JEE Main 26 February 2021 Shift 2 Question Paper with Answers
26 February 2021 · February session · 90 questions
The complete JEE Main 26 February 2021 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 26 February 2021 Shift 2
Q1·PhysicsSingle correct
A tuning fork A of unknown frequency produces 5beats/s with a fork of known frequency 340 HZ. When fork A filed, the beat frequency decreases to 2beats/s. What is the frequency of fork A?
(A)342 Hz
(B)335 Hz
(C)338 Hz
(D)345 Hz
Q2·PhysicsSingle correct
The trajectory a projectile in a vertical plane is y = αx − βx2, where α and β are constants and x & y are respectively the horizontal and vertical distance of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by:
(A)tan−1α,4βα2
(B)tan−1β,2βα2
(C)tan−1(αβ),βα2
(D)tan−1α,β4α2
Q3·PhysicsSingle correct
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance ‘h’, the square of angular velocity of wheel will be:
(A)I+mr22gh
(B)2gh
(C)I+2mr22mgh
(D)I+mr22mgh
Q4·PhysicsSingle correct
Find the peak current and resonant frequency of the following circuit (as shown in figure)
(A)0.2 A and 100 Hz
(B)2 A and 50 Hz
(C)2 A and 100 Hz
(D)0.2 A and 50 Hz
Q5·PhysicsSingle correct
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors a,b and c respectively. Then choose the correct relation for these vectors.
(A)b=2a+c
(B)b=a−c
(C)b=a+2c
(D)b=a−2(a⋅c)c
Q6·PhysicsSingle correct
A radioactive sample is undergoing α decay. At any time t1, its activity is A and another time t2, the activity is 5A. What is the average life time for the sample?
(A)ln5t2−t1
(B)2ln(t2+t1)
(C)ln5t1−t2
(D)t2−t1ln5
Q7·PhysicsSingle correct
A particle executes S.H.M., the graph of velocity as a function of displacement is:
(A)a circle
(B)a parabola
(C)an ellipse
(D)a helix
Q8·PhysicsSingle correct
A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of t2t1 will be:
(A)a2a1+a2
(B)a1a2
(C)a1a1+a2
(D)a2a1
Q9·PhysicsSingle correct
Draw the output Y in the given combination of gates.
(A)(A)
(B)(B)
(C)(C)
(D)(D)
Q10·PhysicsSingle correct
An inclined plane making an angle of 30° with horizontal is placed in a uniform horizontal electric field 200CN as shown in the figure. A body of mass 1 kg and charge 5mC is allowed to slide down from rest at a height of 1m. If the coefficient of frication is 0.2, find the time taken by the body to reach the bottom.
[g=9.8m/s2,sin30∘=21;cos30∘=23]
(A)2.3 s
(B)0.46 s
(C)1.3 s
(D)0.92 s
Q11·PhysicsSingle correct
If ‘C’ and ‘V’ represent capacity and voltage respectively then what are the dimensions of λ where C/V = λ?
(A)[M−2L−4I3T7]
(B)[M−2L−3I2T6]
(C)[M−1L−3I−2T−7]
(D)[M−3L−4I3T7]
Q12·PhysicsSingle correct
Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R.
Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image.
Reason R : Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle.
In the light of the above statements, choose the most appropriate answer from the options given below:
(A)Both A and R are true but R is NOT the correct explanationof A
(B)Both A and R are true and R is the correct explanation of A
(C)A is true but R is false
(D)A is false but R is true
Q13·PhysicsSingle correct
The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be:
(A)4.17 m/s
(B)4.34 m/s
(C)219 m/s
(D)3.25 m/s
Q14·PhysicsSingle correct
Two masses A and B, each of mass M are fixed together by a massless springs. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration ‘a’, than the acceleration of mass B will be:
(A)MF+Ma
(B)MF−Ma
(C)MMa−F
(D)F+MaMF
Q15·PhysicsSingle correct
A wire of 1Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in a resistance to the nearest integer is:
(A)25%
(B)12.5%
(C)76%
(D)56%
Q16·PhysicsSingle correct
Given below are two statements :
Statement (1) :- A second's pendulum has a time period of 1 second.
