JEE Main 2017 Question Paper with Solutions

The following observations were taken for determining surface tensiton T of water by capillary method : Diameter of capilary, D = 1.25 × 10^–2 m rise of water, h = 1.45 × 10^–2 m
Using g = 9.80 m/s² and the simplified relation  N/m, the possible error in surface tension is closest to :

In amplitude modulation , sinusoidal carrier frequency used is denoted by ω_c and the signal frequency is denoted by ω_m. The bandwidth (Δω_m) of the signal is such that Δω_m << ω_c. Which of the following frequencies is not contained in the modulated wave ?

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is :

The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/R such that the moment of inertia is minimum ?

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X - rays. If λ_min is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ_min with log V is correctly represented in :

A radioactive nucleus A with a half life  T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

An electric dipole has a fixed dipole moment  which makes angle q with respect to x-axis. When subjected to an electric field  it experiences a torque  When subjected to another electric field  it experiences torque  . The angle q is :

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be :

C_p and C_v are specific heats at constant pressure and constant volume respectively. It is observed that C_p – C_v = a for hydrogen gas C_p – C_v = b for nitrogen gas The correct relation between a and b is :

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75°C. T is given by : (Given : room temperature = 30° C, specific heat of copper = 0.1 cal/gm°C

A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its intial speed is v₀ = 10 ms^–1. If, after 10 s, its energy is  the value of k will be:-

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into to voltmeter of range 0 -10 V is:

A slender uniform rod of mass M and length ℓ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is :

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = λ₁/λ₂, is given by :

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :

In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :

In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is :

A magnetic needle of magnetic moment 6.7 × 1 0 ^–2 Am² and moment of inertia 7.5 × 10^–6 kg m² is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is : 

The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius):

In the above circuit the current in each resistance is :

A particle A of mass m and initial velocity v collides with a particle B of mass (m/2) which is at rest. The collision is head on, and elastic. The ratio of the de–Broglie wavelengths λ_A to λ_B after the collision is :

An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and a is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be :

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 × 108 ms^–1)

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

A capacitance of 2 μF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 μF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is :

A body is t hrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Let k be an integer such that 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 :

If , for apositive integer n , the quadratic equation, x(x + 1) + (x + 1) (x + 2) + ..... + (x + n) = 10n has two consecutive integral solutions, then n is equal to :

The function f :  defined as

The following statement (p → q) → [(~p → q) → q] is :

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 :

The area (in sq. units) of the region {(x,y) : x > 0, x + y < 3, x² < 4y and y < 1 +  is : 

For any three positive real numbers a, b and c, 9(25a² + b²) + 25(c² – 3ac) = 15b(3a + c).Then:

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 and 3 men, so that 3 friends of each of X and Y are in this party, is :

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 :

A hyperbola passes through the point and has foci at (± 2, 0). Then the tangent to this hyperbola at P also passes through the point :

Let a. b, c ∈ R. If f(x) = ax² + bx + c is such tliat a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, V x, y e R.   is equal to : 

  the angle between is equal to :

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 ∠BPC = β, then tanβ  is equal to :-

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 :-

If  and y(0) = 1, then is equal to :-

. I₄ + I₆ = a tan⁵x + bx⁵ + C, where C is a constant of integration, then the ordered pair (a, b) is equal to :-

Let ω  be a complex number such that 2ω + 1 = z where z = √3 . If

then k is equal to :-

The value of (²¹ C₁ – ¹⁰C₁) + (²¹C₂ – ¹⁰C₂) + (²¹C₃ – ¹⁰C₃) + (²¹C₄ – ¹⁰C₄) + .... + (²¹C₁₀ –  ¹⁰C₁₀) is :-

If 5(tan²x – cos²x) = 2cos 2x + 9, then the value of cos4x is :- 

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to line,  Q, then PQ is equal to :-

The distantce of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both the lines

If for the derivative of  equals :-

The radius of a circle, having minimum area, which touches the curve y = 4 – x² and the lines, y = |x| is :-

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 :-

The eccentricity of an ellipse whose centre is at the origin is 1/2 . If one of its directices is x = –4, then the equation of the normal to it at 

If two different numbers are taken from the set {0, 1, 2, 3, ......., 10), then the probability that their sum as well as absolute difference are both multiple of 4, is :-

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)
= 1/4 and P(All the three events occur simultaneously) = 1/16
Then the probability that at least one of the events occurs, is :-

then adj (3A2 + 12A) is equal to :-

Which of the following compounds will significant amont of meta product during mono-nitration reaction?

ΔU is equal to

The increasing order of t he reactivity of the following halides for the S_N1 reaction is

The radius of the second Bohr orbit for hydrogen atom is : (Plank's const. h = 6.6262 × 10^–34 Js ; mass of electron = 9.1091 × 10^–31 kg ; charge of electron e = 1.60210 × 10^–19 C ; permittivity of vaccum ∈₀ = 8.854158 x 10^-12 kg-¹m^-3A²)  

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 :

The formation of which of the following polymers involves hydrolysis reaction?

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 1H atoms are replaced by 2H atoms is :

Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine ?

In the following reactions, ZnO is respectively acting as a/an :

(a) ZnO + Na₂O → Na₂ZnO₂
(b) ZnO + CO₂ → ZnCO₃

Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is :

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 :

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 :

Two reactions R₁ and R₂ have identical pre-exponential factors.  Activation energy of R₁ exceeds that of R₂ by 10 kJ mol⁻¹.  If k₁ and k₂ are rate constants for reactions R₁ and R₂ respectively at 300 K, then ln(k₂/k₁) is equal to :
(R = 8.314 J mol⁻¹K⁻¹)

The correct sequence of reagents for the following conversion will be :

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 wavelength of the light used.
(c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude.
(d) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.

Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution ?

Given C(graphite)+O₂(g) → CO₂(g) ;
∆_rH^°=−393.5 kJ mol⁻¹
H₂(g)+ 1/2 O₂(g) → H₂O(l) ;
∆_rH^° = −285.8 kJ mol⁻¹
CO₂(g)+2H₂O(l) → CH₄(g)+2O₂(g) ;
∆_rH^°=+890.3 kJ mol⁻¹
Based on the above thermochemical equations, the value of ∆_rH^° at 298 K for the reaction C(graphite)+2H₂(g) → CH₄(g) will be :

Which of the following reactions is an example of a redox reaction ?

The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : 

The major product obtained in the following reaction is :

Sodium salt of an organic acid ‘X’ produces effervescence with conc. H₂SO₄. ‘X’ reacts with the acidified aqueous CaCl₂ solution to give a white precipitate which decolourises acidic solution of KMnO₄. ‘X’ is :

Which of the following species is not paramagnetic?

The freezing point of benzene decreases by 0.458C 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=5.12 K kg mol⁻¹)

Which of the following molecules is least resonance stabilized ?

On treatment of 100 mL of 0.1 M solution of CoCl₃.6H₂O with excess AgNO₃; 1.2×10²² ions are precipitated.  The complex is :

The major product obtained in the following reaction is:

A water sample has ppm level concentration of following anions  F- = 10 ;  = 50 . The anion/anions that make/makes the water sample unsuitable for drinking is/ are :

1 gram of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01186 mole of CO₂.  The molar mass of M₂CO₃ in g mol⁻¹ is :

Given

Among the following, the strongest reducing agent is :

The group having isoelectronic species is :