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 10 cm/s. If the drops coalesce, the new velocity is:
(A)10 cm/s
(B)40 cm/s
(C)16 cm/s
(D)5 cm/s
Q2·PhysicsSingle correct
A car P travelling at 20 ms−1 sounds its horn at a frequency of 400 Hz. Another car Q is travelling behind the first car in the same direction with a velocity 40 ms−1. The frequency heard by the passenger of car Q is approximately [Take velocity of sound =360 ms−1]
(A)514 Hz
(B)421 Hz
(C)485 Hz
(D)471 Hz
Q3·PhysicsSingle correct
A plane electromagnetic wave of frequency 20 MHz propagates in free space along the x-direction. At a particular space and time, E=6.6j^ V/m. What is B at this point?
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:
(A)2ε0CV
(B)ε02CV
(C)ε0CV
(D)Zero
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:
(A)FV−2T2
(B)FV−4T−2
(C)FV4T−6
(D)F2V−2T6
Q6·PhysicsSingle correct
In satellite communication, the uplink frequency band used is:
(A)3.7−4.2 GHz
(B)5.925−6.425 GHz
(C)76−88 MHz
(D)420−890 MHz
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:
(A)23V
(B)V
(C)34V
(D)2V
Q8·PhysicsSingle correct
A body of mass 500 g moves along the x-axis such that its velocity varies with displacement x according to the relation v=10x m/s. The force acting on the body is:
(A)166 N
(B)25 N
(C)125 N
(D)5 N
Q9·PhysicsSingle correct
A projectile is projected at 30∘ from the horizontal with initial velocity 40 ms−1. The velocity of the projectile at t=2 s from the start will be: (Given g=10 m/s2)
(A)203 ms−1
(B)403 ms−1
(C)20 ms−1
(D)Zero
Q10·PhysicsSingle correct
A ray of light is reflected from a plane mirror with 30∘ angle of reflection. The angle of deviation of the ray after reflection is:
(A)60∘
(B)120∘
(C)110∘
(D)130∘
Q11·PhysicsSingle correct
A spaceship of mass 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=10 m/s2 and radius of earth =6400 km)
(A)11.2(2−1) km/s
(B)7.9(2−1) km/s
(C)8(2−1) km/s
(D)4(2−1) km/s
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×1849)
(A)1:43
(B)1:30
(C)1:62
(D)2:43
Q13·PhysicsSingle correct
The thermodynamic process in which the internal energy of the system remains constant is:
(A)Isochoric
(B)Isothermal
(C)Adiabatic
(D)Isobaric
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 eV):
(A)−3.4 eV
(B)−54.4 eV
(C)−13.6 eV
(D)−27.2 eV
Q15·PhysicsSingle correct
The logic operation performed by the given digital circuit is equivalent to:
(A)AND
(B)NOR
(C)OR
(D)NAND
Q16·PhysicsSingle correct
The root mean square speed of molecules of nitrogen gas at 27∘C is: (Given mass of a nitrogen molecule =4.6×10−26 kg and take Boltzmann constant kB=1.4×10−23 JK−1)
(A)523 m/s
(B)1260 m/s
(C)91 m/s
(D)27.4 m/s
Q17·PhysicsSingle correct
In the given circuit, the current flowing through R2 is:
(A)32 A
(B)41 A
(C)23 A
(D)31 A
Q18·PhysicsSingle correct
When the vector A=2i^+3j^+2k^ is subtracted from vector B, it gives a vector equal to 2j^. Then the magnitude of vector B will be:
(A)13
(B)3
(C)6
(D)5
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.
(A)Both A and R are true but R is NOT the correct explanation of A
(B)A is true but R is false
(C)Both A and R are true and R is the correct explanation of A
(D)A is false but R is true
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:
In the given circuit, C1=2μF, C2=0.2μF, C3=2μF, C4=4μF, C5=2μF, C6=2μF. The charge stored on capacitor C4 is ____ μC.
