Courses

# JEE (Advanced) 2018 Paper - 1

## 54 Questions MCQ Test National Level Test Series for JEE Advanced 2020 | JEE (Advanced) 2018 Paper - 1

Description
This mock test of JEE (Advanced) 2018 Paper - 1 for JEE helps you for every JEE entrance exam. This contains 54 Multiple Choice Questions for JEE JEE (Advanced) 2018 Paper - 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this JEE (Advanced) 2018 Paper - 1 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this JEE (Advanced) 2018 Paper - 1 exercise for a better result in the exam. You can find other JEE (Advanced) 2018 Paper - 1 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
*Multiple options can be correct
QUESTION: 1

### The potential energy of a particle of mass m at a distance r from a fixed point O is given by V (r) = kr2/2,where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radiusR about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum aboutO, which of the following statements is (are) true?

Solution:

*Multiple options can be correct
QUESTION: 2

### Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force  is applied on the body, where  and . The torque acting on the body about the origin at time . Which of the following statements is (are) true?

Solution:

*Multiple options can be correct
QUESTION: 3

### A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is σ. The angle of contact between water and the wall of the capillary tube is θ. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Solution:

*Multiple options can be correct
QUESTION: 4

In the figure below, the switches S1 and S2 are
closed simultaneously at t = 0 and a current starts to
flow in the circuit. Both the batteries have the same
magnitude of the electromotive force (emf) and the
polarities are as indicated in the figure. Ignore
mutual inductance between the inductors. The
current I in the middle wire reaches its maximum
magnitude Imax at time . Which of the
following statements is (are) true?

Solution:

*Multiple options can be correct
QUESTION: 5

Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R
carries a constant current I1 and the wire located at x = –R carries a constant current I2. A circular loop of radius R is suspended with its centre at (0, 0, √3R ) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the + ˆj direction. Which of the following statements regarding the magnetic field  is (are) true?

Solution:

(A) If I1 = I2, magnetic field due to infinite wires is equal to zero . So there must be a non–zero magnetic field at O due to the current carrying loop.
(B) If I1 > 0 & I2 < 0 , magnetic field due to straight lines are along positive z–axis and due to loop it
is along negative z–axis.
(C) If I1 < 0 & I2 > 0 magnetic field due to straight wires are along negative z–axis and due to the loop it is also along negative z–axis.
(D)

*Multiple options can be correct
QUESTION: 6

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?

Solution:

Process II is an isothermal expansion
Process IV is an isothermal compression
In isobaric process, volume is directly proportional to temperature.

*Answer can only contain numeric values
QUESTION: 7

Two vectors  are defined as , where a is a constant and  at time t = for the first time, the value of , in seconds, is _____.

Solution:

*Answer can only contain numeric values
QUESTION: 8

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a
speed 1.0 ms −1 and the man behind walks at a speed 2.0 ms−1. A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330 ms−1 At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is __________.

Solution:

*Answer can only contain numeric values
QUESTION: 9

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is , then the height of the top of the inclined plane, in metres, is __________. Take g = 10 ms–2.

Solution:

*Answer can only contain numeric values
QUESTION: 10

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is 2.0 N m−1 and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass 1.0 kg moving with a speed of 2.0 m s−1 collides elastically with the first block. The collision is such that the 2.0 kg block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is _________.

Solution:

For collision :
using com
Using

time taken for the block to came to the unstretched position of spring for the first time after the collision

distance between blocks =

*Answer can only contain numeric values
QUESTION: 11

Three identical capacitors C1 , C2 and C3 have a capacitance of 1.0 each and they are uncharged initially. They are connected in a circuit as shown in the figure and C1 is then filled completely with a dielectric material of relative permittivity . The cell electromotive force (emf) V0 = 8V. First the switch S1 is closed while the switch S2 is kept open. When the capacitor C3 is fully charged, S1 is opened and S2 is closed simultaneously. When all the capacitors reach equilibrium, the charge on C3 is found to be  The value of =_________.

Solution:

After S1 is closed, C3 has charge 8 . when S1 opened and S2 closed, C3 has charge 5 . so remaining 3
resides on C1 and C2

*Answer can only contain numeric values
QUESTION: 12

In the xy-plane, the region y > 0 has a uniform magnetic field B1 kˆ and the region y < 0 has another uniform magnetic field B2 kˆ. A positively charged particle is projected from the origin along the positive y-axis with speed  as shown in the figure. Neglect gravity in this problem. Let t = T be the time when the particle crosses the x-axis from below for the first time. If B2 = 4B1 , the average speed of the particle, in ms–1 , along the x-axis in the time interval T is __________.

