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Q1
A heavy nucleus splits into two fragment nuclei whose surface area are in ratio 9 : 25, the ratio of speeds of the
two fragments is
(1) 25 : 9
(2) 125 : 27
(3) 5 : 3
(4) 625 : 81
Q2
In the following diagram if V > V then 2
(1) λ = √λ
1
(2) λ < λ
1
2
(3) λ = λ
1
2
(4) λ > λ
2
1
1
2
Q3
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In the following circuit, if D and D are ideal diodes, then the value of i and i are respectively
1
2
1
2
(1) Zero, Zero
(2) 5 mA, 5 mA
(3) 5 mA, Zero
(4) Zero, 5 mA
Q4
A ray of light travels from a medium of refractive index μ to air. Its angle of incidence in the medium is θ,
measured from the normal to the boundary and its angle of deviation is δ and the angle of refraction ϕ. A graph
is plotted between δ and θ which is shown in the figure. Choose the correct relation from the following-
(1)
δ2
(2)
δ2
δ1
δ1
= μ
= 2
(3) sin ϕ =
(4) ϕ =
π
2
1
2
− sin
−1
(
1
π
)
Q5
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If all meters are ideal and the reading of the voltmeter V is 6 V, then power supplied by the voltage source is
(all meters are ideal)
(1) 10 W
(2) 38 W
(3) 54 W
(4) 30 W
Q6
A body is moving down a long inclined plane of inclination θ. The coefficient of friction between the body and
inclined plane varies as μ = 0.5x, where x is distance travelled down the plane. The body will have maximum
velocity, when it has travelled a distance x, given by (All quantities are in SI units)
(1) x = 2 tan θ
(2) x =
2
tan θ
(3) x = √2 cot θ
(4) x =
√2
cot θ
Q7
The escape velocity from a spherical planet is v . The escape velocity corresponding to another planet of twice
e
the radius and half the mean density is.
(1) v √2
e
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(2)
MathonGo
ve
√2
(3) 2v
e
(4) 4v
e
Q8
In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of
various energies is passed. In absorption spectrum, five dark lines, are observed. The number of bright lines in
the emission spectrum will be (assume that all transitions takes place).
(1) 5
(2) 10
(3) 15
(4) None of these
Q9
A capacitor, an inductor and an electric bulb are connected in series to an AC supply of variable frequency. As
the frequency of supply is increased gradually, then the electric bulb is found to
(1) Increase in brightness
(2) Decrease in brightness
(3) Increase in brightness, reach a maximum and then decrease in brightness
(4) Of same brightness
Q10
In a cyclic process ABCA, V − T graph is shown in the figure. P − V graph corresponding to the given
process can be best depicted by
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(1)
(2)
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(3)
(4)
Q11
Two particles A and B are projected simultaneously from point O. Their maximum heights and ranges
achieved are shown. Find correct option :
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(1) Necessarily R = 2R
2
MathonGo
1
(2) Ranges may be same
(3) Ranges can't be same
(4) Necessarily 2R = R
2
1
Q12
In the equation ∫
dv
v
(1) [L
−
1
3
2
T 2]
(2) [L T
2
(3) [L
(4) [L
−
−
−
= BCe
−2Ct
, where v is velocity, t is time, e is exponent. The dimensions of B are
3
2
]
1
5
2
T 2]
1
2
3/2
T
−
5
2
]
Q13
Two ideal gases, one monoatomic and another diatomic, are having same pressure P , volume V and
temperature T . Select the correct option
(1) The translational kinetic energy for monatomic gas is
3
2
PV
but for diatomic gas it is
5
2
PV
.
(2) The translational kinetic energy for both monatomic and diatomic gas will be same.
(3) Average velocity of each molecule of any type of gas will be proportional to √T , where T is absolute
5
temperature.
(4) Average energy for one molecule per degree of freedom for monatomic gas is
is 2 ×
1
2
kT
1
2
kT
but that for diatomic it
.