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. 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 xE. The value of x is ____.
Q23·PhysicsNumerical
A nucleus disintegrates into two nuclear parts, in such a way that the ratio of their nuclear sizes is 1:21/3. Their respective speeds have a ratio of n:1. The value of n is ____.
Q24·PhysicsNumerical
Two identical cells each of emf 1.5 V are connected in series across a 10Ω resistance. An ideal voltmeter connected across the 10Ω resistance reads 1.5 V. The internal resistance of each cell is ____ Ω.
Q25·PhysicsNumerical
A block of mass 5 kg starting from rest is pulled up on a smooth inclined plane making an angle of 30∘ with the horizontal with an effective acceleration of 1 ms−2. The power delivered by the pulling force at t=10 s from the start is ____ W. [Use g=10 ms−2] (calculate the nearest integer value)
Q26·PhysicsNumerical
A coil has an inductance of 2 H and resistance of 4Ω. A 10 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 J.
Q27·PhysicsNumerical
A metallic cube of side 15 cm is moving along the y-axis at a uniform velocity of 2 ms−1 in a region of uniform magnetic field of magnitude 0.5 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.
Q28·PhysicsNumerical
A wire of density 8×103 kg/m3 is stretched between two clamps 0.5 m apart. The extension developed in the wire is 3.2×10−4 m. If Y=8×1010 N/m2, the fundamental frequency of vibration in the wire will be ____ Hz.
Q29·PhysicsNumerical
The surface tension of soap solution is 3.5×10−2 Nm−1. The amount of work done required to increase the radius of the soap bubble from 10 cm to 20 cm is ____ ×10−4 J.
Q30·PhysicsNumerical
As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of a tank containing water (μ=34). The height of water in the tank is 8 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.
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–COCl) into a methyl group (R–CH3).
In the light of the above statements, choose the correct answer from the options given below:
(A)Both A and R are true but R is NOT the correct explanation of A
(B)A is true but R is false
(C)A is false but R is true
(D)Both A and R are true and R is the correct explanation of A
The major product formed in the following reaction is: C6H5–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:
(A)A only
(B)B only
(C)C only
(D)D only
Q34·ChemistrySingle correct
Which of the following compounds is an example of Freon?
(A)C2Cl2F2
(B)C2HF3
(C)C2H2F2
(D)C2F4
Q35·ChemistrySingle correct
For a chemical reaction A+B→ Product, the order is 1 with respect to A and B. Given the rate data — Rate (mol L−1s−1)/[A] (mol L−1)/[B] (mol L−1): row 1 = 0.10,20,0.5; row 2 = 0.40,x,0.5; row 3 = 0.80,40,y. What are the values of x and y?
(A)80 and 2
(B)40 and 4
(C)160 and 4
(D)80 and 4
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+ absorbs at lower wavelength of light with respect to [Co(NH3)5(H2O)]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:
(A)A is false but R is true
(B)A is true but R is false
(C)Both A and R are true and R is the correct explanation of A
(D)Both A and R are true and R is NOT the correct explanation of A
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:
(A)A is false but R is true
(B)A is true but R is false
(C)Both A and R are true and R is the correct explanation of A
(D)Both A and R are true and R is NOT the correct explanation of A
Q38·ChemistrySingle correct
H3C–CH2–CH(OH)–CH3(i)NaI,H3PO4;(ii)Mg,Dryether;(iii)D2O [X] Product. The product [X] formed in the above reaction is:
(A)H3C–CH2–CHD–CH3
(B)H3C–CH2–CH(CH3)D (deuterium on the added carbon)
(C)H3C–CH2–CH=CH2
(D)H3C–CH=CH–CH3
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 AlEt3 and TiCl4 undergoes addition polymerization to give LDP.
Statement II: Caprolactam at 533-543 K in H2O through step growth polymerizes to give Nylon 6.
