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JEE Main Mock - 6 (Previous Pattern)

90 Questions MCQ Test Mock Test Series for JEE Main & Advanced 2022 | JEE Main Mock - 6 (Previous Pattern)

Description

Attempt JEE Main Mock - 6 (Previous Pattern) | 90 questions in 180 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mock Test Series for JEE Main & Advanced 2022 for JEE Exam | Download free PDF with solutions

QUESTION: 1

A d.c. motor having an armature of resistance 2 Ω is designed to operate at 220 V mains. At full speed, it develops a back e.m.f. of 210 V. When the motor is running at full speed, the current in the armature is

A.
3 A
B.
5 A
C.
7 A
D.
10 A

Solution:

When motor is running at full speed the electric current is given by:

QUESTION: 2

A solenoid has an inductance of 60 henrys and a resistance of 30 ohms. If it is connected to a 100 volt battery, how long will it take for the current to reach e-1/e=63.2% of its final value

A.
1 second
B.
2 seconds
C.
e seconds
D.
2e seconds

Solution:

QUESTION: 3

A dipole of dipole moment p̅ is placed in uniform electric field E̅, then torque acting on it is given by

A.
τ̅ = p̅ . E̅
B.
τ̅ = p̅ x E̅
C.
τ̅ = p̅ + E̅
D.
τ̅ = p̅ - E̅

Solution:

QUESTION: 4

What fraction of a radioactive material will get disintegrated in a period of two half-lives

A.
Whole
B.
Half
C.
One-fourth
D.
Three-fourth

Solution:

QUESTION: 5

What percentage of original radioactive atoms is left after five half lives ?

A.
0.3%
B.
1%
C.
31%
D.
3.125%

Solution:

QUESTION: 6

An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ is

A.
π/3
B.
π/3 + tan⁻¹√3/2
C.
3π/2
D.
tan⁻¹√3/2

Solution:

QUESTION: 7

Photons of energy 5.5eV fall on the surface of the metal emitting photoelectrons of maximum kinetic energy 4.0eV. The stopping potential required for these electrons are :

A.
5.5V
B.
1.5V
C.
9.5V
D.
4.0V

Solution:

QUESTION: 8

The angular speed of an engine wheel making 90 revolutions per minute is

A.
1.5 π rad/s
B.
3 π rad/s
C.
4.5 π rad/s
D.
6 π rad/s

Solution:

QUESTION: 9

A man of mass 60 kg. records his wt. on a weighing machine placed inside a lift. The ratio of wts. of man recorded when lift is ascending up with a uniform speed of 2 m/s to when it is descending down with a uniform speed of 4 m/s will be

A.
0.5
B.
1
C.
2
D.
None

Solution:

QUESTION: 10

A boat of mass 40 kg is at rest. If a dog of mass 4 kg moves in the boat with a velocity of 10 m/s, then velocity of a boat will be

A.
1 m/s
B.
2 m/s
C.
4 m/s
D.
8 m/s

Solution:

According to law of conservation of momentum
(m_d + m_b)υ_b = m_d υ_d
⇒ 44 υ_b = 4 x 10
⇒ υ_b = 1 m/s

QUESTION: 11

A microammeter has a resistance of 100 Ω and full scale range of 50 μ A. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination

A.
50 V range with 10 K Ω resistance in series
B.
10 V range with 200 K Ω resistance in series
C.
10 mA range with 1 Ω resistance in parallel
D.
10 mA range with 0.1 Ω resistance in parallel

Solution:

QUESTION: 12

Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is

A.
directly proportional to R but inversely proportional to v
B.
directly proportional to both radius R and velocity v
C.
inversely proportional to both radius R and velocity v
D.
inversely proportional to R but directly proportional to velocity v

Solution:

QUESTION: 13

The symbolic representation of four logic gates are given below:

The logic symbols for OR, NOT and NAND gates are respectively:

A.
(iv), (i), (iii)
B.
(iv), (ii), (i)
C.
(i), (iii), (iv)
D.
(iii), (iv), (ii)

Solution:

QUESTION: 14

The size of nucleus of an atom of mass number A is proportional to

A.
A^3/4
B.
A^2/3
C.
A^1/3
D.
A^5/3

Solution:

QUESTION: 15

A ball is moving to and fro about the lowest point A of a smooth hemisphrical bowl. If it is able to rise up to a height of 20 cm on either side of A, its speed at A must be (Take = 10 m/s^2. mass of the body 5 g)

A.
0.2 m/s
B.
2 m/s
C.
4 m/s
D.
4.5 ms^⁻1

Solution:

QUESTION: 16

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): By the study of positive rays, Thomson discovered the existence of isotopes.
Reason(R): Thomson obtained two parabolas for neon gas whose atomic mass is 20.2 .