Q14
A ball of mass 20 g dropped over a large horizontal surface from a height of 5 m, collides elastically with the
surface. If the collision lasts for 10
−2
s
, then which of the following statement is true? (g = 10 m/s )
2
(1) The impulse imparted to the ball is 0.4 N-s
(2) Force applied by the ball on the floor is 50 N
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(3) The impulse imparted to the ball is 0.2 N − s
(4) Force exerted by the surface on the ball is 0.2 N
Q15
A uniform rod of mass 6 kg is lying on a smooth horizontal surface. Its two ends are pulled by strings as
shown in figure. Force exerted by 40 cm part of the rod on 10 cm part of the rod is
(1) 30 N
(2) 16 N
(3) 24 N
(4) 22 N
Q16
A bullet of mass 10 g is fired horizontally with a velocity 1000 ms
−1
from a rifle situated at a height 50 m
above the ground. If the bullet reaches the ground with a velocity 500 ms , the work done against air
−1
resistance in the trajectory of the bullet is : (g = 10 ms
−2
)
(1) 5005 J
(2) 2750 J
(3) 3750 J
(4) 17.5 J
Q17
The 9
th
division of vernier scale coincides with 6
th
division of main scale in a vernier calliper. If one main
scale division is 0.01 mm, then the least count of instrument is
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(1) 0.01 mm
(2) 0.001 mm
(3) 0.0033 mm
(4) 0.0066 mm
Q18
40 g
of ice at −10 C is dropped in a calorimeter having 50 g water at 40 C. The final temperature of mixture
∘
∘
and content of calorimeter are (Specific heat of ice 0.5calg
−1 ∘
C
−1
, latent heat of fusion of ice 80calg ,
−1
neglect heat capacity of calorimeter).
(1) 0 C, 40 g ice and 50 g water
∘
(2) 0 C, 90 g water
∘
(3) 0 C, 17.5 g ice and 72.5 g water
∘
(4) 0 C, 20 g ice and 65 g water
∘
Q19
A point charge Q is located at a distance
R
2
from the centre of an uncharged conducting spherical shell as
shown in below figure. The electric field at a distance 3R from the point charge is
(1)
(2)
1
Q
4πε0
9R
1
Q
4πε0
5R
(
(3)
2
2
1
Q
4πε0
7R
(
2
2
)
2
)
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(4)
1
Q
4πε0
9R
(
2
MathonGo
2
)
Q20
Match List-I (Electromagnetic wave type) with List-II (Its Application) and select the correct option from the
choices given below the lists:
List-I
List-II
a. Infrared waves
(i) To treat muscular strain
b. Radio waves
(ii) For broadcasting
c. X-rays
(iii) To detect fracture of bones
d. Ultraviolet rays
(iv) Absorbed by the ozone layer
(1) a(iv), b(iii), c(ii), d(i)
(2) a(i), b(ii), c(iv), d(iii)
(3) a(iii), b(ii), c(i), d(iv)
(4) a(i), b(ii), c(iii), d(iv)
Q21
A dog is barking at a power of 40πmW. Its intensity level of sound emitted at a distance 1 m from the dog is
(in dB)
Q22
A uniform circular disc of radius R placed on a rough horizontal surface has initially a velocity v and an
0
angular velocity ω as shown in the figure. If the disc comes to rest after moving some distance in direction of
0
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v0
, then
V0
Rω0
MathonGo
is K, find 4K.
Q23
Two solid spheres of same metal but of mass M and 8M fall simultaneously on a viscous liquid and their
terminal velocities are v and nv, then find the value of n.
Q24
In an experiment four quantities a, b, c and d are measured with percentage error 2%, 3%, 1% and 0.5%
respectively. A quantity Q is defined as Q =
a
c
√
3/2
b
d
4
. Maximum percentage error in the calculation of Q will be
Q25
Three blocks of masses 700 g, 500 g and 400 g suspended at the end of a spring as shown in the figure, are in
equilibrium.
When the 700 g block is removed, the system has a period of oscillations of 3 s. If both 700 g and 500 g blocks
are removed, the period of oscillation becomes (in seconds)
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Q26
A beam of plane polarized light falls normally on a polarizer of cross sectional area 3 × 10
energy of incident ray is 10
−3
W
−4
m
2
. Flux of
. The polarizer rotates with an angular frequency of 31.4rad/sec. The average
Intensity is K watts. Find 6 K.
Q27
Two square shaped metal plates of A and B of same thickness ( t ) and of same material are connected as
shown in the figure. The side of B is twice that of A. If the resistance of A and B are R and R respectively
A
then
RA
RB
B
is
Q28
The primary and secondary coils of an ideal transformer have 100 and 500 turns respectively. The magnetic
flux linking the primary coil is given by ϕ = 40t + 5. The output voltage across the secondary coil is (all the
quantities are in SI units)
Q29
Two small spheres of each charge q, mass m and material density d are suspended from a fixed point with the
help of inextensible light thread. When the spheres are in air, the angle between the threads is 90 . When the
∘
spheres are suspended in a liquid of density
2
3
d
, the angle between the threads is 60 . The value of dielectric
constant of the liquid is P, find P √3.
