JEE Main 2023 (25 Jan Shift 2) As Per Reduced Syllabus
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Question Paper
Physics Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A body of mass is taken from earth surface to the height h equal to twice the radius of earth (Re), the increase in potential energy will be : (g= acceleration due to gravity on the surface of earth)
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The resistance of a wire is 5Ω. Its new resistance in ohm, if stretched to 5 times of its original length will be :
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Every planet revolves around the sun in an elliptical orbit :
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below :
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The energy levels of an atom is shown is figure.
Which one of these transitions will result in the emission of a photon of wavelength 124.1nm?
Given (h=6.62×10–34Js)
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I and List II
A
Gauss’s Law in Electrostatics
I
∮E⃗ ⋅dl→=−dϕBdt
B
Faraday's Law
II
∮B⃗ ⋅dA⃗ =0
C
Gauss’s Law in Magnetism
III
∮B⃗ ⋅dl⃗ =μ0ic+μ0∈0dϕEdt
D
Ampere-Maxwell Law
IV
∮E⃗ ⋅ds⃗ =q∈0
Choose the correct answer from the options given below :
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A point charge of 10µC is placed at the origin. At what location on the X-axis should a point charge of 40µC be placed so that the net electric field is zero at x=2cm on the X-axis ?
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Two objects are projected with same velocity u however at different angles α and β with the horizontal. If α+β=90°, the ratio of horizontal range of the first object to the 2nd object will be :
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :-
A. Real
B. Erect
C. Smaller in size than object
D. Laterally inverted
Choose the most appropriate answer from the options given below:
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A particle executes simple harmonic motion between x=–Aandx=+A. If time taken by particle to go from x=0 to A2 is 2s; then time taken by particle in going from x=A2 to A is:
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Length of a string tied to two rigid supports is 40cm. Maximum length (wave length in cm ) of a stationary wave produced on it is
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II :
List I
List II
A
Isothermal Process
I
Work done by the gas decreases internal energy
B
Adiabatic Process
II
No change in internal energy
C
Isochoric Process
III
The heat absorbed goes partly to increase internal energy and partly to do work
D
Isobaric Process
IV
No work is done on or by the gas
Choose the correct answer from the options given below :
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
For a moving coil galvanometer, the deflection in the coil is 0.05rad when a current of 10mA is passed through it. If the torsional constant of suspension wire is 4.0×10–5Nmrad−1, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in cm2 ) is :
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (µ) is equal to :
.
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II
List
List II
A
Young's Modulus (Y)
I
[ML–1T–1]
B
Co-efficient of Viscosity (η)
II
[ML2T–1]
C
Planck's Constant (h)
III
[ML–1T–2]
D
Work Function (ϕ)
IV
[ML2T–2]
Choose the correct answer from the options given below:
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements :
Statement I : Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement II : For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.
In the light of above statements, choose the most appropriate answer from the options given below.
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The distance travelled by a particle is related to time t as x=4t2. The velocity of the particle at t=5s is
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A wire of length 1m moving with velocity 8ms−1 at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be ___________.
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by :
.
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Statement I : When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.
Statement II : When such P-type and N-type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter.
In the light of above statements, choose the most appropriate answer from the options given below.
Physics Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:2. The ratio of their nuclear sizes will be (x3)13. The value of ‘x’ is:
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
If a solid sphere of mass 5kg and a disc of mass 4kg have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be x7. The value of x is ______.
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
A capacitor has capacitance 5µF when its parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness d2 is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ______ µF.
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
5 beats/ second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95m or 1m. The frequency of the fork will be: (mark answer in Hz)
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
A body of mass 1kg collides head on elastically with a stationary body of mass 3kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2ms−1. The initial speed of the smaller body before collision is ______ ms−1.
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
A spherical drop of liquid splits into 1000 identical spherical drops. If ui is the surface energy of the original drop and uf is the total surface energy of the resulting drops, the (ignoring evaporation), ufui=(10x). Then value of x is ______:
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
An object is placed on the principal axis of convex lens of focal length 10cm as shown. A plane mirror is placed on the other side of lens at a distance of 20cm. The image produced by the plane mirror is 5cm inside the mirror. The distance of the object from the lens is ____ cm.
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
Two cells are connected between points A and B as shown. Cell 1 has emf of 12V and internal resistance of 3Ω. Cell 2 has emf of 6V and internal resistance of 6Ω. An external resistor R of 4Ω is connected across A and B. The current flowing through R will be ______ A.
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
A series LCR circuit is connected to an AC source of 220V, 50Hz. The circuit contains a resistance R=80Ω, an inductor of inductive reactance XL=70Ω, and a capacitor of capacitive reactance XC=130Ω. The power factor of circuit is x10. The value of x is:
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is ______ ×10−6T. (Given: 2√=1.4)
Chemistry Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Magnetic moment of Gd3+ ion (Z=64) is
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II.
