JEE Main Sample Paper B.Tech Set A

JEE MAIN
SAMPLE
PAPER
Paper 1 for B.Tech

SET A
For more JEE Main Study Material visit AglaSem Admission

Jee Main Sample Paper

Physics

Q1.
The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal
monoatomic gas. The amount of heat extracted from the source in a single cycle is
1. (13/12)p0 v
2. (11/2)p0 v
3. 4 p0 v
4. p0 v

Q2. A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain
of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 103
kg/m3 and 2.2 × 1011N/m2 respectively?
1. 178.2 Hz
2. 200.5 Hz
3. 770 Hz
4. 188.5 Hz

Correct. 1

Q3. Unpolarized light of intensity I passes through an ideal polarizer A. Another identical
polarizer B is placed behind A. The intensity of light beyond B is found to be 1/2. Now another
identical polarizer C is placed between A and B. The intensity beyond B is now found to be 1/8 .

The angle between polarizer A and C is :
1. 0°
2. 30°
3. 45°
4. 60°

Q4. The variation of acceleration due to gravity g with distance d from centre of the earth is best
represented by (R=Earth’s radius) :

1. ,

2.

3.

4.

Correct. 4

Q5. 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 :
1. 1.56 mm
2. 7.8 mm
3. 9.75 mm
4. 15.6 mm

Q6. 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 λA to λB after
the collision is :
1. λA/λB = 1/3
2. λA/λB = 2
3. λA/λB = 2/3
4. λA/λB = 1/2

Q7. The position co-ordinates of a particle moving in a 3-D coordinate system is given by

X = a cos⍵t
Y = a sin⍵t
and z=a⍵t
The speed of the particle is :

1. 2aw
2. √3a⍵
3. √2a⍵
4. a⍵

Q8. One of the two identical conducting wires of length L is bent in the form of a circular loop and
the other one into a circular coil of N identical turns. If the same current is passed in both, the
ratio of the magnetic eld at the central of the loop (B ) to that at the centre of the coil (B ) i.e.
L C

will be:
BL

BC

1. 1
2
N

2. N
2

3. N
4. 1

N

Correct. 1

Q9. Two Carnot engines A and B are operated in series. The rst one, A, receives heat at T,(=600 K)
and rejects to a reservoir at temperature T . The second engine B receives heat rejected by the rst
2

engine and, in turn, rejects to a heat reservoir at T3(=400 K). Calculate the temperature
T (= 400K) if the work outputs of the two engines are equal :
3

1. 500 K
2. 300 K
3. 400 K
4. 600 K

Correct. 1

Q10. An electric eld of 1000 V/m is applied to an electric dipole at angle of 45°. The value of
electric dipole moment is 10 C.m. What is the potential energy of the electric
−29

dipole?
1. −20 × 10 J
−18

2. −10 × 10 I −29

3. −7 × 10 J
−27

4. −9 × 10 J −20

Q11. In the experimental set up of metre bridge shown in the gure, the null point is obtained at a
distance of 40 cm from A. If a 10 resistor is connected in series with R, the null point shifts by 10
cm. The resistance that should be connected in parallel with (R₁ +10) Ω such that the null point
shifts back to its initial position is :

1. 30 Ω
2. 40 Ω
3. 20 Ω
4. 602

Correct. 4

Q12. A plano convex lens of refractive index μ and focal length f is kept in contact with another
1 1

plano concave lens of refractive index klip and focal length f2. If the radius of curvature of their
spherical faces is R each and f = 2f , then μ and μ are related as
1 2 1 2

1. 2μ − μ = 1
2 1

2. 3μ − 2μ = 1
2 1

3. μ + μ = 3
1 2

4. 2μ − μ = 1
1 2

Correct. 4

Q13. To get output '1' at R, for the given logic gate circuit the input values must be :

1. X=1, Y=1
2. X=1, Y=0

3. X=0, Y=1
4. X=0, Y=0

Q14. In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing
through resistance R and R respectively, are :
1 2

1. 0,1
2. 1, 2
3. 0.5, 0
4. 2,2

Q15. A mixture of 2 moles of helium gas (atomic mass=4u), and 1 mole of argon gas (atomic mass=
40u) is kept at 300 K in a container. The ratio of their rms speeds [
V rms ( helium )

V rms ( argon )
], is close to:
1. 2.24
2. 0.32
3. 0.45
4. 3.16

Correct. 4

Q16. A resistance is shown in the gure. Its value and tolerance are given respectively
by :