Solution:

Avg. speed along x-axis

*Answer can only contain numeric values
QUESTION: 13

Sunlight of intensity 1.3 kWm–2 is incident normally on a thin convex lens of focal length 20 cm. Ignore
the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in kW m–2, at a distance 22 cm from the lens on the other side is __________.

Solution:

The area of A over which the light falls satisfy :

*Answer can only contain numeric values
QUESTION: 14

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T1= 300 K and T2 = 100 K, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller  and the larger cylinders are K1 and K2 respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K1 / K2 =__________.

Solution:

In steady state, heat current in both material is same

QUESTION: 15

The relation between [E] and [B] is

Solution:

QUESTION: 16

The relation between [ ] and [ ] is

Solution:

QUESTION: 17

Consider the ratio to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is , then what is the error Δr in determining r ?

Solution:

QUESTION: 18

In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed in the first 1.0s. For |x| ≪ 1, ln(1 + x) = x up to first power in x . The error , in the determination of the decay constant in s–1, is

Solution:

*Multiple options can be correct
QUESTION: 19

The compound(s) which generate(s) N2 gas upon thermal decomposition below 300°C is (are)

Solution:

(a)  (N2O can further decompose to N2 and O2 at temperature above 300oC)
(b)
(c)
(d) Mg3N2 does not decompose at any temperature.

*Multiple options can be correct
QUESTION: 20

The correct statement(s) regarding the binary transition metal carbonyl compounds is (are)
(Atomic numbers: Fe = 26, Ni = 28)

Solution:

(a) Electronic configuration of central metal atom in both cases is [Ar] 3d104s24p6 (8 electrons in
outermost shell and 18 valence electrons respectively).
(b) Low spin complex because CO is a strong field ligand.
(c) Metal-carbon bond strengthens when the oxidation state of metal is lowered.
(d) The carbonyl C – O bond becomes stronger when the oxidation state is increased.

*Multiple options can be correct
QUESTION: 21

B ased on the compounds of group 15 elements, the correct statement(s) is (are)

Solution:

Bi2O5 is more basic than N2O5.
NF3 is more covalent than BiF3.
PH3 boils at lower temperature than NH3.
N – N single bond is weaker than P – P single bond.

*Multiple options can be correct
QUESTION: 22

In the following reaction sequence, the correct structure(s) of X is (are)

Solution:

*Multiple options can be correct
QUESTION: 23

The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is(are)

Solution:

*Multiple options can be correct
QUESTION: 24

A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and
temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and
internal energy, respectively.

The correct option(s) is (are)

Solution:

*Answer can only contain numeric values
QUESTION: 25

Among the species given below, the total number of diamagnetic species is ___.
H atom, NO2 monomer, O2  (superoxide), dimeric sulphur in vapour phase, Mn3O4, (NH4)2[FeCl4], (NH4)2[NiCl4], K2MnO4, K2CrO4

Solution:

Paramagnetic: H, NO2 monomer O2  superoxide , S2 (Vapour)[Mn3O4 is mixed oxide of Mn+2 and Mn+3],
(NH4)2 [FeCl4], (NH4)2[NiCl4], K2MnO4
Diamagnetic: K2CrO4

*Answer can only contain numeric values
QUESTION: 26

The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by
NiCl2.6H2O to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl2.6H2O are used in the preparation, the combined weight (in grams) of gypsum and the nickel-ammonia coordination compound thus produced is ____.
(Atomic weights in g mol–1 : H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)

Solution:

*Answer can only contain numeric values
QUESTION: 27

Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is
constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge
balance.
(i) Remove all the anions (X) except the central one
(ii) Replace all the face centered cations (M) by anions (X)
(iii) Remove all the corner cations (M)
(iv) Replace the central anion (X) with cation (M)
The value of in Z is _______ .

Solution:

*Answer can only contain numeric values
QUESTION: 28

F or the electrochemical cell,
Mg(s) | Mg2+ (aq, 1 M) || Cu2+ (aq, 1 M) | Cu(s) the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg2+ is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is ______.
(given, = 11500 K V−1, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)

Solution:

*Answer can only contain numeric values
QUESTION: 29

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The
partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old
partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to
leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is

Solution:

*Answer can only contain numeric values
QUESTION: 30

Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar
binary solution of liquids A and B has vapour pressure 45 Torr. At the same temperature, a new solution of A and B having mole fractions xA and xB, respectively, has vapour pressure of 22.5 Torr. The value of xA/xin the new solution is ____.
(given that the vapour pressure of pure liquid A is 20 Torr at temperature T)

Solution:

*Answer can only contain numeric values
QUESTION: 31

The solubility of a salt of weak acid (AB) at pH 3 is Y × 10–3 mol L−1. The value of Y is ____.
(Given that the value of solubility product of AB (Ksp) = 2 × 10–10 and the value of ionization constant of HB (Ka) = 1 × 10–8)

Solution:

*Answer can only contain numeric values
QUESTION: 32

The plot given below shows P—T curves (where P is the pressure and T is the temperature) for two
solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the
solvents.

