JEE Main 2017 ·

JEE Main 2 April 2017 (offline)

89 questions (1 more dropped by NTA): 0 numerical-answer and 89 multiple choice. 12 were rated hard and 26 easy. The biggest chapter was Haloalkanes and Haloarenes, with 4 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 0; 0% of the shift
Hard: 12; 13% of the shift
Chapters asked: 64; 17 questions with a figure

Key findings · 2 Apr 2017 (offline)

1
Maths was the hardest section, with 7 of 29 rated hard; Chemistry had the most easy questions (13 of 30).
2
Biggest chapters: Current Electricity in Physics (3), Haloalkanes and Haloarenes in Chemistry (4) and Determinants in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 0 numerical

Easy 11Medium 17Hard 2

Top chapters

Chemistry

30 Q · 0 numerical

Easy 13Medium 14Hard 3

Top chapters

Maths

29 Q · 0 numerical

Easy 2Medium 20Hard 7

Top chapters

Question format

Single correct87 Q
Other2 Q

What each question asks you to do

Multi-step32 Q
Calculation24 Q
Application11 Q
Conceptual10 Q
Recall7 Q
Data or graph5 Q

Most common: Multi-step.

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

Open30 this shift3092 · 33%33%8/830299720720358540200225
Open30 this shift3084 · 33%33%8/830298716720359538199224
Open29 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 89 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