1. 27 kΩ, 20%
2. 270 Ω, 10%
3. 270 Ω,5%

4. 27 kΩ, 10%

Correct. 4

Q17. For a uniformly charged ring of radius R, the electric eld on its axis has the largest
magnitude at a distance h from its centre. Then value of h is :
1.
R

√5

2.
R

√2

3. R
4. R R√2

Q18. Mobility of electrons in a semiconductor is de ned as the ratio of their drift velocity to the
applied electric eld. If, for an n-type semiconductor, the density of electrons is 10¹⁹ m⁻³ and their
mobility is 1.6 m² / (V.s) then the resistivity of the semiconductor (since it is an n-type
semiconductor contribution of holes is ignored) is close to:
1. 0.2 Ωm
2. 4 Ωm
3. 2 Ωm
4. 0.4 Ωm

Correct. 4

Q19. A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d
(d<
2

1. 1 Kϵ0 a

2 d
2

2.
Kϵ0 a
ln K
d(K−1)

2

3.
Kϵ0 a

2d(K+1)
2

4.
Kϵ0 a
ln K
d

Q20. A travelling harmonic wave is represented by the equation y(x, t) = 10 sin(50t + 2x)
−3

,where x and y are in meter and t is in seconds. Which of the following is a correct
statement about the wave?

1. The wave is propagating along the positive x-axis with speed 25 ms⁻¹.
2. The wave is propagating along the positive x-axis with speed 100 ms⁻¹..
3. The wave is propagating along the negative x-axis with speed 25 ms⁻¹..
4. The wave is propagating along the negative x-axis with speed 100 ms⁻¹.

Q21. A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another
particle B of mass '4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio
of de-Broglie Wavelengths is close to ____ ?
λA

λB

Correct. 14.14

Q22. A magnetic needle of magnetic moment 6.7 × 10 −2 Am m and moment of inertia 7.5×10−6
2

kg m is performing simple harmonic oscillations in a magnetic eld of 0.01 T. Time taken for 10
2

complete oscillations is ___ (s):

Correct. 6.65

Q23. The least count of the main scale of a screw gauge is 1 mm. The minimum number of
divisions on its circular scale required to measure 5μm diameter of a wire is _______.

Correct. 200

Q24. Water ows into a large tank with at bottom at the rate of 10 m s Water is also leaking
−4 3 −1

out of a hole of area 1cm at its bottom. If the height of the water in the tank remains steady, then
2

this height is ____ (cm).

Correct. 5.1

Q25. A long cylindrical vessel is half lled with a liquid. When the vessel is rotated about its own
vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational
speed is 2 rotations per second, then the difference in the heights between the centre and the
sides, in cm, will be _______.

Correct. 2.0

Chemistry

Q1. In which of the following pairs of molecules/ions, both the species are not likely to exist?
1. H2-, He2 2-
2. H22+, He2
3. H2-, He2 2+
4. H2+, He2 2-

Q2. How long (approximate) should water be electrolysed by passing through 100 amperes current
so that the oxygen released can completely burn 27.66 g of diborane ? (Atomic weight of B=10.8 u)

1. 6.4 hours
2. 0.8 hours
3. 3.2 hours
4. 1.6 hours

Q3. Total number of lone pair of electrons in I₃⁻ ion is:
1. 3
2. 6
3. 9
4. 12

Q4. The group having isoelectronic species is :
1. O2−, F−, Na, Mg2+
2. O−, F−, Na+, Mg2+
3. O2−, F−, Na+, Mg2+
4. O−, F−, Na, Mg+

Q5. If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for
the reaction Zn(s) + Cu (aq) ⇌ Zn (aq) + Cu(s) at 300 K is approximately
2+ 2+

−1 −1 −1
(R = 8JK mol , F = 96000Cmol )

1. e −80

2. e
160

3. e
−160

4. e 320

Q6. When the rst electron gain enthalpy (Δ eg H) of oxygen is - 141 kJ/mol, its second electron
gain enthalpy is :
1. negative, but less negative than the rst
2. a positive value
3. a more negative value than the rst

4. almost the same as that of the rst

Q7. The major product obtained in the following conversion is :

1.

2.

3.

4.

Correct. 4

Q8. Which of the following compounds will produce a precipitate with AgNO₃ ?

1.

2.

3.

4.