Statement (2) :- It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options give below.
(A)Both Statement I and Statement II are false
(B)Statement I is true but Statement II is false
(C)Statement I is false but Statement II is true
(D)Both Statement I and Statement II is true
Q17·PhysicsSingle correct
An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5×10−4 Wb/m2 and the angle of dip is 60°. The emf induced between the tips of the plane wings will be __________.
(A)88.37 mV
(B)62.50 mV
(C)54.125 mV
(D)108.25 mV
Q18·PhysicsSingle correct
The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :
(A)2l1+l2
(B)T2−T1T1l1−T2l2
(C)T1+T2T2l1+T1l2
(D)T2−T1T2l1−T1l2
Q19·PhysicsSingle correct
The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is :
(A)polyatomic only
(B)monoatomic only
(C)either monoatomic or diatomic
(D)diatomic only.
Q20·PhysicsSingle correct
Given below are two statements :
Statement – I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement – II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r ( < R) is zero but theelectric flux passing through this closed spherical surface of radius r is not zero.
In the light of the above statements. Choose the correct answerfrom the option given below :
(A)Statement I is true but Statement II is false
(B)Statement I is false but Statement II is true
(C)Both Statement I and Statement II are true
(D)Both Statement I and Statement II are false
Q21·PhysicsNumerical
If thehighest frequency modulating a carrier is 5 kHz, then the number of AM broadcast stations accommodated in a 90 kHz bandwidth are ____________________.
Q22·PhysicsNumerical
1 mole of rigid diatomic gas performs a work of 5Q when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is 8xR. The value of x is __________.
Q23·PhysicsNumerical
A particle excutes S.H.M with amplitude 'a' and time period T. The displacement of the particle when its speed is half of maximum speed is 2xa. The value of x is ______________
Q24·PhysicsNumerical
Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is ________.
Q25·PhysicsNumerical
A point source of light S, placed at a distance 60 cm infront of the centre of plane mirror of width 50 cm, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is _______________cm
Q26·PhysicsNumerical
The zener diode has a VZ= 30 V. The current passing through the diode for the following ciruit is ________________mA.
Q27·PhysicsNumerical
In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is ________________.
Q28·PhysicsNumerical
27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___________________ times that of a smaller drop.
Q29·PhysicsNumerical
The volume V of a given mass of monatomic gas changes with temperature T according to the relation V=KT32. The work done when temperature changes by 90 K will be xR. The value of x is ____________________.
[R =universal gas constant]
Q30·PhysicsNumerical
Time period of a simple pendulum is T. The time taken to complete 85 oscillations starting from mean position is βαT. The value of α is _____________.
Chemistry — JEE Main 26 February 2021 Shift 2
Q31·ChemistrySingle correct
2,4-DNP test can be used to identify:
(A)aldehyde
(B)halogens
(C)ether
(D)amine
Q32·ChemistrySingle correct
Identify A in the following chemical reaction.
(A)(A)
(B)(B)
(C)(C)
(D)(D)
Q33·ChemistrySingle correct
The nature of charge on resulting colloidal particles when FeCl3 is added to excess of hot water is:
(A)positive
(B)neutral
(C)sometimes positive and sometimes negative
(D)negative
Q34·ChemistrySingle correct
Match List-I with List-II
List-I
(c) 2CH3CH2Cl + 2Na Ether C2H5– C2H5 + 2NaCl
(d) 2C2H5Cl +2Na Ether C6H5– C6H5 + 2NaCl
List-II
(i) Wurtz reaction
(ii) Sandmeyer reaction
(iii) Fitting reaction
(iv) Gatterman reaction
Choose the correct answer from the option given below:
(A)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(B)(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(C)(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
(D)(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
Q35·ChemistrySingle correct
In CH2 = C = CH–CH3 molecule, the hybridization of carbon 1, 2, 3 and 4 respectively are:
(A)sp2, sp, sp2, sp3
(B)sp2, sp2, sp2, sp3
(C)sp2, sp3, sp2, sp3
(D)sp3, sp, sp3, sp3
Q36·ChemistrySingle correct
Match List-I with List-II.