89 of 89 questions

Physics30 questions

11 easy17 medium2 hard

Chemistry30 questions

13 easy14 medium3 hard

Q31
Given $\mathrm{C_{(graphite)}+O_2(g)\rightarrow CO_2(g)}$ ; $\Delta_rH^\circ=-393.5\ \mathrm{kJ\,mol^{-1}}$ $\mathrm{H_2(g)+\frac{1}{2}O_2(g)\rightarrow H_2O(l)}$ ; $\Delta_rH^\circ=-285.8\ \mathrm{kJ\,mol^{-1}}$ …
Thermodynamics (Chemistry)Enthalpy and Hess's Law Hess's Law
EasySingle correctNew ideaIdea asked in 5 years
Q32
1 gram of a carbonate ( $\mathrm{M_2CO_3}$ ) on treatment with excess HCl produces 0.01186 mole of $\mathrm{CO_2}$ . The molar mass of $\mathrm{M_2CO_3}$ in g mol $^{-1}$ is :
Some Basic Concepts of Chemistry Mole Concept Molar Mass and Gas Volume
EasySingle correctNew ideaIdea asked in 3 years
Q33
$\Delta U$ is equal to :
Thermodynamics (Chemistry)
EasySingle correct
Q34
The Tyndall effect is observed only when following conditions are satisfied : (a) The diameter of the dispersed particles is much smaller than the wavelength of the light used. (b) The diameter of the dispersed particle is not much smaller than the…
Surface Chemistry Colloids Optical and Kinetic Properties
MediumOtherNew ideaIdea asked in 5 years
Q35
A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be :
The Solid State Crystal Lattices FCC Neighbor Distances
EasySingle correctNew idea
Q36
Given $E^\circ_{\mathrm{Cl_2/Cl^-}}=1.36$ V, $E^\circ_{\mathrm{Cr^{3+}/Cr}}=-0.74$ V $E^\circ_{\mathrm{Cr_2O_7^{2-}/Cr^{3+}}}=1.33$ V, $E^\circ_{\mathrm{MnO_4^-/Mn^{2+}}}=1.51$ V. Among the following, the strongest reducing agent is :
Electrochemistry Nernst Equation Standard Cell Potential
EasySingle correctNew ideaIdea asked in 7 years
Q37
The freezing point of benzene decreases by 0.45°C when 0.2 g of acetic acid is added to 20 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be : ( $K_f$ for benzene…
Solutions Colligative Properties Degree of Association from Van't Hoff Factor
MediumSingle correctNew ideaIdea asked in 3 years
Q38
The radius of the second Bohr orbit for hydrogen atom is : (Planck's Const. $h=6.6262\times10^{-34}$ Js; mass of electron $=9.1091\times10^{-31}$ kg; charge of electron $e=1.60210\times10^{-19}$ C; permittivity of vacuum…
Structure of Atom Bohr's Atomic Theory Bohr Radius Calculation
EasySingle correctNew ideaIdea asked in 6 years
Q39
Two reactions $R_1$ and $R_2$ have identical pre-exponential factors. Activation energy of $R_1$ exceeds that of $R_2$ by 10 kJ mol $^{-1}$ . If $k_1$ and $k_2$ are rate constants for reactions $R_1$ and $R_2$ respectively at 300 K, then $\ln(k_2/k_1)$ is…
Chemical Kinetics Arrhenius Equation Arrhenius Exponential Form
EasySingle correctNew ideaIdea asked in 4 years
Q40
$pK_a$ of a weak acid (HA) and $pK_b$ of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :
Equilibrium pH and Buffers pH of Weak Acid-Weak Base Salts
EasySingle correctNew ideaIdea asked in 3 years
Q41
Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is :
The s-Block Elements s-Block Elements Diagonal Relationship
MediumSingle correctNew ideaIdea asked in 3 years
Q42
Which of the following species is **not** paramagnetic ?
Chemical Bonding and Molecular Structure Molecular Orbital Theory Magnetic Property Prediction
EasySingle correctNew ideaIdea asked in 6 years
Q43
Which of the following reactions is an example of a redox reaction ?
The p-Block Elements Redox Reactions Identifying Non-Redox Reactions
MediumSingle correctNew idea
Q44
A water sample has ppm level concentration of following anions $\mathrm{F^-}=10$ ; $\mathrm{SO_4^{2-}}=100$ ; $\mathrm{NO_3^-}=50$ The anion/anions that make/makes the water sample unsuitable for drinking is/are :
Environmental Chemistry Fluoride Limits in Drinking Water
EasySingle correctNew ideaIdea asked in 3 years
Q45
The group having isoelectronic species is :
Classification of Elements and Periodicity in Properties Quantum Numbers Configurations of Isoelectronic Species
EasySingle correctNew ideaIdea asked in 2 years
Q46