A.
Both Assertion and Reason are true and Reason is the correct explanation of assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of assertion.
C.
Assertion is true but Reason is false.
D.
Both Assertion and Reason are false.

Solution:

QUESTION: 17

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): When a massive projectile collides with a lighter stationary target then maximum speed of target is twice that of projectile.
Reason(R): It is explained by the momentum and energy conservation.

A.
Both Assertion and Reason are true and Reason is the correct explanation of assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of assertion
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 18

Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the ring is (mass = and radius = r)

A.
m r^2/2
B.
m r²
C.
3/2 m r²
D.
2 m r²

Solution:

QUESTION: 19

A process in which volume remains constant is called

A.
Isobaric
B.
Isothermal
C.
Isochoric
D.
None of these

Solution:

QUESTION: 20

Erg-m^⁻1can be the unit of measure for

A.
Force
B.
Momentum
C.
Power
D.
Acceleration

Solution:

QUESTION: 21

In Young's experiment of double slit, the intensity of central bright band is ---- times the individual intensities of the interfering waves

A.
2
B.
3
C.
5
D.
4

Solution:

QUESTION: 22

A train is approaching a platform with a velocity ν. The frequency heard by an observer standing at the station is

A.
(1 + ν/c)f₀
B.
c/ν f₀
C.
ν/c f₀
D.
(c - ν/c) f₀

Solution:

QUESTION: 23

To demonstrate the phenomenon of interference we require two sources which emit radiations of

A.
nearly the same frequency
B.
the same frequency
C.
different wavelength
D.
the same frequency and having a definite phase relationship

Solution:

QUESTION: 24

Standing stationary waves can be obtained in an air column even if the interfering waves are

A.
Of different pitches
B.
Of different amplitudes
C.
Of different qualities
D.
Moving with different velocities

Solution:

QUESTION: 25

The H α line is the first member of the Balmer series of the hydrogen spectrum and it occurs due to the transition of the electron from the 3^rd orbit to the 2^ndorbit. If its wave length is λ , the wave length of the last member of the Balmer series will be

A.
(4/9) λ
B.
(5/9) λ
C.
(7/9) λ
D.
(1/2) λ

Solution:

QUESTION: 26

If the charge on a capacitor is increased by 2 coulomb, the energy stored in it increases by 21%. The original charge on the capacitor is

A.
10C
B.
20C
C.
30C
D.
40C

Solution:

QUESTION: 27

A particle is moving on a circular path with constant speed, then its acceleration will be

A.
Zero
B.
External radial acceleration
C.
Internal radial acceleration
D.
Constant acceleration

Solution:

QUESTION: 28

At what temperature will the resistance of a copper wire be three times its value at 0ºC? (Given Temperature coefficient of resistance for copper = 4x10⁻³ºC⁻¹)

A.
400ºC
B.
450ºC
C.
500ºC
D.
550ºC

Solution: For temp. coeff (a)=4×10^-3,
3R=R(1+(a)t)
2/4×10^-3=t
t=500

QUESTION: 29

How many electrons must be removed from each of two 5.0-kg copper spheres to make the electric force of repulsion between them equal in magnitude to the gravitational attraction between them?

A.
2.7 x 10⁹
B.
2.7 x 10¹⁰
C.
2.7 x 10¹¹
D.
2.7 x 10¹²

Solution:

QUESTION: 30

There are three voltmeters of the same range but of resistance 10000 Ω, 8000 Ω and 4000 Ω respectively. The best voltmeter among these is the one whose resistance is

A.
10000 Ω
B.
8000 Ω
C.
4000 Ω
D.
all are equally good

Solution:

QUESTION: 31

Final product formed on reduction of glycerol by hydriodic acid is

A.
Propane
B.
Propanoic acid
C.
Propene
D.
None of these

Solution:

QUESTION: 32

RCH = O + H₂ → RCH₂OH. For this reaction, catalyst is

A.
Ni only
B.
Pd only
C.
Pt only
D.
Any of the above

Solution:

QUESTION: 33

Night blindness is caused by the deficiency of

A.
vitamin A
B.
vitamin C
C.
vitamin E
D.
vitamin B₁₂

Solution:

QUESTION: 34

For the equilibrium

K p = 9 a t m 2 at 37 º C . A 5 litre vessel contains 0.1 mole of LiCl.NH₃. How many moles of NH₃ should be added to the flask at this temperature to derive the backward reaction for completion?
Use R = 0.082 atm -L/mol K

A.
0.2
B.
0.59
C.
0.69
D.
0.79

Solution:

QUESTION: 35

If initial concentration is reduced to (1/4)th in a zero order reaction, the time taken for half the reaction to complete

A.
remains same
B.
becomes 4 times
C.
becomes one-fourth
D.
doubles

Solution:

QUESTION: 36

Given that heat of neutralisation of strong acid and strong base is -57.1 kJ. Calculate the heat produced when 0.25 mole of HCl is neutralised with 0.25 mole of NaOH in aqueous solution.