List-I
(a) Sucrose
(b) Lactose
(c) Maltose
List-II
(i) β-D-Galactose and β-D-Glucose
(ii) α-D-Glucose and β-D-Fructose
(iii) α-D- Glucose and α-D-Glucose
Choose the correct answer from the options given below:
(A)(a)-(iii), (b)-(ii), (c)-(i)
(B)(a)-(iii), (b)-(i), (c)-(ii)
(C)(a)-(i), (b)-(iii), (c)-(ii)
(D)(a)-(ii), (b)-(i), (c)-(iii)
Q37·ChemistrySingle correct
Which pair of oxides is acidic in nature?
(A)N2O, BaO
(B)CaO, SiO2
(C)B2O3, CaO
(D)B2O3, SiO2
Q38·ChemistrySingle correct
Calgon is used for water treatment. Which of the following statement is NOT true about calgon?
(A)Calgon contains the 2nd most abundant element by weight in the earth's crust.
(B)It is also known as Graham's salt.
(C)It is polymeric compound and is water soluble.
(D)It doesnot remove Ca2+ ion by precipitation.
Q39·ChemistrySingle correct
Ceric ammonium nitrate and CHCl3/alc. KOH are used for the identification of functional groups present in __________and_________respectively.
(A)alcohol, amine
(B)amine, alcohol
(C)alcohol, phenol
(D)amine, phenol
Q40·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In TlI3, isomorphous to CsI3, the metal is present in +1 oxidation state.
Reason R: Tl metals has fourteen f electrons in its electronic configuration.
In the light of the above statements, choose the most appropriate answer from the options given below:
(A)Both A and R are correct and R is the correct explanation of A
(B)A is not correct but R is correct
(C)Both A and R are correct R is NOT the correct explanation of A
(D)A is correct but R is not correct
Q41·ChemistrySingle correct
The correct order of electron gain enthalpy is:
(A)S > Se > Te > O
(B)O > S > Se > Te
(C)S > O > Se > Te
(D)Te > Se > S > O
Q42·ChemistrySingle correct
Identify A in the given chemical reaction.
(A)(A)
(B)(B)
(C)(C)
(D)(D)
Q43·ChemistrySingle correct
Match List-I with List-II
List-I
(a) Siderite
(b) Calamine
(c) Malachite
(d) Cryolite
List-II
(i) Cu
(ii) Ca
(iii) Fe
(iv) Al
(v) Zn
Choose the correct answer from the options given below:
(A)(a)-(i), (b)-(ii), (c)-(v), (d)-(iii)
(B)(a)-(iii), (b)-(v), (c)-(i), (d)-(iv)
(C)(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(D)(a)-(iii), (b)-(i), (c)-(v), (d)-(ii)
Q44·ChemistrySingle correct
Identify A in the given reaction
(A)(A)
(B)(B)
(C)(C)
(D)(D)
Q45·ChemistrySingle correct
Match List-I with List-II.
List-I
(a) Sodium Carbonate
(b) Titanium
(c) Chlorine
(d) Sodium hydroxide
List-II
(i) Deacon
(ii) Caster-Kellner
(iii) Van-Arkel
(iv) Solvay
Choose the correct answer from the option given below:
(A)(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
(B)(a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)
(C)(a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)
(D)(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
Q46·ChemistrySingle correct
Match List-I with List-II.