The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are :
The p-Block Elements Group 17 & 18 Chlorine Disproportionation with Alkalis
EasySingle correctNew idea
Q47
In the following reactions, ZnO is respectively acting as a/an : (a) $\mathrm{ZnO+Na_2O\rightarrow Na_2ZnO_2}$ (b) $\mathrm{ZnO+CO_2\rightarrow ZnCO_3}$
The d- and f-Block Elements d-Block Elements Acid-Base Character of Oxides
MediumSingle correctNew ideaIdea asked in 4 years
Q48
Sodium salt of an organic acid 'X' produces effervescence with conc. $\mathrm{H_2SO_4}$ . 'X' reacts with the acidified aqueous $\mathrm{CaCl_2}$ solution to give a white precipitate which decolourises acidic solution of $\mathrm{KMnO_4}$ . 'X' is :
Aldehydes, Ketones and Carboxylic Acids Anion Analysis Oxalate Calcium Chloride Test
MediumSingle correctNew idea
Q49
The most abundant elements by mass in the body of a healthy human adult are : Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75 kg person would gain if all $^1$ H atoms are replaced by $^2$ H atoms is :
Structure of Atom
MediumSingle correct
Q50
On treatment of 100 mL of 0.1 M solution of $\mathrm{CoCl_3.6H_2O}$ with excess $\mathrm{AgNO_3}$ ; $1.2\times10^{22}$ ions are precipitated. The complex is :
Coordination Compounds Coordination Isomerism Precipitation Tests for Ionization Isomers
MediumSingle correctNew ideaIdea asked in 7 years
Q51
Which of the following compounds will form significant amount of *meta* product during mono-nitration reaction ?
Haloalkanes and Haloarenes Amines Meta-Nitration of Aniline
MediumSingle correct · figureNew idea
Q52
Which of the following, upon treatment with *tert*-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine ?
Haloalkanes and Haloarenes Alkenes and Alkynes Saytzeff vs. Hofmann Elimination
HardSingle correct · figureNew ideaIdea asked in 6 years
Q53
The formation of which of the following polymers involves hydrolysis reaction ?
Polymers Nylon-6 Preparation
EasySingle correctNew idea
Q54
Which of the following molecules is least resonance stabilized ?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
MediumSingle correct · figureNew ideaIdea asked in 5 years
Q55
The increasing order of the reactivity of the following halides for the $\mathrm{S_N1}$ reaction is : $\mathrm{CH_3CHCH_2CH_3}$ with Cl on the middle carbon (I) $\mathrm{CH_3CH_2CH_2Cl}$ (II) $p-\mathrm{H_3CO-C_6H_4-CH_2Cl}$ (III)
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Allylic and Benzylic Reactivity in SN1
MediumOther · figureNew ideaIdea asked in 5 years
Q56
The major product obtained in the following reaction is : [reaction: (+)- $\mathrm{C_6H_5CH(Br)CH_2C_6H_5}$ (Br on wedge, H on hash at the stereocentre) with $\mathrm{{}^tBuOK}$ , $\Delta$ ]
Haloalkanes and Haloarenes Alkenes and Alkynes Saytzeff vs. Hofmann Elimination
MediumSingle correct · figureNew ideaIdea asked in 6 years
Q57
Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution ?
Biomolecules Carbohydrates Reducing vs Non-reducing Sugars
HardSingle correct · figureNew ideaIdea asked in 4 years
Q58
3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :
Hydrocarbons Alkenes and Alkynes Peroxide Effect (Anti-Markovnikov)
MediumSingle correctNew ideaIdea asked in 3 years
Q59
The correct sequence of reagents for the following conversion will be : [reaction: 4-formylcyclohexanone (ring bearing C=O at the top and CHO at the bottom) → cyclohexane ring whose top carbon bears HO and $\mathrm{CH_3}$ , and whose bottom carbon bears a…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Reaction of Esters with Grignard Reagents
HardSingle correct · figureNew ideaIdea asked in 3 years
Q60
The major product obtained in the following reaction is : [reaction: bicyclic lactone (cyclopentene fused to a five-membered lactone, with COOH on the ring double bond carbon) with DIBAL-H]
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives DIBAL-H Selective Reduction
MediumSingle correct · figureNew ideaIdea asked in 3 years