A.
22.5 kJ
B.
57.1 kJ
C.
14.275 kJ
D.
28.6 kJ

Solution:

The heat produced when 0.25 mole of HCl is neutralised with 0.25 mole of NaOH in aqueous solution is 57.1x1/4=14.275kJ

QUESTION: 37

The decreasing order of the ionisation potential of the following elements is

A.
Ne > Cl > P > S > Al > Mg
B.
Ne > Cl > P > S > Mg > Al
C.
Ne > Cl > S > P > Mg > Al
D.
Ne > Cl > S > P > Al > Mg

Solution:

As we move across a period from left to right, the nuclear charge increases and the atomic radius decreases though the principal quantum number of the valence shell remains the same. As a result, the valence electrons are more are more tightly held by the nucleus, hence ionisation potential keep on increasing. However, closed shell configuration (Ne), half-filled configuration (P) and completely-filled configuration (Mg) are responsible for higher values of ionisation energy.

QUESTION: 38

In the complex compound K₄[Ni(CN)₄], the oxidation no. of nickel is

A.
-1
B.
0
C.
+1
D.
+2

Solution:

QUESTION: 39

Which of the following reagent can be used to convert benzene diazonium chloride into benzene ?

A.
CH₃OH
B.
H₃PO₂
C.
Br₂-H₂O
D.
LiAlH₄

Solution:

QUESTION: 40

The element, which forms oxides in all oxidation states + 1 to + 5, is

A.
N
B.
P
C.
As
D.
Sb

Solution:

QUESTION: 41

The e.m.f. of a galvanic cell with electrode potentials of silver equal to + 0.80 V and that of copper equal to + 0.34 V is

A.
- 0.46 V
B.
- 1.14 V
C.
+0.46 V
D.
+1.14 V

Solution:

QUESTION: 42

Which of the following compound is the most soluble in water?

A.
MnS
B.
ZnS
C.
Bi₂S₃
D.
Ag₂S

Solution:

QUESTION: 43

The best indicator for the detection of end point in titration of a strong base is

A.
Methyl orange (3 to 4)
B.
Methyl red (5 to 6)
C.
Bromothymol blue (6 to 7.5)
D.
Phenolphthalein (8 to 9.6)

Solution:

QUESTION: 44

The pH indicates are

A.
Salts of strong acids and strong bases
B.
Salts of weak acids and weak bases
C.
either weak acids or weak bases
D.
either strong acids or strong bases

Solution:

QUESTION: 45

The pH of blood does not appreciably change by a small addition of acid or a base because blood

A.
contains serum protein which act as buffer
B.
contains iron as a part of the molecule
C.
can be easily coagulated
D.
is body fluid

Solution:

QUESTION: 46

Which of the following does not give yellow ppt. with I₂/NaOH?

A.
C₂H₅OH
B.
CH₃CHO
C.
CH₃COCH₃
D.
HCHO

Solution:

QUESTION: 47

Product(s) of the following S N 1 reaction is/are :

A.
B.
C.
both of the above
D.
none of the above

Solution:

QUESTION: 48

An example of natural biopolymer is

A.
Teflon
B.
Nylon-66
C.
Rubber
D.
DNA

Solution:

QUESTION: 49

Which of the following isomers will have the highest octane number ?

A.
n-octane
B.
2-Methylheptane
C.
2,3-Dimethylhexane
D.
2,2,4-Trimethylpentane

Solution:

QUESTION: 50

Which of the following metal oxides is antiferromagnetic in nature?

A.
MnO₂
B.
TiO₂
C.
NO₂
D.
CrO₂

Solution:

QUESTION: 51

The radius of an atom of an element is 500 pm, if it crystallizes as a face-centred cubic lattice, then the edge length of the unit cell is

A.
500 pm
B.
707 pm
C.
1000 pm
D.
1414 pm

Solution:

QUESTION: 52

The normality of orthophosphoric acid having purity of 70% by weight and specific gravity 1.54 would be (H=1;O=16; P=31)

A.
11 N
B.
22 N
C.
33 N
D.
44 N

Solution:

QUESTION: 53

A solution contains non-volatile solute of molecular mass M₂. which of the following can be used to calculate the molecules mass of solute in terms of osmotic pressure ?

