JEE Main Sample Paper B.Tech Set C

JEE MAIN
SAMPLE
PAPER
Paper 1 for B.Tech

SET C
For more JEE Main Study Material visit AglaSem Admission

Jee Main Sample Paper

Physics

Q1. 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

Q2. Two short bar magnets of length 1 cm each have magnetic moments 1.20 Am2 and 1.00 Am2
respectively. They are placed on a horizontal table parallel to each other with their N poles
pointing towards the South. They have a common magnetic equator and are separated by a
distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O
of the line joining their centres is close to (Horizontal component of earth’s magnetic induction is
3.6 × 10-5 Wb/m2)
1. 2.56 × 10–4 Wb/m2
2. 3.50 × 10–4 Wb/m2
3. 5.80 × 10–4 Wb/m2
4. 3.6 × 10–5 Wb/m2

Q3. All the graphs below are intended to represent the same motion. One of them does it
incorrectly. Pick it up.

1.

2.

3.

4.

Q4. An electron from various excited states of hydrogen atom emit radiation to come to the
ground state. Let λn, λg be the de Broglie wavelength of the electron in the nth state and the
ground state respectively. Let Λn be the wavelength of the emitted photon in the transition from
the nth state to the ground state. For large n, (A, B are constants)
1. An = A + B / λ2n
2. An = A+B λn
3. A2n = A + B λ2n
4. A2n = λ

Q5. A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it
is utilized for transmission. How many telephonic channels can be transmitted simultaneously if
each channel requires a bandwidth of 5 kHz ?
1. 2×103
2. 2×104
3. 2×105
4. 2×106

Q6. Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c
(speed of light) is proportional to :

5

1. √
hc

G

2. √ Gh
3
c

3. √ Gh

c
5

4. √
3
c

Gh

Q7. The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5
mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of
its circular scale lies 3 divisions below the mean line. The readings of the main scale and the
circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this
sheet is :
1. 5.950 mm
2. 5.755 mm
3. 5.725 mm
4. 5.740 mm

Q8. A musician using an open ute of length 50 cm produces second harmonic sound waves. A
person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave
speed is 330 m/s, the frequency heard by the running person shall be close to :
1. 500 Hz
2. 753 Hz
3. 666 Hz
4. 333 Hz

Q9. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat
transferred to the gas, so that rms velocity of molecules is doubled, is about : (Take R=8.3J/K mole)
1. 14 kJ
2. 10 kJ
3. 0.9 kJ
4. 6 kJ

Q10. In a car race on straight road, car A takes a time t less than car B at the nish and passes
nishing point with a speed 'v' more than that of car B. Both the cars start from rest and travel
with constant acceleration a and a respectively. Then 'v' is equal to:
1 2

1.
a1 +a2
t
2

2. √a a t 1 2

3. √2a a t 1 2

4.
2a1 a2
t
a1 +a2

Q11. The mass and the diameter of a planet are three times the respective values for the Earth.
The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the
same pendulum on the planet would be:
1. 2√3s
√3
2. s
2

3.
3
s
2

4. 2
s
√3

Q12. In the circuit shown, the potential difference between A and B is :

1. 3 V
2. 1 V
3. 6 V
4. 2 V

Correct. 4

Q13. A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by
a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is :
1. 2F

3mR

2. F

2mR

3. F

3mR

4.
3F

2mR

Q14. 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

Q15. Three Carnot engines operate in series between a heat source at a temperature T, and a heat
sink at temperature T4 (see gure). There are two other reservoirs at temperature T, and T3, as
shown, with T2 > T2 > T2 > T4. The three engines are equally ef cient if

1/4 1/4
1. T
3 3
2 = (T T4 ) ; T3 = (T1 T )
1 4

1/3 1/3
2. T 2
2
= (T T4 )
1
2
; T3 = (T1 T )
4

1/3 1/3
3. T 2 = (T1 T )
2

4
2
; T3 = (T T4 )
1

1/3
4. T
1/2 2
2 = (T1 T4 ) ; T3 = (T T4 )
1

Q16. An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean
time between two successive collisions is 6 × 10 s. If the pressure is doubled and temperature is
−8

increased to 500 K, the mean time between two successive collisions will be
close to:

1. 4 × 10 s −8

2. 3 × 10 s −6

3. 0.5 × 10 s −8

4. 2 × 10 s −7

Q17. A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in
Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the
load is fully immersed in a liquid of relative density 2 . The relative density of the material of load
is 8. The new value of increase in length of the steel wire is :
1. 4.0 mm
2. zero
3. 5.0 mm
4. 3.0 mm

Correct. 4

Q18. In the circuit shown, nd C if the effective capacitance of the whole circuit is to be 0.5 uF. All
values in the circuit are in uF.

