JEE Main 2020 · January session

JEE Main 9 January 2020, Shift 2

73 questions (2 more dropped by NTA): 15 numerical-answer and 58 multiple choice. 5 were rated hard and 20 easy. Its hard-question count was the joint 9th highest of the 12 2020 shifts Lumi analysed. The biggest chapter was Conic Sections, with 3 questions.

Questions: 73; 2 dropped by NTA
Numerical answer: 15; 21% of the shift
Hard: 5; 7% of the shift
Chapters asked: 54; 14 questions with a figure

Key findings · 9 Jan 2020, Shift 2

1
5 hard questions (7%): the joint 9th highest count of the 12 2020 shifts Lumi analysed. Across those shifts the hard share ran from 5% to 16%.
2
Maths was the hardest section, with 2 of 24 rated hard; Chemistry had the most easy questions (9 of 25).
3
61 questions tested a new idea, one no earlier year had asked: 95% of the 64 questions tagged to an idea.
4
3 came back from 2017: the same idea had been asked in the 2017 shifts Lumi analysed.
5
24 shared an idea with another 2020 shift (38% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Motion in a Plane in Physics (2), Amines in Chemistry (2) and Conic Sections in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

24 Q · 5 numerical

Easy 5Medium 18Hard 1

Top chapters

Chemistry

25 Q · 5 numerical

Easy 9Medium 14Hard 2

Top chapters

Maths

24 Q · 5 numerical

Easy 6Medium 16Hard 2

Top chapters

Question format

Single correct56 Q
Numerical value15 Q
Other2 Q

What each question asks you to do

Multi-step35 Q
Calculation15 Q
Application12 Q
Recall5 Q
Conceptual4 Q
Data or graph2 Q

Most common: Multi-step.

Against the other 2020 shifts

This shift next to the 11 other 2020 shifts Lumi analysed

Shares are of each shift’s scored questions. The highlighted row is this shift.

Shift	Questions	Easy	Hard	Numerical	New ideas	Multi-step
8 Jan, Shift 1	74	22%	11%	20%	92%	34%
8 Jan, Shift 2	75	28%	11%	20%	92%	39%
9 Jan, Shift 1	75	23%	16%	20%	99%	40%
9 Jan, Shift 2	73	27%	7%	21%	95%	48%
2 Sep, Shift 1	75	28%	5%	20%	95%	40%
2 Sep, Shift 2	75	20%	7%	20%	97%	32%
3 Sep, Shift 1	74	32%	12%	20%	91%	37%
3 Sep, Shift 2	75	21%	16%	20%	98%	29%
4 Sep, Shift 1	75	20%	16%	20%	98%	37%
4 Sep, Shift 2	75	32%	13%	20%	97%	39%
5 Sep, Shift 1	75	36%	7%	20%	94%	31%
6 Sep, Shift 2	75	31%	13%	20%	97%	41%

New ideas: share of a shift’s questions testing an idea no earlier year had asked. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.

Drill down

What this shift asked, and its history

Every chapter this shift asked, with all its topics and ideas. Counts and squares cover every analysed shift from 2017 to 2026; rows this shift did not ask are faded, and each row lists this shift’s questions with the most recent from other shifts.

subjectAskedShareYears’17’20’21’22’23’24’25’26

Open25 this shift3092 · 33%33%8/830299720720358540200225
Open24 this shift3084 · 33%33%8/830298716720359538199224
Open24 this shift3065 · 33%33%8/829299715710354533200225

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Every question

All 73 questions of this shift

The opening words of each question, with its chapter, topic, idea and how hard it was. Open one for the full text, options and the official answer. “New idea” means no earlier year had tested it.