In the light of the above statements, choose the correct answer from the options given below:
(A)Both Statement I and Statement II are true
(B)Statement I is false but Statement II is true
(C)Statement I is true but Statement II is false
(D)Both Statement I and Statement II are false
Q40·ChemistrySingle correct
In the following reaction sequence, compound 'B' is (choose the correct structure from the options shown in the figure):
(A)(1)
(B)(2)
(C)(3)
(D)(4)
Q41·ChemistrySingle correct
Which one of the following pairs is an example of polar molecular solids?
(A)SO2(s),NH3(s)
(B)SO2(s),CO2(s)
(C)HCl(s),AlN(s)
(D)MgO(s),SO2(s)
Q42·ChemistrySingle correct
One mole of P4 reacts with 8 moles of SOCl2 to give 4 moles of A, x moles of SO2 and 2 moles of B. A, B and x respectively are
(A)PCl3,S2Cl2 and 4
(B)POCl3,S2Cl2 and 4
(C)PCl3,S2Cl2 and 2
(D)POCl3,S2Cl2 and 2
Q43·ChemistrySingle correct
The compound from the following that will not produce a precipitate on reaction with AgNO3 is (choose from the structures shown in the figure):
(A)(1)
(B)(2)
(C)(3)
(D)(4)
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:
(A)20%
(B)5%
(C)2%
(D)10%
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:
(A)Both Statement I and Statement II are correct
(B)Statement I is correct but Statement II is incorrect
(C)Both Statement I and Statement II are incorrect
(D)Statement I is incorrect but Statement II is correct
Q46·ChemistrySingle correct
The alkali metal from the following with the least melting point is:
(A)Rb
(B)K
(C)Na
(D)Cs
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.
(A)4.69 g
(B)3.59 g
(C)2.59 g
(D)3.69 g
Q48·ChemistrySingle correct
The magnetic moment is measured in Bohr Magneton (BM). The spin-only magnetic moment of Fe in [Fe(H2O)6]3+ and [Fe(CN)6]3− complexes respectively is:
(A)6.92 B.M. in both
(B)4.89 B.M. and 6.92 B.M.
(C)3.87 B.M. and 1.732 B.M.
(D)5.92 B.M. and 1.732 B.M.
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)PO4
I.Brown
B.K3[Co(NO2)6]
II.White
C.MnO(OH)2
III.Yellow
D.Fe4[Fe(CN)6]3
IV.Blue
(A)A-II, B-III, C-I, D-IV
(B)A-III, B-IV, C-II, D-I
(C)A-II, B-IV, C-I, D-III
(D)A-II, B-III, C-IV, D-I
Q50·ChemistrySingle correct
If Ni2+ is replaced by Pt2+ in the complex [NiCl2Br2]2−, which of the following properties are expected to get changed? A. Geometry B. Geometrical isomerism C. Optical isomerism D. Magnetic properties.
(A)A, B and C
(B)A, B and D
(C)A and D
(D)B and C
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.
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) is ____.
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.
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.
Q55·ChemistryNumerical
The number of possible isomeric products formed when 3-chloro-1-butene reacts with HCl through carbocation formation is ____.
Q56·ChemistryNumerical
Mg(NO3)2⋅XH2O and Ba(NO3)2⋅YH2O represent the formula of the crystalline forms of nitrate salts. The sum of X and Y is ____.
Q57·ChemistryNumerical
The total number of intensive properties from the following is ____. Volume, Molar heat capacity, Molarity, Ecell, Gibbs free energy change, Molar mass, Mole.
Q58·ChemistryNumerical
The maximum number of lone pairs of electrons on the central atom from the following species is ____. ClO3−,XeF4,SF4 and I3−.
Q59·ChemistryNumerical
The volume of hydrogen liberated at STP by treating 2.4 g of magnesium with excess of hydrochloric acid is ____ ×10−2 L. Given: Molar volume of gas is 22.4 L at STP; molar mass of magnesium is 24 g mol−1.