A.
M₂=[M₂/π]VRT
B.
M₂=[m₂/V]RT/π
C.
M₂=[m₂/V]πRT
D.
M₂=[m₂/V]π/RT

Solution:

QUESTION: 54

Catalyst used in dimerisation of acetylene to prepare chloroprene is

A.
HgSO₄ + H₂SO₄
B.
Cu₂Cl₂
C.
Cu₂Cl₂ + NH₄Cl
D.
Cu₂Cl₂ + NH₄OH

Solution:

QUESTION: 55

The ionisation potential of hydrogen atom is 13.6 eV. The energy required to remove an electron in the n = 2 state of the hydrogen atom is __

A.
27.2 eV
B.
13.6 eV
C.
6.8 eV
D.
3.4 eV

Solution:

QUESTION: 56

The electronic configuration of the atom with atomic number 47 is ___

A.
[Kr]4d¹⁰ 5s²
B.
[Ar]4d¹⁰ 5s¹
C.
[Kr]4d¹⁰ 5s¹5d¹
D.
[Kr]4d¹⁰5s¹

Solution:

Element with atomic number 47 is silver (Ag) with configuration (actual is 1s² 2² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s¹, i.e. its shows preference for completely filled orbital.

QUESTION: 57

The change in entropy ∆S is positive for certain reaction and enthalpy change ∆H is also greater than zero at temperature T.The reaction is

A.
feasible at all values of T
B.
feasible only when T∆S >∆H
C.
feasible only ∆H > T∆S
D.
not feasible at all

Solution:

QUESTION: 58

The reaction of acidified, aqueous potassium iodide with aqueous hydrogen peroxide

is thought to involve the following steps

Which one of the following conclusions cannot be drawn from this information?

A.
The iodide ion is oxidised by the hydrogen peroxide
B.
The acid acts as a catalyst
C.
The rate determining step is
H₂O₂ + I − → H₂O + OI −
D.
The rate equation for the reaction is
rate = k [ H ²O² ] [ I − ]

Solution:

QUESTION: 59

Which of the following sequence follows the Irwing-William order?

A.
M n² + < F e² + < C o²+ < N i² + < C u² + < Z n² +
B.
M n²+ < F e² + < C o² + < N i² + < C u²+ > Z n² +
C.
Mn² + < Fe² + > Co²+ < N i ² + < Cu² + > Zn² +
D.
M n²+ > F e² + < C o² + < N i²+ < C u² + < Z n²+

Solution:

The correct order is according to decreasing charge to radius ratio.

QUESTION: 60

Which of the following compounds to does not show Lassaigne's test for nitrogen?

A.
Urea
B.
Hydrazine
C.
Phenylhydrazine
D.
Azobenzene

Solution:

QUESTION: 61

If (a²)+16(b²)+49(c²)-4ab-28bc-7ac=0, then a,b,c are in:

A.
AP
B.
GP
C.
HP
D.
none of these

Solution:

QUESTION: 62

If 2^x + 3 ^y = 17 and 2^{x + 2} − 3^{y + 1} = 5, then what is the value of x ?

A.
3
B.
2
C.
1
D.
0

Solution:

QUESTION: 63

AOB is the positive quadrant of the ellipse x ² ∕ a² + y 2 ∕ b² = 1, where OA = a, OB = b. The area between the arc AB and the chord AB of the ellipse is

A.
π a b
B.
(π − 2)ab
C.
(π − 2)ab/ 2
D.
(π − 2) ab/ 4

Solution:

QUESTION: 64

The angle between the tangents drawn from (0,0) to the circle x² + y² + 4x - 6y + 4 = 0 is

A.
sin ^{− 1} 5/ 13
B.
sin ^{− 1} 5 /12
C.
sin^{− 1} 12/ 13
D.
π 2

Solution:

QUESTION: 65

If 2x - 3y = 0 is the equation of the common chord of the circles x²+ y² + 4x = 0 and x² + y²+ 2λy = 0, then the value of λ is

A.
3
B.
2
C.
1
D.
0

Solution:

QUESTION: 66

If the cube roots of unity are 1,ω,ω² then the roots of the equation (x - 1)³ + 8 = 0,are

A.
-1,-1 +2ω,-1-2ω²
B.
-1,-1,-1
C.
-1,1 - 2ω,1-2ω²
D.
-1,1 + 2ω,1 + 2ω²

Solution:

QUESTION: 67

The differential equation obtained by eliminating the arbitrary constants a and b from

Solution:

QUESTION: 68

At x=3, (d/dx)[|x-1|+|x-5|]=

A.
-2
B.
0
C.
2
D.
4

Solution:

QUESTION: 69

Let f(x) = x, g(x) = 1/x and h(x) = f(x)g(x). Then h(x) = 1 if

A.
x is a real number
B.
x is a rational number
C.
x is an irrational number
D.
x is a real number ≠ 0

Solution:

QUESTION: 70

Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?