1. 6

5
μF

2. 4 μF
3. μF7

11

4. 7

10
μF

Q19. A paramagnetic material has atoms/. Its magnetic susceptibility at temperature 350 K is 2.8 x

. Its susceptibility at 300 K is :
1. 3.267 x
2. 3.672 x
3. 2.672 x
4. 3.726 X

Q20. In a radioactive decay chain, the initial nucleus is 232

90
Th . At the end there are 6 α-particles
and 4 β-particles which are emitted. If the end nucleus is A
Z
X , A and Z are given by :
1. A= 202; Z=80
2. A= 200; Z=81
3. A= 208; Z=80
4. A= 208 ; Z=82

Correct. 4

Q21. Surface of certain metal is rst illuminated with light of wavelength λ₁ = 350 nm and then, by
light of wavelength λ₂ = 540 nm. It is found that the maximum speed of the photo electrons in the
two cases differ by a factor of 2 . The work function of the metal (in eV) is close to :
(Energy of photon = 1240
eV )
λ( in nm)

1. 5.6
2. 2.5
3. 1.4
4. 1.8

Correct. 4

Q22. Temperature difference of 120°C is maintained between two ends of a uniform rod AB of
length 2L. Another bent rod PQ, 3L of same cross-sectionas AB and length 3L/2, is connected
across AB (See gure). In steady state, temperature difference between P and Q will be close to :

1. 35 °C
2. 45 °C
3. 60°C
4. 75 °C

Q23. 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

Q24. A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible
mass) of spring constant k. The other end of the spring is xed, as shown in the gure. The block is
initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the
maximum speed of the block is :

1.
F

√mk

2.
F

π√mk

3. πF

√mk

4. 2f

√mk

Q25. A point source of light, S is placed at a distance L in front of the centre of plane mirror of
width d which is hanging vertically on a wall. A man walks in front of the mirror along a line
parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see
the image of the light source in the mirror is :

1. 3d
2. 2d
3. d

4. d/2

Chemistry

Q1. The recommended concentration of uoride ion in drinking water is up to 1 ppm as uoride
ion is required to make teeth enamel harder by converting [3Ca₃(PO₄)₂.Ca(OH)₂] to :
1. [CaF₂]
2. [3(CaF₂).Ca(OH)₂]
3. [3Ca₃(PO₄)₂.CaF₂]
4. [3{Ca(OH)₂}.CaF₂]

Q2. Which of the following are Lewis acids ?
1. PH₃ and BCl₃
2. AlCl₃ and SiCl₄
3. PH₃ and SiCl₄
4. BCl₃ and AlCl₃

Correct. 4

Q3. 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 :
1. √ 2 a
2. a/√ 2
3. 2a
4. 2√ 2a

Q4. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are :
1. Cl− and ClO−
2. Cl− and ClO2-
3. ClO− and ClO-3
4. ClO2− and ClO3-

Q5. The correct match between Item 1 and Item II is :
Item I ( A) Benzaldehyde ( B) Alumina ( C) Acetonitrile
Item II (P) Mobile phase (Q) Adsorbent (R) Adsorbate Options

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

Q6. For the following reaction, the mass of water produced from 445g of C 57 H110 O6 is
2C57 H110 O6 (s) + 163O2 (g) → 114CO2 (g) + 110H2 O(l)

1. 490 g
2. 495 g
3. 445 g
4. 890 g

Q7. The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (v) of
the incident radiation as, [ν₀ is threshold frequency]:
1. λ ∝ 1

(v−v0 )

2. λ ∝ 1
1

(v−v0 ) 4

3. λ ∝ 1

1

(v−v0 ) 2

4. λ ∝
1

3

(v−v0 ) 2

Q8. The reaction, MgO(s) +C(s) >Mg(s) +CO(g), for which Δ H = +491.1 kJ mol and
r
∘ −1