List-I (Molecule) List-II (Bond order)
(a) Ne2 (i) 1
(b) N2 (ii) 2
(c) F2 (iii) 0
(d) O2 (iv) 3
Choose the correct answer from the options given below:
(A)(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(B)(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(C)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(D)(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
Q47·ChemistrySingle correct
Which of the following forms of hydrogen emits low energy β− particles?
(A)Proton H+
(B)Deuterium 12H
(C)Protium 11H
(D)Tritium 13H
Q48·ChemistrySingle correct
A. Phenyl methanamine
B. N, N-Dimethylaniline
C. N-Methyl aniline
D. Benzenamine
Choose the correct order of basic nature of the above amines.
(A)D > C > B > A
(B)D > B > C > A
(C)A > C > B > D
(D)A > B > C > D
Q49·ChemistrySingle correct
Considering the above reaction, the major product among the following is:
(A)(A)
(B)(B)
(C)(C)
(D)(D)
Q50·ChemistrySingle correct
Seliwanoff test and Xanthoproteic test are used for the identification of ___________ and ____________ respectively
(A)ketoses, proteins
(B)proteins, ketoses
(C)aldoses, ketoses
(D)ketoses, aldoses
Q51·ChemistryNumerical
The NaNO3 weighed out to make 50 mL of an aqueous solution containing 70.0 mg Na+ per mL is_________g. (Rounded off to the nearest integer)
[Given: Atomic weight in g mol−1. Na: 23; N: 14; O : 16]
Q52·ChemistryNumerical
The number of stereoisomers possible for [Co(ox)2(Br)(NH3)]2− is _____________[ox = oxalate]
Q53·ChemistryNumerical
The average S−F bond energy in kJ mol−1 of SF6 is ____________. (Rounded off to the nearest integer)
[Given : The values of standard enthalpy of formation of SF6(g), S(g) and F(g) are - 1100, 275 and 80 kJ mol−1 respectively.]
Q54·ChemistryNumerical
Emf of the following cell at 298 K in V is x ×10−2.
Zn∣Zn2+ (0.1 M)∣∣Ag+(0.01 M)∣ Ag
The value of x is ___________. (Rounded off to the nearest integer)
[Given: EZn2+/Zn0 = −0.76V; EAg+/Ag0 = +0.80V; F2.303RT = 0.059]
Q55·ChemistryNumerical
A ball weighing 10g is moving with a velocity of 90ms−1. If the uncertainty in its velocity is 5%, then the uncertainty in its position is _________×10−33m. (Rounded off to the nearest integer)
[Given : h = 6.63×10−34 Js]
Q56·ChemistryNumerical
In mildly alkaline medium, thiosulphate ion is oxidized by MnO4− to "A". The oxidation state of sulphur in "A" is_________.
Q57·ChemistryNumerical
When 12.2 g of benzoic acid is dissolved in 100g of water, the freezing point of solution was found to be −0.93°C (Kf (H2O) = 1.86 K kg mol−1). The number (n) of benzoic acid molecules associated (assuming 100% association ) is_______________.
Q58·ChemistryNumerical
If the activation energy of a reaction is 80.9 kJ mol−1, the fraction of molecules at 700K, having enough energy to react to form products is e−x. The value of x is _______.
(Rounded off to the nearest integer)
[Use R = 8.31 JK−1mol−1]
Q59·ChemistryNumerical
The pH of ammonium phosphate solution, if pka of phosphoric acid and pkb of ammonium hydroxide are 5.23 and 4.75 respectively, is_______________.
Q60·ChemistryNumerical
The number of octahedral voids per lattice site in a lattice is ___________.
