person standing due West of the tower is 30∘30^\circ30∘. If the height of the tower is 555 metres, then the distance (in metres) between the two persons is equal to
  1. (A)101010
  2. (B)52\dfrac{5}{2}25​
  3. (C)555\sqrt{5}55​
  4. (D)525\dfrac{5}{2}\sqrt{5}25​5​

Correct answer: (A)

Step-by-step solution →
Q73·MathematicsSingle correct
Let aaa, bbb, ccc and ddd be positive real numbers such that a+b+c+d=11a+b+c+d=11a+b+c+d=11. If the maximum value of a5b3c2da^5 b^3 c^2 da5b3c2d is 3750β3750\beta3750β, then the value of β\betaβ is
  1. (A)909090
  2. (B)110110110
  3. (C)555555
  4. (D)108108108

Correct answer: (A)

Step-by-step solution →
Q74·MathematicsSingle correct
If the radius of the largest circle with centre (2,0)(2,0)(2,0) inscribed in the ellipse x2+4y2=36x^2+4y^2=36x2+4y2=36 is rrr, then 12r212r^212r2 is equal to
  1. (A)727272
  2. (B)115115115
  3. (C)929292
  4. (D)696969

Correct answer: (C)

Step-by-step solution →
Q75·MathematicsSingle correct
If the mean of the observations 1,2,4,5,x1,2,4,5,x1,2,4,5,x and yyy be 555 and their variance be 101010, then their mean deviation about the mean is equal to
  1. (A)103\dfrac{10}{3}310​
  2. (B)73\dfrac{7}{3}37​
  3. (C)333
  4. (D)83\dfrac{8}{3}38​

Correct answer: (D)

Step-by-step solution →
Q76·MathematicsSingle correct
The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)n+2(1+x)^{n+2}(1+x)n+2, which are in the ratio 1:3:51:3:51:3:5, is equal to
  1. (A)25
  2. (B)63
  3. (C)41
  4. (D)92

Correct answer: (B)

Step-by-step solution →
Q77·MathematicsSingle correct
If the letters of the word MATHS are permuted and all possible words so formed are arranged in a dictionary with serial numbers, then the serial number of the word THAMS is
  1. (A)103103103
  2. (B)104104104
  3. (C)101101101
  4. (D)102102102

Correct answer: (A)

Step-by-step solution →
Q78·MathematicsSingle correct
For a∈Ca\in\mathbb{C}a∈C, let A={z∈C:Re⁡(a+zˉ)>Im⁡(aˉ+z)}A=\{z\in\mathbb{C}:\operatorname{Re}(a+\bar{z})>\operatorname{Im}(\bar{a}+z)\}A={z∈C:Re(a+zˉ)>Im(aˉ+z)} and B={z∈C:Re⁡(a+zˉ)<Im⁡(aˉ+z)}B=\{z\in\mathbb{C}:\operatorname{Re}(a+\bar{z})<\operatorname{Im}(\bar{a}+z)\}B={z∈C:Re(a+zˉ)<Im(aˉ+z)}. Then among the two statements: (S1): If Re⁡(a),Im⁡(a)>0\operatorname{Re}(a),\operatorname{Im}(a)>0Re(a),Im(a)>0, then the set AAA contains all the real numbers; (S2): If Re⁡(a),Im⁡(a)<0\operatorname{Re}(a),\operatorname{Im}(a)<0Re(a),Im(a)<0, then the set BBB contains all the real numbers,
  1. (A)Only (S1) is true
  2. (B)Both are false
  3. (C)Only (S2) is true
  4. (D)Both are true

Correct answer: (B)

Step-by-step solution →
Q79·MathematicsSingle correct
Let A={1,3,4,6,9}A=\{1,3,4,6,9\}A={1,3,4,6,9} and B={2,4,5,8,10}B=\{2,4,5,8,10\}B={2,4,5,8,10}. Let RRR be a relation defined on A×BA\times BA×B such that R={((a1,b1),(a2,b2)):a1≤b2 and b1≤a2}R=\{((a_1,b_1),(a_2,b_2)):a_1\le b_2 \text{ and } b_1\le a_2\}R={((a1​,b1​),(a2​,b2​)):a1​≤b2​ and b1​≤a2​}. Then the number of elements in the set RRR is
  1. (A)26
  2. (B)160
  3. (C)180
  4. (D)52

Correct answer: (B)

Step-by-step solution →
Q80·Mathematics·Limits and ContinuitySingle correct
Let ggg and fff be two functions defined as f(x)={x+1,x<0∣x−1∣,x≥0f(x)=\begin{cases} x+1, & x<0 \\ |x-1|, & x\ge 0 \end{cases}f(x)={x+1,∣x−1∣,​x<0x≥0​ and g(x)={x+1,x<01,x≥0g(x)=\begin{cases} x+1, & x<0 \\ 1, & x\ge 0 \end{cases}g(x)={x+1,1,​x<0x≥0​. Then (g∘f)(x)(g\circ f)(x)(g∘f)(x) is
  1. (A)differentiable everywhere
  2. (B)continuous everywhere but not differentiable exactly at one point
  3. (C)not continuous at x=−1x=-1x=−1
  4. (D)continuous everywhere but not differentiable at x=1x=1x=1

Correct answer: (B)

Step-by-step solution →
Q81·MathematicsNumerical
The number of points, where the curve f(x)=e8x−e6x−3e4x−e2x+1f(x)=e^{8x}-e^{6x}-3e^{4x}-e^{2x}+1f(x)=e8x−e6x−3e4x−e2x+1, x∈Rx\in\mathbb{R}x∈R cuts the x-axis, is equal to