, is not feasible at 298 K. Temperature above which reaction will be
∘ −1 −1
Δ S
r = 198.0JK mol

feasible is :
1. 2380.5 K
2. 2480.3 K
3. 2040.5 K
4. 1890.0 K

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 values of K /K for the following reactions at 300 K are, respectively : (At 300 K,
p c

3 −1
RT = 262dm atmmol )

N2 (g) + O2 (g) = 2NO(g)

N2 O4 (g) = 2NO2 (g)

N2 (g) + 3H2 (g) = 2NH3 (g)
3 −1
262dm atmmol
1. 6 −2
2
606.0dm atm mol
−2 −3 −1
1, 1 × 10 dm atm mol
2. 6 −2
2
606dm atm mol
3 −1
1, 262dm atm mol ,
3. 6 −2
2
606.0dm atm mol
3 −1
1, 262dm atmmol .
4. −3 −6 2
−2
1.65 × 10 dm atm mol

Correct. 4

Q11. Which premitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles
different from 90° ?
1. Monoclinic
2. Hexagonal
3. Triclinic
4. Tetragonal

Q12. 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 2+
(aq) + H2 (g) → Cu(s) + 2H
+
(aq)

Q13. Which of the following is not an example of heterogeneous catalytic reaction ?
1. Ostwald's process
2. Hydrogenation of vegetable oils
3. Haber's process
4. Combustion of coal

Correct. 4

Q14. The aldehydes which will not form Grignard product with one equivalent Grignard reagents
are:

( A)

( B)

( C)

( D)
1. ( C), ( D)
2. ( B), ( D)
3. ( B), ( C), ( D)
4. ( B), ( C)

Q15. The combination of plots which does not represent isothermal expansion of an ideal gas is :

( A)

( B)

( C)

( D)
1. ( B) and ( D)
2. ( A) and ( D)
3. ( B) and ( C)
4. ( A) and ( C)

Q16. For a reaction, consider the plot of In k versus 1/T given in the gure. If the rate constant of
this reaction at 400 K is 10 s , then the rate constant at 500 K is :
−5 −1

1. 10 s−4 −1

2. 4 x 10⁻⁴s⁻¹
3. 10 s
−6 −1

4. 2 × 10 s −4 −1

Q17. For emission line of atomic hydrogen from n = 8 to n = n, the plot of wave number (v )
i f
¯
¯¯

against ( 1

2
) will be (The Rydberg constant, R is in wave number unit)
H
n

1. Linear with intercept - R H

2. Non linear
3. Linear with slope RH

4. Linear with slope - R H

Correct. 4

Q18. The following results were obtained during kinetic studies of the reaction
2A+B Products

The time (in minutes) required to consume half of A is:
1. 5
2. 1
3. 10
4. 100

Q19. The highest value of the calculated spin-only magnetic moment (in BM) among all
the transition metal complexes is :
1. 5.92
2. 6.93
3. 4.90
4. 3.87

Q20.

Cannot be prepared by:

1. PhCOCH₃ + CH₃CH₂MgX
2. HCHO + PHCH(CH₃)CH₂MgX
3. PHCOCH₂CH₃ + CH₃MgX
4. CH₃CH₂COCH₃ + PhMgX

Q21. Water samples with BOD values of 4 ppm and 18 ppm, respectively, are:
1. Clean and Highly polluted
2. Highly polluted and Highly polluted
3. Highly polluted and Clean
4. Clean and Clean

Q22. 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

Q23. The increasing order of reactivity of the following compounds towards reaction with alkyl
halides directly is :

1. ( B) < ( A) < ( D) < ( C)
2. ( A) < ( C) < ( D) < ( B)
3. ( B) < ( A) < ( C) < ( D)

4. ( A) < ( B) < ( C) < ( D)

Q24. The pair of metal ions that can give a spin only magnetic moment of 3.9 BM for the complex
[M(H₂O)₆]Cl₂ is :
1. Cr²⁺ and Mn²⁺
2. V²⁺ and Co²⁺
3. V²⁺ and Fe²⁺
4. Co²⁺ and Fe²⁺

Q25. Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous
solution of Y. If molecular weight of X is A, then molecular weight of Y is :
1. 2A
2. 3A
3. A
4. 4A

Maths

Q1. A ray of light along x + √3y = √3 gets re ected upon reaching x-axis, the equation of the
re ected rays is
1. √3y = x-√3
2. y = √3x - √3
3. √3y = x-1
4. y = x+√3

Q2. All the students of a class performed poorly in Mathematics. The teacher decided to give grace
marks of 10 to each of the students. Which of the following statistical measures will not change
even after the grace marks were given ?