On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is _________.

Solution:

QUESTION: 33

The compound Y is

Solution:

QUESTION: 34

The compound Z is

Solution:

QUESTION: 35

The compound P undergoes the following reactions and forms the compound R. The compound R is:

Solution:

QUESTION: 36

The compound S is

Solution:

*Multiple options can be correct
QUESTION: 37

For a non-zero complex number z, let arg(z) denote the principal argument with < arg(z) Then, which of the following statement(s) is (are) FALSE ?

Solution:

*Multiple options can be correct
QUESTION: 38

In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 10√3 and 10, respectively.
Then, which of the following statement(s) is (are) TRUE ?

Solution:

*Multiple options can be correct
QUESTION: 39

Let P1 : 2x + y – z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE ?

Solution:

(A) Direction ratios of line of intersection are given by

(B)
(C) Angle between
(D) P3 : x – y + z = 0
Distance of (2, 1, 1) from the plane =

*Multiple options can be correct
QUESTION: 40

For every twice differentiable function f : R → [–2, 2] with (f(0))2 + (f '(0))2 = 85, which of the following
statement(s) is (are) TRUE ?

Solution:

*Multiple options can be correct
QUESTION: 41

Let f : R → R and g : R → R be two non-constant differentiable functions. If

and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE ?

Solution:

*Answer can only contain numeric values
QUESTION: 42

The value of  is ______ .

Solution:

*Multiple options can be correct
QUESTION: 43

Let f : [0, ∝) → R be a continuous function such that

for all x ∈[0, ∝). Then, which of the following statement(s) is (are) TRUE ?

Solution:

*Answer can only contain numeric values
QUESTION: 44

The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the
repetition of digits is allowed, is ______ .

Solution:

Divisible by 4 ⇒ last 2 digits divisible by 4 ⇒ ends in 12, 24, 32, 44 or 52
∴ 53 x 5 = 625

*Answer can only contain numeric values
QUESTION: 45

Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ….. , and Y be the set consisting of the first 2018 terms of arithmetic progression 9, 16, 23, ….. . Then, the number of
elements in the set X ∪ Y is _____ .

Solution:

n(X ∪Y) = n(X) + n(Y) – n(X ∪Y)
1, 6, 11, …. 2018 term
Tn = 1 + (n – 1)5 = 5n – 4
UK = 9 + (K – 1)7 = 7K + 2
for common terms
5n – 4 = 7K + 2

*Answer can only contain numeric values
QUESTION: 46

The number of real solutions of the equation

lying in the interval
(Here, the inverse trigonometric functions sin–1x and cos–1x assume values in respectively.)

Solution:

*Answer can only contain numeric values
QUESTION: 47

For each positive integer n, let .
For x ∈ R, let [x] be the greatest integer less than or equal to x. If  ,  then the value of [L] is_____ .

Solution:

*Answer can only contain numeric values
QUESTION: 48

Let  and   be two unit vectors such that . For some x, y ∈ R, let  and the vector c  is inclined at the same angle α to both and , then the value of 8cos2 α is _____ .

Solution:

*Answer can only contain numeric values
QUESTION: 49

Let a, b, c be three non - zero real numbers such that the equation

has two distinct real roots α and ß with . Then, the value of is ____ .

Solution:

*Answer can only contain numeric values
QUESTION: 50

A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring f armer F2 takes away the region which lies between the side PQ and a curve of the form y = xn (n > 1). If the area of the region taken away by the farmer F2 is exactly 30% of the area of ΔPQR, then the value of n is _____ .

Solution:

QUESTION: 51

Let E1E2 and F1F2 be the chords of S passing through the point P0(1, 1) and parallel to the x-axis and the yaxis, respectively. Let G1G2 be the chord of S passing through P0 and having slope –1. Let the tangents to S at E1 and E2 meet at E3, the tangents to S at F1 and F2 meet at F3, and the tangents to S at G1 and G2 meet at G3. Then, the points E3, F3, and G3 lie on the curve

Solution:

Clearly they lie on x + y = 4

QUESTION: 52

Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect thecoordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

Solution:

QUESTION: 53

The probability that, on the examination day, the student S1 gets the previously allotted seat R1 , and
NONE of the remaining students gets the seat previously allotted to him/her is

Solution:

QUESTION: 54

For i = 1, 2, 3, 4, let Ti denote the event that the students Si and Si+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T1 ∩ T2 ∩ T3 ∩ T4 is

Solution: