JEE Main Sample Paper B.Tech Set B

JEE MAIN
SAMPLE
PAPER
Paper 1 for B.Tech

SET B
For more JEE Main Study Material visit AglaSem Admission

Jee Main Sample Paper

Physics

Q1. A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its
length vertical, from a xed point by a massless spring, such that it is half submerged in a liquid of
density σ at equilibrium position. The extension X0 of the spring when it is in equilibrium is:

1.

2.

3.
4. Mg/k

Q2. A projectile is given an initial velocity of (i + 2j) m/s, where i is along the ground and j is along
the vertical. If g = 10 m/s2, the equation of its trajectory is:
1. y=2x-5x2
2. 4y=2x-5x2
3. 4y=2x-25x2
4. y=x-5x2

Correct. 1

Q3. In a collinear collision, a particle with an initial speed vo strikes a stationary particle of the
same mass. If the nal total kinetic energy is 50% greater than the original kinetic energy, the
magnitude of the relative velocity between the two particles, after collision, is :
1. v o/4
2. √ 2vo

3. vo /2
4. vo/√ 2

Q4. In an a.c. circuit, the instantaneous e.m.f. and current are given by e=100 sin 30 t, i=20 sin
(30t - π/4) In one cycle of a.c., the average power consumed by the circuit and the wattless current
are, respectively :
1. 50, 10
2. 1000/√2, 10
3. 50/√2 , 0
4. 50 , 0

Q5. Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10 Ω.
The internal resistances of the two batteries are 1 Ω and 2 Ω respectively. The voltage across the
load lies between :
1. 11.6 V and 11.7 V
2. 11.5 V and 11.6 V
3. 11.4 V and 11.5 V
4. 11.7 V and 11.8 V

Q6. 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 α is its coef cient of linear expansion.
Suppose we want to bring the cube to its original size by heating. The temperature should be
raised by:

1. P/3αK
2. P/αK
3. 3α/PK
4. 3PKα

Correct. 1

Q7. A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30° from
the horizontal as shown and released from rest. Its angular speed when it passes through the
horizontal ( in rads −1
) will be (g = 10ms −2
)

1. √30/2
2. v30/2
3. √30
4. √20/3

Q8. An amplitude modulated signal is plotted below:

Which one of the following best describes the above signal ?
1. (9 + sin(2.5π × 10 t)) sin(2π × 10 t)V
5 4

2. (1 + 9 sin(2π × 10 t)) sin(2.5π × 10 t)V
4 5

3. (9 + sin(2π × 10 t)) sin(2.5π × 10 t)V
4 5

4. (9 + sin(4π × 10 t)) sin(5π × 10 t)V
4 5

Q9. 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

Q10. Seven capacitors, each of capacitance 2μF, are to be connected in a con guration to
obtain an effective capacitance of (6/13 ) μF. Which of the combinations, shown in
gures below, will achieve the desired value ?

1.

2.

3.

4.

Q11. A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed
of 6 m/s. There is a uniform magnetic eld of 0.1 T in the positive z-direction. The potential
difference between the two faces of the cube perpendicular to the x-axis, is
1. 1 mV
2. 12 mV
3. 2 MILV
4. 6 mV

Q12. A 2 W carbon resistor is color coded with green, black, red and brown respectively. The
maximum current which can be passed through this resistor is :
1. 100 mA
2. 0.4 mA
3. 20 mA

4. 63 mA

Q13. Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius
R, and Bis in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies,
TА/Tв, is :
1. 1
2. 2
3. √ 1

2

4. 1

2

Correct. 1

Q14. A resonance tube is old and has jagged end. It is still used in the laboratory to determine
velocity of sound in air. A tuning fork of frequency 512 Hz produces rst resonance when the tube
is lled with water to a mark 11 cm below a reference mark, near the open end of the tube. The
experiment is repeated with another fork of frequency 256 Hz which produces rst resonance
when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained
in the experiment, is close to :
1. 335
2. 322
3. 328
4. 341

Q15. In the given circuit diagram, the currents, = -0.3 A, =0.8 A and =0.4 A, are owing as shown.
The currents ,, and respectively, are :

1. 1.1 A, 0.4 A, 0.4 A

2. -0.4 A, 0.4 A, 1.1 A
3. 1.1 A, -0.4 A, 0.4 A
4. 0.4 A, 1.1 A, 0.4 A

Correct. 1

Q16. Consider a tank made of glass(refractive index 5) with a thick bottom. It is lled with a liquid
of refractive index u. A student nds that, irrespective of what the incident angle i (see gure) is
for a beam of light entering the liquid, the light re ected from the liquid glass interface is never
completely polarized. For this to happen, the minimum value of u is :

1. √
5

3

2.
4

3

3.
3

√5

4.
5

√3

Q17. A current loop, having two circular arcs joined by two radial lines is shown in the gure. It
carries a current of 10 A. The magnetic eld at point O will be close to :

1. 1.0 x 10⁻⁵ T

2. 1.5 x 10⁻⁵ T
3. 1.0 x 10⁻⁷ T
4. 1.5 x 10⁻⁷ T

Correct. 1

Q18. The position vector of the centre of mass r→ cm cm of an asymmetric uniform bar of negligible
area of cross-section as shown in gure is :

1. r→ cm =
11

8
^ +
Lx
3

8
^
Ly

2. r→ cm =
13

8
^ +
Lx
5

8
^
Ly

3. r→ cm =
3

8
^ +
Lx
11

8
^
Ly

4. r→ cm =
5

8
^ +
Lx
13

8
^
Ly

Q19. A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A
meteorite of the same mass, falling towards the earth, collides with the satellite completely
inelastically. The speeds of the satellite and the meteorite are the same, just before the collision.
The subsequent motion of the combined body will be:
1. in an elliptical orbit
2. in the same circular orbit of radius R
3. in a circular orbit of a different radius
4. such that it escapes to in nity

Correct. 1

Q20. An ideal gas occupies a volume of 2 mat a pressure of 3 x 10⁶ Pa. The energy of the gas
is :
1. 9 x 10⁶ J
2. 3 x 10² J
3. 6 x 10⁴ J
4. 10⁸ J

Correct. 1

Q21. Using a nuclear counter the count rate of emitted particles from a radioactive source is

measured. At t=0 it was 1600 counts per second and t=8 seconds it was 100 counts per second. The
count rate observed, as counts per second, at t=6 seconds is close to _____.

Correct. 200

Q22. 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 _____(°).

Correct. 45

Q23. In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing
through resistance R and R
1 2

respectively, are _________ and ________.

Correct. 0.5, 0

24. A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a
dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of
the induced charge will be ____ (nC).

Correct. 1.2

Q25. Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer
radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its
moment of inertia about its axis is also I, is ______ (cm).

Correct. 16

Chemistry

Q1. An aqueous solution contains 0.10 M H₂S and 0.20 M HCl. If the equilibrium constants for the
formation of HS⁻ from H₂S is 1.0 × 10⁻⁷ and that of S²⁻ from HS⁻ ions is 1.2 × 10⁻¹³ then the
concentration of S²⁻ ions in aqueous solution is:
1. 5×10⁻⁸
2. 3×10⁻²⁰

3. 6×10⁻²¹
4. 5×10⁻¹⁹

Q2. An aqueous solution contains an unknown concentration of Ba²⁺. When 50 mL of a 1 M
solution of Na₂SO₄ is added, BaSO₄ just begins to precipitate. The nal volume is 500 mL. The
solubility product of BaSO₄ is 1×10⁻¹⁰. What is the original concentration of Ba²⁺ ?
1. 5×10⁻⁹ M
2. 2 ×10⁻⁹ M
3. 1.1×10⁻⁹ M
4. 1.0×10⁻⁹ M

Q3. Sodium salt of an organic acid ‘X’ produces effervescence with conc. H2SO4. ‘X’ reacts with the
acidi ed aqueous CaCl2 solution to give a white precipitate which decolourises acidic solution of
KMnO4.‘X’ is :
1. CH3COONa
2. Na2C2O4
3. C6H5COONa
4. HCOONa

Q4. The pH of rain water , is approximately :
1. 7.5
2. 6.5
3. 7.0
4. 5.6

Correct. 4

Q5. The major product obtained in the following reaction is:

1.

2.

3.

4.

Q6. For the equilibrium,
2H2 O = H3 O
+
+ OH
−
, the value of ΔG at 298 K is approximately :
∘

1. 80 kJ mol⁻¹
2. – 80 kJ mol⁻¹
3. 100 kJ mol⁻¹
4. - 100 kJ mol⁻¹

Correct. 1

Q7. The effect of lanthanoid contraction in the lanthanoid series of element by and large means:
1. Increase in both atomic and ionic radii
2. Decrease on both atomic and ionic radii
3. Decrease in atomic radii and increase in ionic radii
4. Increase in atomic radii and decrease in ionic radii

Q8. Hall-Heroult's process is given by:

1. ZnO + C Coke, 1673K → Zn + CO
2. 2Al O + 3C → 4Al + 3CO
2 3 2

3. Cr O + 2Al → Al O + 2Cr
2 3 2 3

4. Cu (aq) + H (g) → Cu(s) + 2H (aq)
2+
2
+

Q9. The decreasing order of ease of alkaline hydrolysis for the following esters is

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

Q10. The correct structure of product 'p' in the following reaction is :
NEt1

Asn − Ser + (GH3 CO) O → ,P
2

1.