Maths29 questions

2 easy20 medium7 hard

Q61
The function $f:\mathbf{R}\rightarrow\left[-\frac{1}{2},\frac{1}{2}\right]$ defined as $f(x)=\frac{x}{1+x^2}$ , is :
Relations and Functions
MediumSingle correct
Q62
If, for a positive integer n, the quadratic equation, $x(x+1)+(x+1)(x+2)+\ldots+(x+\overline{n-1})(x+n)=10n$ has two consecutive integral solutions, then n is equal to :
Complex Numbers and Quadratic Equations Quadratic Roots Integer Roots Condition
HardSingle correctNew ideaIdea asked in 2 years
Q63
Let $\omega$ be a complex number such that $2\omega+1=z$ where $z=\sqrt{-3}$ . If $\begin{vmatrix}1&1&1\\1&-\omega^2-1&\omega^2\\1&\omega^2&\omega^7\end{vmatrix}=3k$ , then k is equal to :
Determinants Roots of Unity Evaluating Determinants with Cube Roots
MediumSingle correctNew ideaIdea asked in 2 years
Q64
If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ , then $\mathrm{adj}(3A^2+12A)$ is equal to :
Determinants Matrix Inverse Cofactor Matrix and Adjoint
MediumSingle correctNew ideaIdea asked in 5 years
Q65
If S is the set of distinct values of 'b' for which the following system of linear equations $x+y+z=1$ $x+ay+z=1$ $ax+by+z=0$ has no solution, then S is :
Determinants Cramer's Rule Condition for No Solution
MediumSingle correctNew ideaIdea asked in 6 years
Q66
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies…
Permutations and Combinations Combinations of Distinct Objects
HardSingle correctNew ideaIdea asked in 8 years
Q67
The value of $(^{21}C_1-{}^{10}C_1)+(^{21}C_2-{}^{10}C_2)+(^{21}C_3-{}^{10}C_3)+(^{21}C_4-{}^{10}C_4)+\ldots+(^{21}C_{10}-{}^{10}C_{10})$ is :
Binomial Theorem Binomial Coefficients Sum of all Coefficients
MediumSingle correctNew ideaIdea asked in 4 years
Q68
For any three positive real numbers a, b and c, $9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c)$ . Then :
Sequences and Series AP and GP Conditions for Three Terms in AP or GP
HardSingle correctNew ideaIdea asked in 5 years
Q69
Let $a,b,c\in\mathbf{R}$ . If $f(x)=ax^2+bx+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+xy,\ \forall\ x,y\in\mathbf{R}$ , then $\sum_{n=1}^{10}f(n)$ is equal to :
Sequences and Series
MediumSingle correct
Q70
$\lim_{x\to\frac{\pi}{2}}\frac{\cot x-\cos x}{(\pi-2x)^3}$ equals :
Limits and Derivatives L'Hopital's Rule Repeated L'Hopital Application
HardSingle correctNew idea
Q71
If for $x\in\left(0,\frac{1}{4}\right)$ , the derivative of $\tan^{-1}\left(\frac{6x\sqrt{x}}{1-9x^3}\right)$ is $\sqrt{x}\cdot g(x)$ , then $g(x)$ equals :
Continuity and Differentiability Inverse Trig Identities tan^-1(2x/(1-x^2)) Piecewise Conversion
MediumSingle correctNew idea
Q72
The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the $y$ -axis passes through the point :
Application of Derivatives Tangents and Normals Equation of Normal
MediumSingle correctNew ideaIdea asked in 3 years
Q73
Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :
Application of Derivatives Maxima and Minima Optimization Problems
MediumSingle correctNew ideaIdea asked in 5 years
Q74
Let $I_n=\int\tan^n x\,dx,\ (n>1)$ . If $I_4+I_6=a\tan^5x+bx^5+C$ , where C is a constant of integration, then the ordered pair (a, b) is equal to :
Integrals Integration by Parts Trigonometric Reduction Formulas
MediumSingle correctNew ideaIdea asked in 2 years
Q75
The integral $\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos x}$ is equal to :
Integrals Integration by Substitution Weierstrass Substitution
EasySingle correctNew ideaIdea asked in 2 years
Q76
The area (in sq. units) of the region $\{(x,y):x\geq0,\ x+y\leq3,\ x^2\leq4y\ \text{and}\ y\leq1+\sqrt{x}\}$ is :
Application of Integrals Area Under Curves Area of Inequalities
HardSingle correctNew ideaIdea asked in 8 years
Q77
If $(2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ and $y(0)=1$ , then $y\left(\frac{\pi}{2}\right)$ is equal to :
Differential Equations Variable Separable Form Initial Value Problem
MediumSingle correctNew ideaIdea asked in 7 years
Q78
Let k be an integer such that the triangle with vertices $(k,-3k)$ , $(5,k)$ and $(-k,2)$ has area 28 sq. units. Then the orthocentre of this triangle is at the point :
Straight Lines
MediumSingle correct
Q80
The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$ . If one of its directrices is $x=-4$ , then the equation of the normal to it at $\left(1,\frac{3}{2}\right)$ is :
Conic Sections Normals to Conics Ellipse Normal Point Form
MediumSingle correctNew ideaIdea asked in 2 years
Q81
A hyperbola passes through the point $P(\sqrt{2},\sqrt{3})$ and has foci at $(\pm2,0)$ . Then the tangent to this hyperbola at P also passes through the point :
Conic Sections
MediumSingle correct
Q82
The distance of the point $(1,3,-7)$ from the plane passing through the point $(1,-1,-1)$ , having normal perpendicular to both the lines $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$ , is :
Three Dimensional Geometry Point-Plane Distance Unknown Parameter from Distance
MediumSingle correctNew idea
Q83
If the image of the point $P(1,-2,3)$ in the plane, $2x+3y-4z+22=0$ measured parallel to the line, $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is Q, then PQ is equal to :
Three Dimensional Geometry Point-Plane Distance Image of a Point
MediumSingle correctNew ideaIdea asked in 4 years
Q84
Let $\vec{a}=2\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . Let $\vec{c}$ be a vector such that $|\vec{c}-\vec{a}|=3$ , $|(\vec{a}\times\vec{b})\times\vec{c}|=3$ and the angle between $\vec{c}$ and $\vec{a}\times\vec{b}$ be $30^\circ$ . Then…
Vector Algebra Cross Product Magnitude and Sine Formula
HardSingle correctNew ideaIdea asked in 7 years
Q85
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :
Probability
EasySingle correct
Q86
For three events A, B and C, P(Exactly one of A or B occurs) $=$ P(Exactly one of B or C occurs) $=$ P(Exactly one of C or A occurs) $=\frac{1}{4}$ and P(All the three events occur simultaneously) $=\frac{1}{16}$ . Then the probability that at least one of…
Probability
HardSingle correct
Q87
If two different numbers are taken from the set $\{0,1,2,3,\ldots\ldots,10\}$ ; then the probability that their sum as well as absolute difference are both multiple of 4, is :
Probability
MediumSingle correct
Q88
If $5(\tan^2x-\cos^2x)=2\cos2x+9$ , then the value of $\cos4x$ is :
Trigonometric Functions Trigonometric Identities Multiple Angle Formulas
MediumSingle correctNew idea
Q89
Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that $AP=2AB$ . If $\angle BPC=\beta$ , then $\tan\beta$ is equal to :
Trigonometric Functions
MediumSingle correct
Q90
The following statement $(p\rightarrow q)\rightarrow[(\sim p\rightarrow q)\rightarrow q]$ is :
Mathematical Reasoning
MediumSingle correct

Dropped from the final key and left out of every count: Q79.

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