1. median
2. mode
3. variance
4. mean

Q3. 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

Q4.
1. (−4, −5)
2. (−4, 3)
3. (−4, 5)
4. (4, 5)

Q5. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be
selected and arranged in a row on a shelf so that the dictionary is always in the middle. The
number of such arrangements is :
1. at least 1000
2. less than 500
3. at least 500 but less than 750
4. at least 750 but less than 1000

Q6. Let f(x)=x²+1/x² and g(x)=x-1/x, x∊R-{-1,0,1}. If h(x)=f(x)/g(x), then the local minimum value
of h(x) is:
1. 3
2. -3
3. -2√2
4. 2√2

Correct. 4

Q7. 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

Q8. 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

Q9. Let In = ∫ tanⁿ x dx, (n>1). If I₄ + I₆ = a tan⁵ x + bx⁵ + C, where C is a constant of integration,
then the ordered pair (a,b) is equal to:
1. (1/5,0)
2. (1/5,-1)
3. (-1/5,0)
4. (-1/5,1)

Q10. 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

Q11.
1. 2
2. 5
3. 1/8
4. 25/8

Q12. If 5(tan²x - cos²x) = 2 cos 2x + 9, then the value of cos 4x is:
1. 1/3
2. 2/9

3. -7/9
4. -3/5

403

Q13. If the fractional part of the number 2

15
is k/15, then k is equal to :
1. 6
2. 8
3. 14
4. 4

Q14. Let A = { θ ∊ (− is purely imaginary } .Then the sum of the elements in A is:
π 3+2i sin θ
, π) :
2 1−2i sin θ

1. 3π/4
2. 2π/3
3. π
4. 5π/6

Q15. For any θ ∊ ( , the expression 3(sinθ - cosθ)⁴+ 6(sinθ + cosθ)² + 4sin⁶θ equals:
π π
, )
4 2

1. 13- 4cos²θ + 6sin²θcos²θ
2. 13-4cos⁶θ
3. 13 - 4cos⁴θ + 2sin²θcos²θ
4. 13 - 4 cos²θ+6 cos⁴θ

Q16. The expression ∼ (∼ p → q) is logically equivalent to :
1. p ∧ q
2. ∼ p ∧ q
3. ∼ p∧ ∼ q
4. p∧ ∼ q

Q17. 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
+ y )
2
= 4R x y
2 2 2

2
2. (x 2
+ y )
2
= 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

Q18. Consider the quadratic equation (c − 5)x 2
− 2cx + (c − 4) = 0, c = 5 . Let S be the set of
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

2
Q19. All x satisfying the inequality (cot −1
x) − 7 (cot
−1
x) + 10 > 0 , lie in the interval :
1. (−∞, cot 5) ∪ (cot 4, cot 2)
2. (cot 2, ∞)
3. (−∞, cot 5) ∪ (cot 2, ∞)
4. (cot 5, cot 4)

Q20. The integral ∫ equals :
π/4 dx

π/6 sin 2x(tan
5
x+cot
5
x)

1. 1

10
(
π

4
− tan
−1
(
1
))
9√3

2. π

40

3. 1

5
(
π

4
− tan
−1
(
1
))
3√3

4. 1
tan
−1
(
1
)

20
9√3

Q21. Let a function f : (0, ∞) → (0, ∞) be de ned by f (x) = ∣∣1 − . Then f is :
1
∣
x
∣

1. injective only
2. both injective as well as surjective
3. not injective but it is surjective
4. neither injective nor surjective

Correct. 4

Q22. 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.
4√3

3

Q23. Let z be a root of the quadratic equation, x
0
2
+ x + 1 = 0 . If z = 3 + 6iz 81

0
− 3iz
93

0
then
arg z is equal to :
1. π/4
2. π/6
3. π/3
4. 0

Q24. If both the roots of the quadratic equation x − mx + 4 = 0 are real and distinct and they
2

lie in the interval [1, 5] , then m lies in the interval :
1. (4,5)
2. (5,6)
3. (-5,-4)
4. (3,4)

Q25. The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1,
3, 7, 9 (repitition of digits allowed) is equal to :
1. 375

2. 374
3. 250
4. 372