Correct. 4

Q9. The higher concentration of which gas in air can cause stiffness of ower buds ?
1. CO₂
2. CO
3. SO₂
4. NO₂

Q10. The correct match between Item I and Item II is :

1. (A) → (P); (B) → (R); (C) → (D); (D) → (Q)
2. (A) → (R); (B) → (P); (C) → (Q); (D) → (S)
3. (A) → (P); (B) → (R); (C) → (Q); (D) → (S)
4. (A) → (R); (B) → (P); (C) → (S); (D) → (Q)

Q11. The major product of the following reaction is :

1.

2.

3.

4.

Q12. The decreasing order of ease of alkaline hydrolysis for the following esters is AglaSem Admission

1. III > II >IV>I
2. II > III >I> IV
3. II > II >I>IV
4. IV > II > III >I

Q13. The major product formed in the reaction given below will be:

1.

2.

3.

4.

Correct. 4

Q14. 8 g of NaOH is dissolved in 18 g of H₂O. Mole fraction of NaOH in solution and molality (in
mol kg⁻¹) of the solution respectively are :
1. 0.167, 22.20
2. 0.167, 11.11
3. 0.2, 22.20
4. 0.2, 11.11

Q15. The correct match between Item-I and Item-II is :

1. A➝Q; B➝P; C➝S; D➝R
2. A➝R; B➝S; C➝P; D➝Q
3. A➝R; B➝P; C➝S; D➝Q

4. A➝Q; B➝S; C➝P; D➝R

Q16. Consider the reversible isothermal expansion of an ideal gas in a closed system at two
different temperatures T₁ and T₂ (T₁ < T₂). The correct graphical depiction of the dependence of
work done (w) on the nal volume (V) is :

1.

2.

3.

4.

Correct. 1

Q17. Two complexes [Cr(H₂O)₆]Cl₃( A) and [Cr(NH₃)₆]Cl₃ ( B) are violet and yellow coloured,
respectively. The incorrect statement regarding them is :
1. Δₒ value for ( A) is less than that of ( B).
2. Δₒ values of ( A) and ( B) are calculated from the energies of violet and yellow light, respectively.

3. both absorb energies corresponding to their complementary colors.
4. both are paramagnetic with three unpaired electrons.

Q18. Major product of the following reaction is:

1.

2.

3.

4.

Correct. 4

Q19. Which amongst the following is the strongest acid ?
1. CHI₃
2. CHBr₃
3. CH(CN)₃
4. CHCl₃

Q20. Two solids dissociate as follows
A(s) ⇌ B(g) + C(g); Kp = xatm
2
,

1

2
D(s) ⇌ C(g) + E(g); Kp = yatm
2

The total pressure when both the solids dissociate simultaneously is :
1. √x + y atm
2. x + y atm
2 2

3. 2(√x + y) atm
4. (x + y) atm

Q21. At 518⁰ C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a
pressure of 363 Torr, was 1.00 Torr s⁻¹ when 5% had reacted and 0.5 Torr s⁻¹ when 33% had
reacted. The order of the reaction is _________?

Q22. Iodine reacts with concentrated HNO₃ to yield Y along with other products. The oxidation
state of iodine in Y, is _______?

Correct. 5

Q23. Decomposition of X exhibits a rate constant of 0.05 μg/year. How many years are required for
the decomposition of 5 μg of X into 2.5 μg is _________?

Correct. 50

Q24. The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M)HCl
will be ____ (M).

Correct. 0.875

Q25. Molecules of benzoic acid (C H COOH) dimerise in benzene. 'w' g of the acid dissolved in
6 5

30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of
the acid to form dimer in the solution is 80, then w is : (Given that K = 5Kkg, mol ,Molar
t
−1

mass of benzoic acid 122gmol ___________ (g).
−1

Correct. 2.4

Maths

Q1. If x, y, z are in A.P. and tan−1x, tan−1y and tan−1z are also in A.P., then
1. 2x = 3y = 6z
2. 6x = 3y = 2z
3. 6x = 4y = 3z

4. x = y = z

Correct. 4

Q2.
1. π/8
2. π/2
3. 4π
4. π/4

Correct. 4

Q3. Let y=y(x) be the solution of the differential sinx dy/dx+y cosx=4x,x∊(0,π). If y(π/2)=0, then
y(π/6) is equal to:
1. 4/9√3 π²
2. -8/9√3 π²
3. -8/9 π²
4. -4/9 π²

Q4. If the tangent at (1, 7) to the curve x²=y−6 touches the circle x²+y²+16x+12y+c=0 then the
value of c is :
1. 195
2. 185
3. 85
4. 95

Correct. 4

Q5. 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 :
1. 468
2. 469
3. 484
4. 485