A.
Today is Sunday and Matt can play hockey.
B.
If Matt plays hockey, then today is not Sunday.
C.
Today is Sunday and Matt cannot play hockey.
D.
Today is not Sunday if and only if Matt plays hockey.

Solution:

Statements are logically equivalent to their contrapositives.

QUESTION: 71

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): Sum of the last 30 coefficients in the expansion of (1+x)⁵⁹, when expanded in ascending powers of x, is 2⁵⁸.
Reason(R): pth term from the end in the expansion of (x+y)ⁿ is (n - p + 2)th term from the beginning.

A.
Both Assertion and Reason are true and Reason is the correct explanation of assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 72

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The number of terms in the expansion of which are integers is equal to 32.
Reason(R): In the binomial expansion of (x+y)ⁿ , the (r+1)th term from the beginning is called general term (T_r+1) i.e, T_r+1 = ⁿC_r x^n+ry^r.

A.
Both Assertion and Reason are true and Reason is the correct explanation of assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution: The correct option is B.
Using Binomial approximation every 4 th term and the first term is an integer
hence no. of integral values=1+(124/4)=1+31=32
this is not explained by the reason

QUESTION: 73

If ⁿP₄:ⁿP₃=1:2, then n=

A.
4
B.
5
C.
6
D.
7

Solution:

QUESTION: 74

The line, among the following, that touches the parabola y² = 4ax is

A.
x + my + a m 3 = 0
B.
x − my + a m 2 = 0
C.
x + my − a m 2 = 0
D.
y + mx + a m 2 = 0

Solution:

QUESTION: 75

Each coefficients in the equation ax²+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is

A.
5/216
B.
7/216
C.
9/216
D.
none of these

Solution:

QUESTION: 76

If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρ satisfies

A.
ρ = 0
B.
ρ > 0
C.
ρ < 0
D.
ρ = 1 or -1

Solution:

QUESTION: 77

The foot of perpendicular from (2,4) on the line x+y=1 is

A.
[(1/2),(3/2)]
B.
[-(1/2),(3/2)]
C.
[(1/2),(-3/2)]
D.
[-(1/2),(-3/2)]

Solution:

QUESTION: 78

The length of the subnormal to the curve y² = 2px is

A.
p
B.
2p
C.
3p
D.
4p

Solution:

QUESTION: 79

Set of equations a+b-2c = 0, 2a-3b+c = 0 and a-5b+4c = α is consistent, if α equal to

A.
1
B.
0
C.
-1
D.
2

Solution:

QUESTION: 80

If 1, ω, ω² are cube roots of unity, the root of the equation (x-1)³ + 8 = 0 are

A.
-1, 1 + 2ω, 1 + 2ω²
B.
-1, 1 - 2ω, 1 - 2ω²
C.
-1, -1, 1
D.
-2, -2, -2

Solution:

QUESTION: 81

If cot (α+β)=0, then sin (α+2β) is equal to

A.
sin α
B.
cos 2β
C.
cos α
D.
sin 2α

Solution:

QUESTION: 82

The angle between the planes 2x - y + z = 6 and x + y + 2z = 7 is

A.
π/4
B.
π/6
C.
π/3
D.
π/2

Solution:

QUESTION: 83

The area of a parallelogram whose adjacent sides are a=i+2j+3k, b=3i-2j+k, is

A.
5/√2
B.
8/√3
C.
6
D.
-5/√2

Solution:

QUESTION: 84

A.
5
B.
2
C.
4
D.
6

Solution:

QUESTION: 85

Solution:

QUESTION: 86

A.
2
B.
-2
C.
0
D.
1

Solution:

QUESTION: 87

Suppose a,b,c are in A.P. and a^2,b²,c² are in G.P. If a < b< c and a + b + c =3/2,then the value of a is

A.
1/2√2
B.
1/2√3
C.
(1/2)-(1/√3)
D.
(1/2)-(1/√2)

Solution:

QUESTION: 88

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.
Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.