Subject

Difficulty

Idea

Find

73 of 73 questions

Physics24 questions

5 easy18 medium1 hard

Q2
A particle starts from the origin at $t=0$ with an initial velocity of $3.0\,\hat{i}$ m/s and moves in the $x$ - $y$ plane with a constant acceleration $(6.0\,\hat{i} + 4.0\,\hat{j})$ m/s $^2$ . The $x$ -coordinate of the particle at the instant when its…
Motion in a Plane Kinematics in 2D Independence of Axes
EasySingle correctNew ideaIdea asked in 2 years
Q3
A uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses $m_1$ and $m_2$ ( $m_1 > m_2$ ) are attached to the ends of the string.…
System of Particles and Rotational Motion Torque and Equilibrium Torque of Tension on Pulleys
MediumSingle correct · figureNew ideaIdea asked in 3 years
Q4
A particle of mass $m$ is projected with a speed $u$ from the ground at an angle $\theta = \frac{\pi}{3}$ w.r.t. horizontal ( $x$ -axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and…
Motion in a Plane Collisions Inelastic Collisions
MediumSingle correctNew ideaIdea asked in 3 years
Q5
A rod of length $L$ has non-uniform linear mass density given by $\rho(x) = a + b\left(\frac{x}{L}\right)^2$ , where $a$ and $b$ are constants and $0 \le x \le L$ . The value of $x$ for the centre of mass of the rod is at :
System of Particles and Rotational Motion Center of Mass COM of Non-Uniform Rod
EasySingle correctNew ideaIdea asked in 2 years
Q6
A spring mass system (mass $m$ , spring constant $k$ and natural length $l$ ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with…
Laws of Motion Circular Motion Spring-Mass in Circular Motion
MediumSingle correctNew ideaIdea asked in 3 years
Q7
Planet A has mass $M$ and radius $R$ . Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are $v_A$ and $v_B$ , respectively, then $\frac{v_A}{v_B} = \frac{n}{4}$ . The value of $n$ is :
Gravitation Orbital Mechanics Escape Velocity
EasySingle correctNew ideaIdea asked in 5 years
Q8
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1:4$ , the ratio of their diameters is :
Mechanical Properties of Solids Elasticity Elastic Energy Density
MediumSingle correctNew ideaIdea asked in 4 years
Q9
A small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $\rho$ and surface tension $T$ . The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :
Mechanical Properties of Fluids Surface Tension Surface Tension Force on a Floating Sphere
MediumSingle correctNew idea
Q10
Two gases - argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to :
Kinetic Theory Kinetic Theory of Gases Relaxation Time
MediumSingle correctNew idea
Q11
A wire of length $L$ and mass per unit length $6.0\times10^{-3}\ \mathrm{kg\,m^{-1}}$ is put under tension of 540 N. Two consecutive frequencies that it resonates at are : 420 Hz and 490 Hz. Then $L$ in meters is :
Waves Waves on Strings Sonometer Laws
MediumSingle correctNew ideaIdea asked in 4 years
Q12
Two identical capacitors A and B, charged to the same potential 5V are connected in two different circuits as shown below at time $t=0$ . If the charge on capacitors A and B at time $t=CR$ is $Q_A$ and $Q_B$ respectively, then (Here $e$ is the base of natural…
Electrostatic Potential and Capacitance RC Circuits RC Circuits with Ideal Diodes
MediumSingle correct · figureNew idea
Q13
A small circular loop of conducting wire has radius $a$ and carries current $I$ . It is placed in a uniform magnetic field $B$ perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic…
Moving Charges and Magnetism Magnetic Dipole Moment Small Oscillations of a Magnetic Dipole
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q14
An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns/length and carries a current $I$ . The electron gun shoots an electron along the radius of the solenoid with speed $v$ . If the electron does not hit the…
Moving Charges and Magnetism Lorentz Force Circular Motion in Uniform B-Field
MediumSingle correct · figureNew ideaIdea asked in 4 years
Q15
In LC circuit the inductance $L = 40$ mH and capacitance $C = 100\ \mu$ F. If a voltage $V(t) = 10\sin(314\,t)$ is applied to the circuit, the current in the circuit is given as :
Alternating Current Phasor Diagrams Phase Relations in RLC
MediumSingle correctNew ideaIdea asked in 5 years
Q16
A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$ , with its polarization along the direction $\hat{k}$ . The correct form of the magnetic field of the wave would be (here $B_0$ is an appropriate constant) :
Electromagnetic Waves
MediumSingle correct
Q17
There is a small source of light at some depth below the surface of water (refractive index $= \frac{4}{3}$ ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges…
Ray Optics and Optical Instruments Refraction and Snell's Law Total Internal Reflection
HardSingle correctNew ideaIdea asked in 6 years
Q18
An electron of mass $m$ and magnitude of charge $|e|$ initially at rest gets accelerated by a constant electric field $E$ . The rate of change of de-Broglie wavelength of this electron at time $t$ ignoring relativistic effects is :
Dual Nature of Radiation and Matter Matter Waves Time Rate of Change of Wavelength
MediumSingle correctNew ideaIdea asked in 3 years
Q19
The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?
Atoms Bohr's Atomic Model Identifying Atomic Number from Spectra
MediumSingle correctNew ideaIdea asked in 2 years
Q20
The current $i$ in the network is :
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Ideal vs. Practical Diode Circuit Analysis
MediumSingle correct · figureNew ideaIdea asked in 7 years
Q21
Starting at temperature 300 K, one mole of an ideal diatomic gas ( $\gamma = 1.4$ ) is first compressed adiabatically from volume $V_1$ to $V_2 = \frac{V_1}{16}$ . It is then allowed to expand isobarically to volume $2V_2$ . If all the processes are the…
Thermodynamics Thermodynamic Processes Adiabatic T-V and P-T Relations
MediumNumerical valueNew ideaIdea asked in 4 years
Q22
An electric field $\vec{E} = 4x\,\hat{i} - (y^2+1)\,\hat{j}$ N/C passes through the box shown in figure. The flux of the electric field through surfaces ABCD and BCGF are marked as $\phi_I$ and $\phi_{II}$ respectively. The difference between…
Electric Charges and Fields Gauss's Law Electric Flux Calculation
MediumNumerical value · figureNew ideaIdea asked in 4 years
Q23
In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is $l = 25$ cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing distance $l'$ (in…
Current Electricity Wheatstone Bridge Meter Bridge Principles
EasyNumerical value · figureNew ideaIdea asked in 4 years
Q24
In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when another light source of wavelength $\lambda$ is used. Then…
Wave Optics Young's Double Slit YDSE Fringe Width
EasyNumerical valueNew ideaIdea asked in 5 years
Q25
The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is used as input, the power dissipated (in mW) in each diode is; (considering both zener diodes are identical) ______.
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Zener Diode Regulation
MediumNumerical value · figureNew ideaIdea asked in 5 years