2.

3.

4.

Correct. 1

Q11. The major product of the following reaction

is :

1.

2.

3.
4. [(Ph P) Ir Cl]
3 3

Q12. The two monomers for the synthesis of Nylon 6, 6 are :
HOOC(CH2 ) COOH
1. 6

H2 N(CH2 ) NH2
6

HOOC(CH2 ) COOH
2.
6

H2 N(CH2 ) NH2
4

HOOC(CH2 ) COOH
3. 4

H2 N(CH2 ) NH2
6

HOOC(CH2 ) COOH
4.
4

H2 N(CH2 ) NH2
4

Q13. The correct statement(s) among I to III with respect to potassium ions that are abundant
within the cell uids is/are:
I. They activate many enzymes
II. They participate in the oxidation of glucose to produce ATP
III. Along with sodium ions, they are responsible for the transmission of
nerve signals
1. III only
2. I and II only
3. I, II and III
4. I and III only

Q14. The element that shows greater ability to form pF − pπ multiple bonds, is :
1. C
2. Ge
3. Sn
4. Si

Correct. 1

Q15. The major product of the following reaction is :

1. CH₃CH=C=CH₂
2. CH₃CH₂C=CH

3.
4. CH₃CH=CHCH₂NH₂

Q16. If K of Ag CO is 8 × 10 , the molar
sp 2 3
−12

solubility of Ag CO in 0.1MAgNO is :
2 3 3

1. 8 × 10−11
M

2. 8 × 10−10
M

3. 8 × 10−13
M

4. 8 × 10−12
M

Q17. The correct decreasing order for acid strength is :
1. FCH₂COOH > NCCH₂COOH > NO₂CH₂COOH > CICH₂COOH
2. CNCH₂COOH > O₂NCH₂COOH > FCH₂COOH > CICH₂COOH
3. NO₂CH₂COOH > NCCH₂COOH > FCH₂COOH > CICH₂COOH
4. NO₂CH₂COOH > FCH₂COOH > CNCH₂COOH > CICH₂COOH

Q18. A solution of sodium sulfate contains 92 g of Na⁺ ions per kilogram of water. The molality of

Na⁺ ions in that solution in mol kg⁻¹ is:
1. 8
2. 4
3. 12
4. 16

Q19.

Cannot be prepared by:
1. PhCOCH₃ + CH₃CH₂MgX
2. HCHO + PHCH(CH₃)CH₂MgX
3. PHCOCH₂CH₃ + CH₃MgX
4. CH₃CH₂COCH₃ + PhMgX

Q20. In a chemical reaction,

the initial concentration of B was 1.5 times of the concentration of A, but the equilibrium
concentrations of A and B were found to be equal. The equilibrium constant(K) for the aforesaid
chemical reaction is:
1. 1
2. ¼
3. 4
4. 16

Q21. 20 mL of 0.1 M H₂SO₄ solution is added to 30 mL of 0.2 M NH₄ OH solution. The pH of the

resultant mixture is _______ ? [ pk of NH₄OH=4.7 ]
b

Correct. 9.0

Q22. ________ litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to

create an aqueous solution with pH of 2?

Correct. 9.0

Q23. Total number of lone pair of electrons in I₃⁻ ion is _________.

Correct. 9

Q24. A solution containing 62 g ethylene glycol in 250 g water is cooled to -10°C. If K for water is
f

−1
1.86Kkgmol

the amount of water (in g) separated as ice is ___________.

Correct. 64

Q25. The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was
__________.

Correct. Methylisocyanate

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. If ∫f (x) dx =Ψ(x) , then ∫x5f(x3) dx is equal to
1. (1/3)x3Ψ(x3) - 3 ∫x3Ψ(x3) dx + C
2. (1/3)x3Ψ(x3) - ∫x2Ψ(x3) dx + C
3. (1/3)[x3Ψ(x3) - ∫x3Ψ(x3) dx] + C
4. (1/3)[x3Ψ(x3) - ∫x2Ψ(x3) dx ]+ C

Q3. Tangent and normal are drawn at P(16, 16) on the parabola y²=16x, which intersect the axis of
the parabola at A and B, respectively. If C is the centre of the ∠CPB=θ, then a value of tan θ is :
1. 1/2
2. 2

3. 3
4. 4/3

Q4. 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 :
1. an in nite set
2. a nite set containing two or more elements
3. a singleton
4. an empty set

Q5. If (2+sin x)dy/dx + (y+1)cos x = 0 and y(0) = 1, then y(π/2) is equals to:
1. -2/3
2. -1/3
3. 4/3
4. 1/3