Choose the correct answer from the options given below :-
List I Isomeric pairs
List II Type of isomers
A
Propanamine and N- Methylethanamine
I
Metamers
B
Hexan-2-one Hexan-3-one
II
Positional isomers
C
Ethanamide and Hydroxyethanimine
III
Functional isomers
D
o-nitrophenol and pnitrophenol
IV
Tautomers
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The order of increasing sizes of atomic radii among the elements O, S, Se and As is :
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements, one is labelled as AssertionA and the other is labelled as Reason R
Assertion A :- Carbon forms two important oxides CO and CO2. CO is neutral whereas CO2 is acidic in nature.
Reason R : CO2 can combine with water in a limited way to form carbonic acid, while CO is sparingly soluble in water.
In the light of the above statements, choose the most appropriate answer from the options given below :-
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
When the hydrogen ion concentration [H+]changes by a factor of 1000 , the value of pH of the solution
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The isomeric deuterated bromide with molecular formula C4H8DBr having two chiral carbon atoms is
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which one among the following metals is the weakest reducing agent?
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
What is the mass ratio of ethylene glycol (C2H6O2, molar mass =62g/mol) required for making 500g of 0.25 molal aqueous solution and 250mL of 0.25 molar aqueous solution?
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The electronic configuration with the highest ionization enthalpy is:
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Find out the major product from the following reaction.
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II
List I (Amines)
List II (pKb)
A.
Aniline
I.
3.25
B.
Ethanamine
II.
3.00
C.
N-Ethylethanamine
III.
9.38
D.
N, N-Diethylethanamine
IV.
3.29
Choose the correct answer from the options given below:-
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
' A ' in the given reaction is
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A:- Butylated hydroxyl anisole when added to butter increases its shelf life.
Reason R:- Butylated hydroxyl anisole is more reactive towards oxygen than food.
In the light of the above statements, choose the most appropriate answer from the options given below:-
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A chloride salt solution acidified with dil. HNO3 gives a curdy white precipitate, [A], on addition of AgNO3. [A] on treatment with NH4OH gives a clear solution, B.
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The rate of a reaction doubles when its temperature changes from 300Kto310K. Activation energy of such a reaction will be: (R=8.314 JK-1mol-1andlog 2=0.301)
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following statements is wrong?
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Statement I:- Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre.
Statement II:- The crossed arrow of the dipole moment symbolizes the direction of the shift of charges in the molecules.
In the light of the above statements, choose the most appropriate answer from the options given below:-
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II
List I Coordination entity
List II Wavelength of light absorbed in nm
A
[CoCl(NH3)5]2+
I.
310
B
[Co(NH3)6]3+
II.
475
C
[Co(CN)6]3−
III.
535
D
[Cu(H2O)4]2+
IV.
600
Choose the correct answer from the options given below :-
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following represents the correct order of metallic character of the given elements?
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state changes from
Chemistry Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
Numerical Type The answer has to be filled into the input box provided below.
The number of given orbitals which have electron density along the axis is
px,py,pz,dxy,dyz,dxz,d2z,dx2−y2
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
28.0 L of CO2 is produced on complete combustion of 16.8L gaseous mixture of ethene and methane at 25°C and 1 atm. Heat evolved during the combustion process is kJ
Given:ΔHC(CH4)=−900kJmol−1
ΔHC(C2H4)=−1400kJmol−1.
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4 respectively. The pH of their salt (AB) solution at 25oC is (round off answer to nearest integer)
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
The volume of 0.1 M strong dibasic acid sufficient to neutralize 1g of a base that furnishes 0.04 mole of OH− in aqueous solution is : (mark answer in mL)
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
The number of pairs of the solution having the same value of the osmotic pressure from the following is (Assume 100% ionization)
A. 0.500MC2H5OH(aq) and 0.25MKBr(aq) B. 0.100MK4[Fe(CN)6](aq) and 0.100MFeSO4(NH4)2SO4(aq)
C. 0.05MK4[Fe(CN)6] (aq) and 0.25MNaCl(aq) D. 0.15MNaCl(aq) and 0.1MBaCl2(aq) E. 0.02MKCl.MgCl2.6H2O(aq) and 0.05MKCl(aq)
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following is _________
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is (Given : Molar mass of A=84gmol−1 )
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
A first order reaction has the rate constant, k=4.6×10−3s−1. The number of correct statement/s from the following is/are Given: log3=0.48.
A. Reaction completes in 1000s. B. The reaction has a half-life of 500s. C. The time required for 10% completion is 25 times the time required for 90% completion. D. The degree of dissociation is equal to (1−e−kt). E. The rate and the rate constant have the same unit.