(Rounded off to the nearest integer)
Mathematics — JEE Main 26 February 2021 Shift 2
Q61·MathematicsSingle correct
Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and y + 2z = 4. If point P(α, β, γ) is the foot of perpendicular from (3, 2, 1) on L, then the value of 21(α + β + γ) equals :
(A)142
(B)68
(C)136
(D)102
Q62·MathematicsSingle correct
The sum of the series ∑n=1∞(2n+1)!n2+6n+10 is equal to :
(A)841e+819e−1−10
(B)−841e+819e−1−10
(C)841e−819e−1−10
(D)841e+819e−1+10
Q63·MathematicsSingle correct
Let f(x) be a differentiable function at x = a with f′(a)=2 and f(a) = 4. Then limx→ax−axf(a)−af(x) equals :
(A)2a + 4
(B)2a − 4
(C)4 − 2a
(D)a + 4
Q64·MathematicsSingle correct
Let A (1, 4) and B(1, −5) be two points. Let P be a point on the circle (x−1)2+(y−1)2=1 such that (PA)2+(PB)2 have maximum value, then the points, P, A and B lie on :
(A)a parabola
(B)a straight line
(C)a hyperbola
(D)an ellipse
Q65·MathematicsSingle correct
If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2+y2=1 is a circle of the radius r, then r is equal to :
(A)41
(B)21
(C)1
(D)31
Q66·MathematicsSingle correct
Let slope of the tangent line to a curve at any point P(x, y) be given by xxy2+y. If the curve intersects the line x + 2y = 4 at x = − 2, then the value of y, for which the point (3, y) lies on the curve, is :
(A)−1118
(B)−1918
(C)−34
(D)3518
Q67·MathematicsSingle correct
Let A1 be the area of the region bounded by the curves y = sinx, y = cos x and y-axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y = sin x, y = cos x, x-axis and x= 2π in the first quadrant. Then,
(A)A1=A2 and A1+A2=2
(B)A1:A2=1:2 and A1+A2=1
(C)2A1=A2 and A1+A2=1+2
(D)A1:A2=1:2 and A1+A2=1
Q68·MathematicsSingle correct
If 0 < a, b < 1, and tan−1a+tan−1b=4π, then the value of (a+b)−(2a2+b2)+(3a3+b3)−(4a4+b4)+… is :
(A)loge2
(B)loge(2e)
(C)e
(D)e2−1
Q69·MathematicsSingle correct
Let F1(A, B, C) = (A ∧ ~B) ∨ [~C ∧ (A ∨ B)] ∨ ~A and F2(A, B) = (A ∨ B) ∨ (B → ~A) be two logical expressions. Then :
(A)F1 is not a tautology but F2 is a tautology
(B)F1 is a tautology but F2 is not a tautology
(C)F1 and F2 both area tautologies
(D)Both F1 and F2 are not tautologies
Q70·MathematicsSingle correct
Consider the following system of equations :
x + 2y − 3z = a
2x + 6y − 11 z = b
x − 2y + 7z = c,
Where a, b and c are real constants. Then the system of equations :
(A)has a unique solution when 5a = 2b + c
(B)has infinite number of solutions when 5a = 2b +c
(C)has no solution for all a, b and c
(D)has a unique solution for all a, b and c
Q71·MathematicsSingle correct
A seven digit number is formed using digit 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is :
(A)76
(B)74
(C)73
(D)71
Q72·MathematicsSingle correct
If vectors a1=xi^−j^+k^ and a2=i^+yj^+zk^ are collinear, then a possible unit vector parallel to the vector xi^+yj^+zk^ is :
(A)21(−j^+k^)
(B)21(i^−j^)
(C)31(i^−j^+k^)
(D)31(i^+j^−k^)
Q73·MathematicsSingle correct
For x>0, if f(x)=∫1x(1+t)logetdt, then f(e)+f(e1) is equal to :
(A)21
(B)−1
(C)1
(D)0
Q74·MathematicsSingle correct
Let f : R → R be defined as f(x)=⎩⎨⎧2sin(−2πx),∣ax2+x+b∣,sin(πx)if x<−1if −1≤x≤1if x>1 If f(x) is continuous on R, then a + b equals :
(A)3
(B)−1
(C)−3
(D)1
Q75·MathematicsSingle correct
Let A = {1,2,3……,10} and f: A→ A be defined as f(k)={k+1kif k is oddif k is even Then the number of possible functions g : A→A such that gof = f is :
(A)105
(B)10C5
(C)55
(D)5!