Q60·ChemistryNumerical
The number of correct statements from the following is ____. A. Ecell is an intensive parameter. B. A negative E∘ means that the redox couple is a stronger reducing agent than the H+/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.
If x+1xxxx+λxxxx+λ2=89(103x+81), then λ,3λ are the roots of the equation
(A)4λ2+24λ+27=0
(B)4λ2−24λ+27=0
(C)4λ2+24λ−27=0
(D)4λ2−24λ−27=0
Q62·MathematicsSingle correct
Let the line passing through the points P(2,−1,2) and Q(5,3,4) meet the plane x−y+z=4 at the point R. Then the distance of the point R from the plane x+2y+3z+2=0 measured parallel to the line 2x−7=2y+3=1z−2 is equal to
(A)31
(B)189
(C)61
(D)3
Q63·MathematicsSingle correct
If the 1011th term from the end in the binomial expansion of (54x−2x5)2022 is 1024 times the 1011th term from the beginning, then ∣x∣ is equal to
(A)12
(B)8
(C)10
(D)15
Q64·MathematicsSingle correct
Let the function f:[0,2]→R be defined as f(x)={emin{x2,x−[x]},e[x−logex],x∈[0,1)x∈[1,2] where [t] denotes the greatest integer less than or equal to t. Then the value of the integral ∫02xf(x)dx is
(A)2e−1
(B)2e+23e
(C)2e−21
(D)(e−1)(e2+21)
Q65·MathematicsSingle correct
Let y=y(x) be the solution of the differential equation dxdy+x(x5+1)5y=x7(x5+1)2, x>0. If y(1)=2, then y(2) is equal to
(A)128637
(B)128679
(C)128693
(D)128697
Q66·MathematicsSingle correct
If four distinct points with position vectors a,b,c and d are coplanar, then [abc] is equal to
(A)[dca]+[bad]+[cdb]
(B)[dba]+[acd]+[dbc]
(C)[adb]+[dca]+[bdc]
(D)[bcd]+[abc]+[dba]
Q67·MathematicsSingle correct
If f:R→R be a continuous function satisfying ∫0π/2f(sin2x)sinxdx+α∫0π/4f(cos2x)cosxdx=0, then α is equal to
If the system of linear equations 7x+11y+αz=13, 5x+4y+7z=β, 175x+194y+57z=361 has infinitely many solutions, then α+β+2 is equal to
(A)4
(B)3
(C)5
(D)6
Q69·MathematicsSingle correct
The domain of the function f(x)=[x]2−3[x]−101 is (where [x] denotes the greatest integer less than or equal to x)
(A)(−∞,−3)∪(5,∞)
(B)(−∞,−2)∪(6,∞)
(C)(−∞,−3]∪(6,∞)
(D)(−∞,−3]∪[6,∞)
Q70·MathematicsSingle correct
Let P be the plane passing through the points (5,3,0), (13,3,−2) and (1,6,2). For α∈N, if the distances of the points A(3,4,α) and B(2,α,a) from the plane P are 2 and 3 respectively, then the positive value of a is
(A)6
(B)4
(C)3
(D)5
Q71·MathematicsSingle correct
The converse of the statement ((∼p)∧q)⇒r is
(A)(∼r)⇒p∧q
(B)(∼r)⇒((∼p)∧q)
(C)r⇒((∼p)∧q)
(D)(p∨(∼q))⇒(∼r)
Q72·MathematicsSingle correct
The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45∘ and from the feet of another person standing due West of the tower is 30∘. If the height of the tower is 5 metres, then the distance (in metres) between the two persons is equal to
(A)10
(B)25
(C)55
(D)255
Q73·MathematicsSingle correct
Let a, b, c and d be positive real numbers such that a+b+c+d=11. If the maximum value of a5b3c2d is 3750β, then the value of β is
(A)90
(B)110
(C)55
(D)108
Q74·MathematicsSingle correct
If the radius of the largest circle with centre (2,0) inscribed in the ellipse x2+4y2=36 is r, then 12r2 is equal to
(A)72
(B)115
(C)92
(D)69
Q75·MathematicsSingle correct