Correct. 4

Q6. Integration ∫ cos(log x)dx is equals to :
e

(Where C is an integration constant )
1. [sin(log x) − cos(log x)] + C
x

2 e e

2. x [cos(log x) − sin(log x)] + C
e e

3. [cos(log x) + sin(log x)] + C
x

2 e e

4. x [cos(log x) + sin(log x)] + C
e e

Q7. Let a₁, a₂........, a₃ₒ be an A.P., S = ∑ and T = ∑ . If a₅ = 27 and S-2T = 75,
30 15
ai a(2i−1)
i=1 i=1

then a₁₀ is equal to:
1. 47
2. 52
3. 42
4. 57

Q8. If a circle of radius R passes through the origin O and intersects the coordinate axes at A and

B, then the locus of the foot of perpendicular from O on AB is :
3
1. (x 2 2
+ y )
2
= 4R x y
2 2

2
2. (x 2 2
+ y ) = 4Rx y
2 2

3. (x 2 2
+ y ) (x + y) = R xy
2

2
4. (x 2
+ y )
2
= 4R x y
2 2 2

Correct. 1

Q9. Let z and z be two complex numbers satisfying |z | = 9 and |z
1 2 1 2 − 3 − 4i| = 4 . Then
the minimum value of |z − z | is : 1 2

1. √2
2. 2
3. 0
4. 1

Q10. If the area enclosed between the curves y = kx , is 1 square unit.
2 2
and x = ky , (k > 0)

Then k is:
1.
√3

2

2. 1

√3

3. 2

√3

4. √3

Q11. Let I = ∫ . If I is minimum then the ordered pair (a, b) is :
b
4 2
(x − 2x ) dx
a

1. (0, √2)
2. (−√2, √2)
3. (√2, −√2)
4. (−√2, 0)

Q12. Let z 1 and z2 be any two non-zero complex numbers such that 3 |z | = 4 |z |. If 1 2

then,
3z1 2z2
z = +
2z2 3z1

1. Im(z)=0
2. |z| = 1

2
√
17

2

3. Re(z)=0

4. |z| = √ 5

2

Correct.

Q13. If 5, 5r, 5r are the lengths of the sides of a triangle, then r cannot be equal to:
2

1. 3/4
2. 5/4
3. 7/4
4. 3/2

Q14. Let f : R → K be a function such that f (x) = x 3 2 ′
+ x f (1) + xf
′′
(2) + f
′′′
(3), x ∈ R .
Then f (2) equals :
1. -4
2. 8
3. 30
4. - 2

Correct. 4

Q15. Let z be a complex number such that |2|+z=3 +i (where i= √-1). Then z is equal to :
1. 5

4

2. 5

3

3.
√34

3

√41
4.
4

Q16. A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from
the bag with replacement. If X be the number of white balls drawn, then ( mean of X

standard deviation of X
) is
equal to:

1. 4
2. 3√2
3. 4√3
4√3
4. 3

Q17. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is
13, then the eccentricity of the hyperbola is :
1. 13/12
2. 13/6
3. 2
4. 13/8

Correct. 1

Q18. The logical statement [∼ (∼ p ∨ q) ∨ (p ∧ r)] ∧ (∼ q ∧ r) is equivalent to :
1. (p∧ ∼ q) ∨ r
2. ∼ p ∨ r
3. (∼ p∧ ∼ q) ∧ r
4. (p ∧ r)∧ ∼ q

Correct. 4

6
3

Q19. The coef cient of t in the expansion of ( is :
4 1−t
)
1−t

1. 10
2. 12
3. 15
4. 14

t −t −t
e e cos t e sin t
⎡ ⎤
Q20. If A = ⎢ e t
−e
−t
cos t − t
−t
sin t −e
−t
sin t + e
−t
cos t ⎥ then A is :
⎣ t −t −t ⎦
e 2e sin t −2e cos t

1. invertible only if t = π
2. invertible only if t =
π

2

3. not invertible for any teR.
4. invertible for all teR.

Correct. 4

Q21. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and
3 boys that can be formed from this class, if there are two speci c boys A and B, who refuse to be
the members of the same team, is _________?

Correct. 300

Q22. 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 _______?

Correct. 95

Q23. The intercepts on x-axis made by tangents to the curve, y= 0∫x |t| dt, x ∈ R, which are parallel
to the line y = 2x, are equal to (±)___________.

Correct. 1

Q24. The sum of the following series
2 2 2 2 2 2 2 2 2 2
9(1 +2 +3 ) 12(1 +2 +3 +4 ) 15(1 +2 +…+5 )
1 + 6 +
7
+
9
+
11
+ ⋯ upto 15 terms is _______?

Correct. 7820

Q25. Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular
polygon. If Tn+1 − Tn = 10, then the value of n is ________?

Correct. 5