Chemistry25 questions

9 easy14 medium2 hard

Q26
The true statement amongst the following is :
Thermodynamics (Chemistry)Entropy Temperature Dependence of Reaction Entropy
EasySingle correctNew idea
Q27
The solubility product of $\mathrm{Cr(OH)_3}$ at 298 K is $6.0\times10^{-31}$ . The concentration of hydroxide ions in a saturated solution of $\mathrm{Cr(OH)_3}$ will be :
Equilibrium Solubility Product Solubility-Ksp Relationship
MediumSingle correctNew ideaIdea asked in 5 years
Q28
Amongst the following, the form of water with the lowest ionic conductance at 298 K is :
Electrochemistry
EasySingle correct
Q29
A mixture of gases $\mathrm{O_2}$ , $\mathrm{H_2}$ and $\mathrm{CO}$ are taken in a closed vessel containing charcoal. The graph that represents the correct behaviour of pressure with time is :
Surface Chemistry
EasySingle correct · figure
Q30
In the figure shown below reactant A (represented by square) is in equilibrium with product B (represented by circle). The equilibrium constant is :
Equilibrium Chemical Equilibrium Kc Expression
EasySingle correct · figureNew ideaIdea asked in 2 years
Q31
The number of $sp^2$ hybrid orbitals in a molecule of benzene is :
Chemical Bonding and Molecular Structure
EasySingle correct
Q32
The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol $^{-1}$ , respectively. How many moles of HCl and $\mathrm{H_2SO_4}$ , respectively, will be needed to react completely with 1 mole of the metal hydroxide ?
Classification of Elements and Periodicity in Properties Periodic Trends Successive Ionization Enthalpy Jumps
EasySingle correctNew ideaIdea asked in 3 years
Q33
5 g of zinc is treated separately with an excess of (a) dilute hydrochloric acid and (b) aqueous sodium hydroxide. The ratio of the volumes of $\mathrm{H_2}$ evolved in these two reactions is :
The d- and f-Block Elements s-Block Elements NaOH Reactions with Amphoteric Elements
MediumSingle correctNew idea
Q34
Among the statements (a)-(d), the correct ones are : (a) Lithium has the highest hydration enthalpy among the alkali metals. (b) Lithium chloride is insoluble in pyridine. (c) Lithium cannot form ethynide upon its reaction with ethyne. (d) Both lithium and…
The s-Block Elements s-Block Elements Diagonal Relationship
MediumOtherIdea asked in 3 yearsAsked the year before
Q35
The reaction of $\mathrm{H_3N_3B_3Cl_3}$ (A) with $\mathrm{LiBH_4}$ in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of (A) with (C) leads to $\mathrm{H_3N_3B_3(Me)_3}$ . Compounds (B) and (C) respectively, are :
The p-Block Elements Group 13 & 14 Borazine Structure and Reactivity
MediumSingle correctNew ideaIdea asked in 3 years
Q36
The isomer(s) of $\mathrm{[Co(NH_3)_4Cl_2]}$ that has/have a Cl-Co-Cl angle of $90^\circ$ , is/are :
Coordination Compounds Coordination Isomerism Geometrical Isomerism in MA4B2 Octahedral Complexes
EasySingle correctNew idea
Q37
The correct order of the spin-only magnetic moments of the following complexes is : (I) $\mathrm{[Cr(H_2O)_6]Br_2}$ (II) $\mathrm{Na_4[Fe(CN)_6]}$ (III) $\mathrm{Na_3[Fe(C_2O_4)_3]}$ ( $\Delta_0 > P$ ) (IV) $\mathrm{(Et_4N)_2[CoCl_4]}$
Coordination Compounds Crystal Field Theory High and Low Spin States