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
Total number of moles of AgCl precipitated on addition of excess of AgNO3 to one mole each of the following complexes [Co(NH3)4Cl2]Cl, [Ni(H2O)6]Cl2,[Pt(NH3)2Cl2] and [Pd(NH3)4]Cl2 is
Mathematics Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let y=y(t) be a solution of the differential equation dydt+αy=γe−βt Where, α>0,β>0 and γ>0. Then Limt→∞y(t)
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let x¯, M and σ2 be respectively the mean, mode and variance of n observations x1,x2,....,xn and di=−xi−a,i=1,2,....,n, where a is any number.
Statement I: Variance of d1,d2,...,dn is σ2.
Statement II: Mean and mode of d1,d2,....,dn are −x¯−a and −M−a, respectively.
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let O be the vertex and Q be any point on the parabola, x2=8y. If the point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N−2,3N−−−√,N+2 are in geometric progression be k48. Then the value of k is
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let A,B,C be 3×3 matrices such that A is symmetric and B and C are skew-symmetric.
Consider the statements
(S1)A13B26−B26A13 is symmetric
(S2)A26C13−C13A26 is symmetric
Then,
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let f:R→R be a function defined by f(x)=logm√{2√(sinx−cosx)+m−2}, for some m, such that the range of f is [0,2]. Then the value of m is _____ .
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The shortest distance between the lines x+1=2y=−12z and x=y+2=6z−6 is
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let T and C respectively, be the transverse and conjugate axes of the hyperbola 16x2−y2+64x+4y+44=0. Then the area of the region above the parabola x2=y+4, below the transverse axis T and on the right of the conjugate axis C is:
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If a⃗ and b⃗ are non-collinear vectors, then the value of α for which the vectors u⃗ =(α−2)a⃗ +b⃗ and v⃗ =(2+3α)a⃗ −3b⃗ are collinear is :
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The foot of perpendicular of the point (2,0,5) on the line x+12=y−15=z+1−1 is (α,β,γ). Then. Which of the following is NOT correct?
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If the function f(x)=⎧⎩⎨⎪⎪⎪⎪⎪⎪(1+|cosx|)λ|cosx|μ,ecot6xcot4x,0<x<π2x=π2π2<x<π is continuous at x=π2, then 9λ+6logcμ+μ6−e6λ is equal to
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let the function f(x)=2x3+(2p−7)x2+3(2p−9)x−6 have a maxima for some value of x<0 and a minima for some value of x>0. Then, the set of all values of p is
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The number of functions f:{1,2,3,4}→{a∈Z:|a|≤8} satisfying f(n)+1nf(n+1)=1,∀n∈{1,2,3} is
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let a⃗ =−iˆ−jˆ+kˆ,a⃗ ⋅b⃗ =1 and a⃗ ×b⃗ =iˆ−jˆ. Then a⃗ −6b⃗ is equal to
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The middle term in the expansion of (1−1x)n(1−x)n in powers of x is
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The integral 16∫21dxx3(x2+2)2 is equal to
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let A=⎡⎣110√−310√310√110√⎤⎦ and B=[10−i1], where i=−1−−−√. If M=ATBA, then the inverse of the matrix AM2023AT is
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let z be a complex number such that ∣∣z−2iz+i∣∣=2,z≠−i. Then z lies on the circle of radius 2 and centre
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let f(x)=2xn+λ,λ∈R,n∈N, and f(4)=133, f(5)=255. Then the sum of all the positive integer divisors of (f(3)−f(2)) is
Mathematics Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
If ∫313|logex|dx=mnloge(n2e), where m and n are coprime natural numbers, then m2+n2−5 is equal to _____ .
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
The number of common tangents to the circles x2+y2−4x−6y−12=0 and x2+y2+6x+18y+26=0, is
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
For the two positive numbers a,b, if a,b and 118 are in a geometric progression, while 1a,10 and 1b are in an arithmetic progression, then, 16a+12b is equal to _____ .
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is k10.Then the value of k is _____ .
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is _____ .
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
If m and M are the minimum and the maximum values of 4+12sin22x−2cos4x,x∈R, then M−m is equal to: K, find 4K.
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
A triangle is formed by X-axis, Y-axis and the line 3x+4y=60. Then the number of points P(a,b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is _____ .
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
Let a∈R and let α,β be the roots of the equation x2+6014x+a=0. If α4+β4=−30, then the product of all possible values of a is _____ .
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
The remainder when (2023)2023 is divided by 35 is
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
If the shortest distance between the line joining the points (1,2,3) and (2,3,4), and the line x−12=y+1−1=z−20 is α, then 28α2 is equal to _____ .
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