If the mean of the observations 1,2,4,5,x and y be 5 and their variance be 10, then their mean deviation about the mean is equal to
(A)310
(B)37
(C)3
(D)38
Q76·MathematicsSingle correct
The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)n+2, which are in the ratio 1:3:5, is equal to
(A)25
(B)63
(C)41
(D)92
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
(A)103
(B)104
(C)101
(D)102
Q78·MathematicsSingle correct
For a∈C, let A={z∈C:Re(a+zˉ)>Im(aˉ+z)} and B={z∈C:Re(a+zˉ)<Im(aˉ+z)}. Then among the two statements: (S1): If Re(a),Im(a)>0, then the set A contains all the real numbers; (S2): If Re(a),Im(a)<0, then the set B contains all the real numbers,
(A)Only (S1) is true
(B)Both are false
(C)Only (S2) is true
(D)Both are true
Q79·MathematicsSingle correct
Let A={1,3,4,6,9} and B={2,4,5,8,10}. Let R be a relation defined on A×B such that R={((a1,b1),(a2,b2)):a1≤b2 and b1≤a2}. Then the number of elements in the set R is
Let g and f be two functions defined as f(x)={x+1,∣x−1∣,x<0x≥0 and g(x)={x+1,1,x<0x≥0. Then (g∘f)(x) is
(A)differentiable everywhere
(B)continuous everywhere but not differentiable exactly at one point
(C)not continuous at x=−1
(D)continuous everywhere but not differentiable at x=1
Q81·MathematicsNumerical
The number of points, where the curve f(x)=e8x−e6x−3e4x−e2x+1, x∈R cuts the x-axis, is equal to
Q82·MathematicsNumerical
The probability of getting a head for a biased coin is 41. It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation 64x2+5Nx+1=0 has no real root is qp, where p and q are co-prime, then q−p is equal to
Q83·MathematicsNumerical
Let a=i^+2j^+3k^ and b=i^+j^−k^. If c is a vector such that a⋅c=11, b⋅(a×c)=27 and b⋅c=−3∣b∣, then ∣a×c∣2 is equal to
Q84·MathematicsNumerical
Let S={z∈C−{i,2i}:z2−3iz−2z2+8iz−15∈R}. If α−1113i∈S, α∈R−{0}, then 242α2 is equal to
Q85·MathematicsNumerical
For k∈N, if the sum of the series 1+k4+k28+k313+k419+⋯ is 10, then the value of k is
Q86·MathematicsNumerical
Let A={1,2,3,4,5} and B={1,2,3,4,5,6}. Then the number of functions f:A→B satisfying f(1)+f(2)=f(4)−1 is equal to
Q87·MathematicsNumerical
Let the tangent to the parabola y2=12x at the point (3,α) be perpendicular to the line 2x+2y=3. Then the square of the distance of the point (6,−4) from the normal to the hyperbola α2x2−9y2=9α2 at its point (α−1,α+2) is equal to
Q88·MathematicsNumerical
Let the line ℓ:x=−21−y=λz−3, λ∈R meet the plane P:x+2y+3z=4 at the point (α,β,γ). If the angle between the line ℓ and the plane P is cos−1(145), then α+2β+6γ is equal to
Q89·MathematicsNumerical
If the line ℓ1:3y−2x=3 is the angular bisector of the lines ℓ2:x−y+1=0 and ℓ3:αx+βy+17=0, then α2+β2−α−β is equal to
Q90·MathematicsNumerical
If A is the area in the first quadrant enclosed by the curve C:2x2−y+1=0, the tangent to C at the point (1,3) and the line x+y=1, then the value of 60A is
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.
Take the 11 April 2023 Shift 2 paper as a timed mock and Jarvis marks it, then tells you which errors were conceptual gaps, which were silly mistakes, and which pattern you have now repeated. Step-by-step solutions for every question included.