MediumOtherNew ideaIdea asked in 7 years
Q38
Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm) :
Environmental Chemistry Water Quality BOD and COD
EasySingle correctNew ideaIdea asked in 4 years
Q39
The decreasing order of basicity of the following amines is :
Amines Basicity of Nitrogen Heterocycles
MediumSingle correct · figureNew ideaIdea asked in 3 years
Q40
Which of the following has the shortest C-Cl bond ?
Haloalkanes and Haloarenes Resonance and Hyperconjugation Mesomeric Effect
MediumSingle correctNew ideaIdea asked in 3 years
Q41
A, B and C are three biomolecules. The results of the tests performed on them are given below : | | Molisch's Test | Barfoed Test | Biuret Test | |---|---|---|---| | A | Positive | Negative | Negative | | B | Positive | Positive | Negative | | C | Negative |…
Biomolecules Carbohydrates Molisch Test
MediumSingle correctNew idea
Q42
Which polymer has 'chiral' monomer(s) ?
Polymers PHBV Monomers
MediumSingle correctNew ideaIdea asked in 2 years
Q43
Which of the following reactions will not produce a racemic product ?
Haloalkanes and Haloarenes Alkenes and Alkynes Markovnikov's Rule Application
HardSingle correct · figureNew ideaIdea asked in 6 years
Q44
In the following reaction A is : A $\xrightarrow{\text{(i) } Br_2, h\nu;\ \text{(ii) KOH (alc.)};\ \text{(iii) } O_3;\ \text{(iv) } (CH_3)_2S;\ \text{(v) NaOH (aq)} + \Delta}$ cyclopent-1-ene-1-carbaldehyde
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Intramolecular Aldol
MediumSingle correct · figureNew ideaIdea asked in 5 years
Q45
Consider the following reactions, [P] $\xrightarrow{\text{(i) NaNO}_2\text{/HCl, 0-5 °C; (ii) }\beta\text{-naphthol/NaOH}}$ Colored Solid [P] $\xrightarrow{Br_2/H_2O}$ $\mathrm{C_7H_6NBr_3}$ The compound [P] is :
Amines Diazonium Salts Coupling with Beta-Naphthol
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q46
A cylinder containing an ideal gas (0.1 mol of 1.0 dm $^3$ ) is in thermal equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at its freezing point. If the stoppers $S_1$ and $S_2$ (as shown in the figure) are suddenly withdrawn,…
Solutions Colligative Properties Freezing Point Depression
HardNumerical value · figureNew ideaIdea asked in 4 years
Q47
10.30 mg of $\mathrm{O_2}$ is dissolved into a liter of sea water of density 1.03 g/mL. The concentration of $\mathrm{O_2}$ in ppm is ______.
Solutions Mole Concept PPM and Mass Percentage
EasyNumerical valueNew ideaIdea asked in 5 years
Q48
A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activation energy (in kJ/mol) for this process is closest to ______. (Given, $R = 8.3\ \mathrm{J\,mol^{-1}K^{-1}}$ ,…
Chemical Kinetics Arrhenius Equation Two-Point Arrhenius Equation
MediumNumerical valueNew ideaIdea asked in 4 years
Q49
The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is ______.
The d- and f-Block Elements
MediumNumerical value
Q50
Consider the following reactions A $\xrightarrow[\text{(ii) } H_3O^+]{\text{(i) } CH_3MgBr}$ B $\xrightarrow[573\text{ K}]{Cu}$ 2-methyl-2-butene The mass percentage of carbon in A is ______.
Alcohols, Phenols and Ethers Alcohols and Phenols Grignard Synthesis of Alcohols
MediumNumerical valueNew ideaIdea asked in 3 years