Q30
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∘
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^ and the electric field produced by it at a distant
A charged particle is moving with a velocity v→ = −^i + ^j − k
→
^
point is E = ^i + ^j + k
. The magnetic field produced at the same point due to the same charged particle is
Kμ0 ε0
. Find the value of 10K. (All quantities are in S.I. units, take √2 = 1.4 and √3 = 1.7)
Q31
What is the correct mode of hybridization of the central atom in the following compounds : NO , SF , PF
+
2
(1) sp , sp , d sp
2
3
2
3
2
3
(3) sp, sp d, sp d
3
3
(4) sp, sp , sp
2
−
6
3
(2) sp , sp d , sp d
3
4
2
2
3
Q32
Select incorrect order :
(1) NH > PH > AsH > SbH (order of acidic strength)
3
3
3
3
(2) S > Se > Te > O (order of electron affinity)
(3) Si < S < P < Cl (order of IE)
(4) S
−2
> Cl
−
> K
+
> Ca
2+
(order of radius)
Q33
An element with (Z = 69) emits 2α and 1β particles in succession. What will be the group number of new
element formed?
(1) Group 2
(2) Group 13
(3) Group 5
(4) Group 3
Q34
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Which of the following set of reagent(s) give cis-but-2-ene as a final major product starting with (+)-2chlorobutane.
(1) Alcoholic KOH
(2) (i) CH COOAg, (ii) Δ
3
(3) (i) Alc. KOH, (ii) Br /CCl , (iii) Alc. KOH; NaNH , (iv) H /Pd − BaSO
2
4
2
2
(4) (i) Alc. KOH, (ii) Br /CCl , (iii) Alc. KOH; NaNH , (iv) Na/ Liq. NH
2
4
2
4
3
Q35
The order of stability of the carbocations
is
(1) VI > V > IV > III > II > I
(2) I > II > III > VI > V > IV
(3) V > VI > III > IV > I > II
(4) I > II > III > IV > V > VI
Q36
Statement 1: Addition of HgI to aqueous solution of KI increases the freezing point
2
Statement 2: A complex K [HgI ] is formed
2
4
(1) Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1
(2) Statement 1 is True, Statement 2 is true; Statement 2 is NOT a correct explanation for Statement 1
(3) Statement I is True, Statement 2 is False
(4) Statement 1 is False, Statement is True
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Q37
The first and second ionisation potential of helium atoms are 24.6eV and 54.4eV respectively. The energy
required to convert 1 mole of He atoms into He
2+
ions in kJ is :
(1) 758.4
(2) 7584
(3) 7.584
(4) 75.84
Q38
Assertion : Azeotropic mixtures are formed only by nonideal solutions and they may have boiling points either
greater than both the components or less than both the components.
Reason : The composition of the vapour phase is same as that of the liquid phase of an azeotropic mixture.
(1) both assertion and reason are true and the reason is the correct explanation of the assertion.
(2) both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) assertion is true but reason is false.
(4) the assertion and reason both are false.
Q39
The correct order of dipole moments of NH , H O and NF is
3
(1) H O > NH > NF
3
(2) H O > NF > NH
3
2
3
2
3
2
3
(3) NF > NH > H O
3
3
2
(4) NH > NF > H O
3
3
2
Q40
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Which common factor is responsible for the regioselective nature of the following reactions.
(1) - I effect of halogens
(2) + I effect of halogens
(3) +M effect of halogens
(4) - M effect of halogens
Q41
Amongst TiF
2−
6
, CoF
T i = 22,
Co = 27,
(1) CoF
and NiCl
(2) TiF
3−
6
and CoF
2−
6
(4) TiF
2
2
6
, Cu2 Cl2
and NiCl
Cu = 29,
2−
4
(Atomic number
N i = 28)
. The colourless species are
4
3−
6
2−
4
and Cu Cl
2−
6
2−
(3) Cu Cl and NiCl
2
3−
2
Q42
Which of the following complexes entities are square planar in shape?