Correct answer: 2

Step-by-step solution →
Q82·MathematicsNumerical
The probability of getting a head for a biased coin is 14\dfrac{1}{4}41​. It is tossed repeatedly until a head appears. Let NNN be the number of tosses required. If the probability that the equation 64x2+5Nx+1=064x^2+5Nx+1=064x2+5Nx+1=0 has no real root is pq\dfrac{p}{q}qp​, where ppp and qqq are co-prime, then q−pq-pq−p is equal to

Correct answer: 27

Step-by-step solution →
Q83·MathematicsNumerical
Let a⃗=i^+2j^+3k^\vec{a}=\hat{i}+2\hat{j}+3\hat{k}a=i^+2j^​+3k^ and b⃗=i^+j^−k^\vec{b}=\hat{i}+\hat{j}-\hat{k}b=i^+j^​−k^. If c⃗\vec{c}c is a vector such that a⃗⋅c⃗=11\vec{a}\cdot\vec{c}=11a⋅c=11, b⃗⋅(a⃗×c⃗)=27\vec{b}\cdot(\vec{a}\times\vec{c})=27b⋅(a×c)=27 and b⃗⋅c⃗=−3 ∣b⃗∣\vec{b}\cdot\vec{c}=-\sqrt{3}\,|\vec{b}|b⋅c=−3​∣b∣, then ∣a⃗×c⃗∣2|\vec{a}\times\vec{c}|^2∣a×c∣2 is equal to

Correct answer: 285

Step-by-step solution →
Q84·MathematicsNumerical
Let S={z∈C−{i,2i}:z2+8iz−15z2−3iz−2∈R}S=\left\{z\in\mathbb{C}-\{i,2i\}:\dfrac{z^2+8iz-15}{z^2-3iz-2}\in\mathbb{R}\right\}S={z∈C−{i,2i}:z2−3iz−2z2+8iz−15​∈R}. If α−1311i∈S\alpha-\dfrac{13}{11}i\in Sα−1113​i∈S, α∈R−{0}\alpha\in\mathbb{R}-\{0\}α∈R−{0}, then 242α2242\alpha^2242α2 is equal to

Correct answer: 1680

Step-by-step solution →
Q85·MathematicsNumerical
For k∈Nk\in\mathbb{N}k∈N, if the sum of the series 1+4k+8k2+13k3+19k4+⋯1+\dfrac{4}{k}+\dfrac{8}{k^2}+\dfrac{13}{k^3}+\dfrac{19}{k^4}+\cdots1+k4​+k28​+k313​+k419​+⋯ is 101010, then the value of kkk is

Correct answer: 2

Step-by-step solution →
Q86·MathematicsNumerical
Let A={1,2,3,4,5}A=\{1,2,3,4,5\}A={1,2,3,4,5} and B={1,2,3,4,5,6}B=\{1,2,3,4,5,6\}B={1,2,3,4,5,6}. Then the number of functions f:A→Bf:A\to Bf:A→B satisfying f(1)+f(2)=f(4)−1f(1)+f(2)=f(4)-1f(1)+f(2)=f(4)−1 is equal to

Correct answer: 360

Step-by-step solution →
Q87·MathematicsNumerical
Let the tangent to the parabola y2=12xy^2=12xy2=12x at the point (3,α)(3,\alpha)(3,α) be perpendicular to the line 2x+2y=32x+2y=32x+2y=3. Then the square of the distance of the point (6,−4)(6,-4)(6,−4) from the normal to the hyperbola α2x2−9y2=9α2\alpha^2 x^2-9y^2=9\alpha^2α2x2−9y2=9α2 at its point (α−1,α+2)(\alpha-1,\alpha+2)(α−1,α+2) is equal to

Correct answer: 116

Step-by-step solution →
Q88·MathematicsNumerical
Let the line ℓ:x=1−y−2=z−3λ\ell:x=\dfrac{1-y}{-2}=\dfrac{z-3}{\lambda}ℓ:x=−21−y​=λz−3​, λ∈R\lambda\in\mathbb{R}λ∈R meet the plane P:x+2y+3z=4P:x+2y+3z=4P:x+2y+3z=4 at the point (α,β,γ)(\alpha,\beta,\gamma)(α,β,γ). If the angle between the line ℓ\ellℓ and the plane PPP is cos⁡−1(514)\cos^{-1}\left(\sqrt{\dfrac{5}{14}}\right)cos−1(145​​), then α+2β+6γ\alpha+2\beta+6\gammaα+2β+6γ is equal to

Correct answer: 11

Step-by-step solution →
Q89·MathematicsNumerical
If the line ℓ1:3y−2x=3\ell_1:3y-2x=3ℓ1​:3y−2x=3 is the angular bisector of the lines ℓ2:x−y+1=0\ell_2:x-y+1=0ℓ2​:x−y+1=0 and ℓ3:αx+βy+17=0\ell_3:\alpha x+\beta y+17=0ℓ3​:αx+βy+17=0, then α2+β2−α−β\alpha^2+\beta^2-\alpha-\betaα2+β2−α−β is equal to

Correct answer: 348

Step-by-step solution →
Q90·MathematicsNumerical
If AAA is the area in the first quadrant enclosed by the curve C:2x2−y+1=0C:2x^2-y+1=0C:2x2−y+1=0, the tangent to CCC at the point (1,3)(1,3)(1,3) and the line x+y=1x+y=1x+y=1, then the value of 60A60A60A is

Correct answer: 16

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
  • Current Electricity 160/186
  • 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
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Laws of Motion 130/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Dual Nature of Matter and Radiation 155/186
  • Work, Energy and Power 132/186
  • Some Basic Concepts in Chemistry 129/186
  • Electromagnetic Induction 120/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Hydrogen 81/186
  • Hyperbola 77/186
  • Polymers 64/186
  • Solid State 63/186
  • Diazonium Salts and Reactions 53/186
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