Maths24 questions

6 easy16 medium2 hard

Q51
If $A=\{x\in\mathbf{R}:|x|<2\}$ and $B=\{x\in\mathbf{R}:|x-2|\ge 3\}$ ; then :
Relations and Functions Sets and Relations Intervals as Subsets of R
EasySingle correctNew ideaIdea asked in 3 years
Q52
Let $a,b\in\mathbf{R}$ , $a\ne0$ be such that the equation, $ax^2-2bx+5=0$ has a repeated root $\alpha$ , which is also a root of the equation, $x^2-2bx-10=0$ . If $\beta$ is the other root of this equation, then $\alpha^2+\beta^2$ is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Common Root Condition
MediumSingle correctNew ideaIdea asked in 3 years
Q53
If $z$ be a complex number satisfying $|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4$ , then $|z|$ cannot be :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
MediumSingle correctNew ideaIdea asked in 5 years
Q54
Let $a-2b+c=1$ . If $f(x)=\begin{vmatrix}x+a&x+2&x+1\\x+b&x+3&x+2\\x+c&x+4&x+3\end{vmatrix}$ , then :
Determinants
MediumSingle correct
Q55
The following system of linear equations $7x+6y-2z=0$ $3x+4y+2z=0$ $x-2y-6z=0$ , has
Determinants Cramer's Rule Homogeneous System Solutions
EasySingle correctNew ideaIdea asked in 4 years
Q56
In the expansion of $\left(\frac{x}{\cos\theta}+\frac{1}{x\sin\theta}\right)^{16}$ , if $l_1$ is the least value of the term independent of $x$ when $\frac{\pi}{8}\le\theta\le\frac{\pi}{4}$ and $l_2$ is the least value of the term independent of $x$ when…
Binomial Theorem
HardSingle correct
Q57
Let $a_n$ be the $n^{\mathrm{th}}$ term of a G.P. of positive terms. If $\sum_{n=1}^{100}a_{2n+1}=200$ and $\sum_{n=1}^{100}a_{2n}=100$ , then $\sum_{n=1}^{200}a_n$ is equal to :
Sequences and Series AP and GP GP Sum of n terms
MediumSingle correctNew ideaIdea asked in 5 years
Q58
Let $[t]$ denote the greatest integer $\le t$ and $\lim_{x\to0}x\left[\frac{4}{x}\right]=A$ . Then the function, $f(x)=[x^2]\sin(\pi x)$ is discontinuous, when $x$ is equal to :
Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumSingle correctNew ideaIdea asked in 6 years
Q60
Let $f$ and $g$ be differentiable functions on $\mathbf{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in\mathbf{R}$ , $g'(a)=5$ and $g(a)=b$ , then $f'(b)$ is equal to :
Continuity and Differentiability Chain Rule Derivative of Inverse Functions via Chain Rule
EasySingle correctNew ideaIdea asked in 3 years
Q61
Let a function $f:[0,5]\to\mathbf{R}$ be continuous, $f(1)=3$ and $F$ be defined as : $F(x)=\int_1^x t^2g(t)\,dt$ , where $g(t)=\int_1^t f(u)\,du$ . Then for the function $F$ , the point $x=1$ is :
Application of Derivatives Maxima and Minima Extrema of Integral Functions
MediumSingle correctNew ideaIdea asked in 2 years
Q62
If $\int\frac{d\theta}{\cos^2\theta(\tan2\theta+\sec2\theta)}=\lambda\tan\theta+2\log_e|f(\theta)|+C$ where $C$ is a constant of integration, then the ordered pair $(\lambda,f(\theta))$ is equal to :
Integrals Integration by Substitution Even Power of Secant Substitution
MediumSingle correctNew ideaIdea asked in 2 years
Q63
Given : $f(x)=\begin{cases}x, & 0\le x<\frac{1}{2}\\ \frac{1}{2}, & x=\frac{1}{2}\\ 1-x, & \frac{1}{2}<x\le1\end{cases}$ and $g(x)=\left(x-\frac{1}{2}\right)^2$ , $x\in\mathbf{R}$ . Then the area (in sq. units) of the region bounded by the curves, $y=f(x)$ and…
Application of Integrals Area Under Curves Area Between Curves