Q76·MathematicsSingle correct
A natural number has prime factorization given by n=2x3y5z, where y and z are such that y+z=5 and y−1+z−1=65, y>z. Then the number of odd divisors of n, including 1, is :
(A)11
(B)6x
(C)12
(D)6
Q77·MathematicsSingle correct
Let f(x)=sin−1x and g(x)=2x2−x−6x2−x−2. If g(2)=limx→2g(x), then the domain of the function fog is :
(A)(−∞,−2]∪[−34,∞)
(B)(−∞,−1]∪[2,∞)
(C)(−∞,−2]∪[−1,∞)
(D)(−∞,−2]∪[−23,∞)
Q78·MathematicsSingle correct
If the mirror image of the point (1,3,5) with respect to the plane 4x−5y+2z=8 is (α,β,γ), then 5(α+β+γ) equals:
(A)47
(B)39
(C)43
(D)41
Q79·MathematicsSingle correct
Let f(x)=∫0xetf(t)dt+ex be a differentiable function for all x∈R. Then f(x) equals.
(A)2e(ex−1)−1
(B)e(ex−1)
(C)2eex−1
(D)eex−1
Q80·MathematicsSingle correct
The triangle of maximum area that can be inscribed in a given circle of radius 'r' is:
(A)A right angle triangle having two of its sides of length 2r and r.
(B)An equilateral triangle of height 32r.
(C)An isosceles triangle with base equal to 2r.
(D)An equilateral triangle having each of its side of length 3 r.
Q81·MathematicsNumerical
The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is
Q82·MathematicsNumerical
Let α and β be two real numbers such that α+β=1 and αβ=−1. Let Pn=(α)n+(β)n, Pn−1=11 and Pn+1=29 for some integer n≥1. Then, the value of Pn2 is ________________.
Q83·MathematicsNumerical
Let X1, X2,……….. X18 be eighteen observation such that ∑i=118(Xi−α)=36 and ∑i=118(Xi−β)2=90, where α and β are distinct real numbers. If the standard deviation of these observations is 1, then the value of ∣α−β∣ is ________________.
Q84·MathematicsNumerical
In Im,n=∫01xm−1(1−x)n−1dx, for m, n ≥ 1 and ∫01(1+x)m+nxm−1+xn−1dx=αIm,n, α∈R, then α equals______________ .
Q85·MathematicsNumerical
Let L be a common tangent line to the curves 4x2+9y2=36 and (2x)2+(2y)2=31. Then the square of the slope of the line L is ________________.
Q86·MathematicsNumerical
If the matrix A=10302000−1 satisfies the equation A20+αA19+βA=100040001 for some real numbers α and β, then β−α is equal to________________.
Q87·MathematicsNumerical
If the arithmetic mean and geometric mean of the pth and qth terms of the sequence −16, 8, −4, 2, ………… satisfy the equation 4x2−9x+5=0, then p+q is equal to ________________.
Q88·MathematicsNumerical
Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, -3) and (4,−22), and given that a−22b=3, then (a2+b2+ab) is equal to________________.
Q89·MathematicsNumerical
Let z be those complex number which satisfy ∣z+5∣≤4 and z(1+i)+zˉ(1−i)≥−10,i=−1. If the maximum value of ∣z+1∣2 is α+β2, then the value of (α+β) is ________________.
Q90·MathematicsNumerical
Let a be an integer such that all the real roots of the polynomial 2x5+5x4+10x3+10x2+10x+10 lie in the interval (a, a + 1). Then, ∣a∣ is equal to________________.
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 26 February 2021 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.