Correct. 4

Q6. The value of (²¹C₁ − ¹⁰C₁) + (²¹C₂ − ¹⁰C₂) + (²¹C₃ − ¹⁰C₃) + (²¹C₄ − ¹⁰C₄) + .........+(²¹C₁₀ − ¹⁰C₁₀)
is :
1. 2²¹ − 2¹⁰

2. 2²⁰ − 2⁹
3. 2²⁰ − 2¹⁰
4. 2²¹ − 2¹¹

Q7. 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 :
1. (1,3/4)
2. (1,-3/4)
3. (2,1/2)
4. (2,-1/2)

Q8. The radius of a circle, having minimum area, which touches the curve y=4−x² and the lines,
y=∣x∣ is :
1. 2(√2-1)
2. 4(√2-1)
3. 4(√2+1)
4. 2(√2+1)

Q9. The sum of the distinct real values of μ, for which the vectors,μ^i + ^
j + k,
^

^ ^ ^
i + μ j + k,
^ ^ ^
i + j + μk are co-planar, is :
1. 2
2. 0
3. -1
4. 1

Q10. If the straight line, 2x – 3y + 17 =0 is perpendicular to the line passing through the points (7,
17) and (15, β), then β equals :
1. 5
2. 35/3
3. -35/3
4. - 5

Correct. 1

Q11. If λ be the ratio of the roots of the quadratic equation in x, 3m²x² +m(m - 4)x+2=0, then the
least value of m for which λ + = 1 , is:
1

λ

1. −2 + √2
2. 4 − 3√2
3. 4 − 2√3

4. 2 − √3

dy
Q12. Lety=y(x) be the solution of the differential equation, x dx
+ y = x log
e
x , (x > 1). If
2y(2) = log
e
4 − 1 , then y(e) is equal to :
1.
2
e

4

2. −
2
e

2

3. −
e

2

4. e

4

Correct. 4

Q13. If the vertices of hyperbola be at (-2,0) and (2,0) and one of its foci be at (-3,0), then which
one of the following points does not lie on this hyperbola ?
1. (2√6, 5)
2. (−6, 2√10)
3. (6, 5√2)
4. (4, √15)

Q14. Let a→ = ^i − ^j, →b = ^i + ^j + k
^
and → → × c→ + →b = →0 and a
c be a vector that a → ⋅ c→ = 4, then |c→| is 2

equal to:
1. 8
2. 19/2
3. 9
4. 17/2

√ −1
√π− 2 sin x
Q15. lim x→1
−

√1−x

1. √π
2. 1

√2π

3. √
π

2

4. √ 2

π

Correct. 4

Q16. If a circle C passing through the point (4,0) touches the circle x 2
+ y
2
+ 4x − 6y = 12

externally at the point (1, -1), then the radius of C is:
1. √57
2. 5
3. 2√5
4. 4

Correct. 1

Q17. Consider the quadratic equation (c − 5)x − 2cx + (c − 4) = 0, c = 5. Let S be the set of
2

all integral values of c for which one root of the equation lies in the interval (0, 2) and its other
root lies in the interval (2,3). Then the number of elements in Sis:
1. 18
2. 12
3. 11
4. 10

dy
Q18. The solution of the differential equation, dx
2
= (x − y) , when y(1) = 1, :
1+x−y
1. − log ∣∣ e 1−x+y ∣
∣
= x + y − 2

2. − log ∣∣
1−x+y
∣
= 2(x − 1)
e 1+x−y ∣

3. log ∣∣
2−y
∣
= 2(y − 1)
e 2−x ∣

4. log ∣∣
2−x ∣
= x − yv
e 2−y ∣

Q19. A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse
axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :
1. √3

2. 2
3. 2/√3
4. 3/2

Q20. If the system of linear equations
x-4y+7z=g
3y - 5z=h
-2x+54-92=k is consistent, then :
1. g+2h+k=0
2. g+h+k=0
3. 2g +h+k=0
4. g+h+2k=0

Q21. If

is the adjoint of a 3 × 3 matrix A and |A| = 4, then a is equal to _________ ?

Correct. 11

Q22. Let A and B be two sets containing 2 elements and 4 elements respectively. The number of
subsets of A × B having 3 or more elements is ____?

Correct. 219

Q23. If the sum of the deviations of 50 observations from 30 is 50, then the mean of these
observations is ____?

Correct. 31

Q24. In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics
course, those whose number is divisible by 3 opted Physics course and those whose number is
divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the

three courses is _____ ?

Correct. 38

6
3

Q25. The coef cient of t in the expansion of (
4 1−t

1−t
) is _______?

Correct. 15