MediumSingle correctNew ideaIdea asked in 7 years
Q64
If $\frac{dy}{dx}=\frac{xy}{x^2+y^2}$ ; $y(1)=1$ ; then a value of $x$ satisfying $y(x)=e$ is :
Differential Equations Homogeneous Equations Substitution y = vx
MediumSingle correctNew ideaIdea asked in 6 years
Q65
The length of the minor axis (along $y$ -axis) of an ellipse in the standard form is $\frac{4}{\sqrt3}$ . If this ellipse touches the line, $x+6y=8$ ; then its eccentricity is :
Conic Sections Ellipse Eccentricity Eccentricity calculation
MediumSingle correctNew ideaIdea asked in 6 years
Q66
If one end of a focal chord AB of the parabola $y^2=8x$ is at $A\left(\frac{1}{2},-2\right)$ , then the equation of the tangent to it at B is :
Conic Sections Parabola Focal Chords Parameter relation t1*t2 = -1
MediumSingle correctNew ideaIdea asked in 2 years
Q67
A random variable X has the following probability distribution : | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | $K^2$ | $2K$ | $K$ | $2K$ | $5K^2$ | Then $P(X>2)$ is equal to :
Probability
EasySingle correct
Q68
If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :
Probability Permutations and Combinations Distribution of Distinct Objects into Distinct Boxes
MediumSingle correctNew ideaIdea asked in 3 years
Q69
If $x=\sum_{n=0}^{\infty}(-1)^n\tan^{2n}\theta$ and $y=\sum_{n=0}^{\infty}\cos^{2n}\theta$ , for $0<\theta<\frac{\pi}{4}$ , then :
Sequences and Series AP and GP Infinite GP Sum
EasySingle correctNew ideaIdea asked in 6 years
Q70
If $p\to(p\wedge\sim q)$ is false, then the truth values of $p$ and $q$ are respectively :
Mathematical Reasoning
EasySingle correct
Q71
If $C_r\equiv{}^{25}C_r$ and $C_0+5\cdot C_1+9\cdot C_2+\ldots+(101)\cdot C_{25}=2^{25}\cdot k$ , then $k$ is equal to ______.
Binomial Theorem Binomial Coefficients Differentiation Method for Sums
MediumNumerical valueNew idea
Q72
The number of terms common to the two A.P.'s $3,7,11,\ldots,407$ and $2,9,16,\ldots,709$ is ______.
Sequences and Series AP and GP Counting Common Terms of Finite APs
MediumNumerical valueNew ideaIdea asked in 3 years
Q73
If the curves, $x^2-6x+y^2+8=0$ and $x^2-8y+y^2+16-k=0$ , $(k>0)$ touch each other at a point, then the largest value of $k$ is ______.
Conic Sections Circle Tangents Number of Common Tangents
MediumNumerical valueNew ideaIdea asked in 4 years
Q74
If the distance between the plane, $23x-10y-2z+48=0$ and the plane containing the lines $\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}$ and $\frac{x+3}{2}=\frac{y+2}{6}=\frac{z-1}{\lambda}$ ( $\lambda\in\mathbf{R}$ ) is equal to $\frac{k}{\sqrt{633}}$ , then $k$ is…
Three Dimensional Geometry Planes in 3D Distance Between Parallel Planes
HardNumerical valueNew idea
Q75
Let $\vec{a}$ , $\vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}|=\sqrt3$ , $|\vec{b}|=5$ , $\vec{b}\cdot\vec{c}=10$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$ . If $\vec{a}$ is perpendicular to the vector…
Vector Algebra Cross Product Magnitude and Sine Formula
MediumNumerical valueIdea asked in 7 yearsAsked the year before

Dropped from the final key and left out of every count: Q1, Q59.

Questions from the official paper published by NTA, answers from the final key. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026; see the other 2020 shifts.