[Ni(CN)4 ]
(P)
[PdCl4 ]
−2
[MnCl4 ]
−2
[Zn(NH3 ) ]
(Q)
−2
+2
4
(R)
+2
[Ni(NH3 ) ]
(S)
4
(T)
(1) P, T
(2) P, Q, T
(3) R, S, T
(4) P, S
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Q43
An aqueous solution containing 1M each of Au
+3
, Cu
+2
, Ag
+
, Li
+
is being electrolysed by using inert
electrodes. The value of standard potentials are :
E
E
∘
Ag
+
/Ag
= 0.80 V, E
∘
Au
+3
/Au
∘
Cu
= 1.50 V, E
+
/Cu
∘
Li
+
/Li
= 0.34 V and
= −3.03 V
with increasing voltage, the sequence of deposition of metals on the cathode will be :
(1) Li, Cu, Ag, Au
(2) Cu, Ag, Au
(3) Au, Ag, Cu
(4) Au, Ag, Cu, Li
Q44
Product (B) contains _______ π electrons
(1) 10
(2) 12
(3) 13
(4) 14
Q45
In Aniline & water mixture, Aniline can be separated by :
(1) Steam distillation
(2) Fractional distillation
(3) Simple distillation
(4) Distillation under reduced pressure
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Q46
Which of the following statement is not correct?
(1) [Ni(CN) ]
−2
4
(2) [NiCl ]
4
−2
and [Ni(CO) ] have the same magnetic moment
4
and [PtCl ]
4
−2
have different shape.
(3) Hybrid state of Co in [Co(Ox) ]
−3
3
is sp d
3
2
(4) In brown-ring complex [Fe(H O) NO] SO oxidation state of Fe is +1
2
5
4
Q47
Product (A) is -
(1)
(2)
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(3)
(4)
Q48
Consider the reaction given below
How many hydrogen atoms are replaced by deuterium atoms in the major product?
(1) 1
(2) 0
(3) 4
(4) 3
Q49
Chromyl chloride vapours are dissolved in NaOH and acetic acid and lead acetate solution is added, then
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(1) The solution will remain colourless
(2) The solution will become dark green
(3) A yellow solution will be obtained
(4) A yellow precipitate will be obtained
Q50
On performing a borax-bead test with a given inorganic mixture for qualitative analysis, the colour of the bead
was found to be emerald green both in oxidising and reducing flame. It indicates the possibility of the presence
of
(1) Co
(2) Ni
(3) Cr
(4) Cu
Q51
Find the total number of compounds which do not give Fehling's test.
Fructose, Sucrose, Glyoxal, HCHO, glyoxalic acid, CH COCH , N H , benzaldehyde, HCOOH
3
3
2
4
Q52
For the redox reaction,
MnO
−
4
+ C2 O
−2
4
+ H
+
⟶ Mn
+2
+ CO2 + H2 O
the correct coefficient of reactants MnO , C O , H for the balanced reaction are respectively 2, a and b.
−
4
−2
2
+
4
Find a + 2b.
Q53
Find the number of spectral lines in Paschen series emitted by atomic H, when electron is excited from ground
state to 7
th
energy level returns back.
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Q54
A weak base BOH was titrated against a strong acid. The pH at 1/4 th equivalence point was 8.0 . Enough
strong base was now added (7.5 millimole) to completely convert the salt. The total volume was 10ml. Find
the pOH at this point.
Q55
Total number of possible stereoisomers of the following co-ordinate compound Mabcdef where - a, b, c, d, e
and f are mono dentate ligands.
Q56
A tetrapeptide on hydrolysis produced glycine (gly), Leucine (Leu.), Alanine (Ala), Valine (Val.). Count
number of possible tetrapeptides (structural isomers only) which can produce above four amino acids with the
following both conditions.
(i) Glycine is not present at N-terminal
(ii) Alanine in present at C-terminal
Q57
Find the difference between the number of optically active and optically inactive isomers of
Q58
If 0.01% of a substance undergoing decomposition is consumed in 1 millisecond when the concentration is
0.02M
and in 0.25 millisecond when the concentration is 0.04M, what is the order of the reaction?
Q59
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major organic product will have Bromine at ______ position. (Mark carbon number where boron will be
attached as answer.)
Q60
Use the data from table to estimate the enthalpy of formation of CH CHO (Mark absolute value of enthalpy in
3
KJ per mol as answer).
Bond enthalpy
400 kJ mol
350 kJ mol
700 kJ mol
−1
−1
−1
Bond
Enthalpy of formation
−1
C − H
C(g)
700 kJ mol
C − C
H(g)
200 kJ mol
C = O
O(g)
250 kJ mol
−1
−1
Q61
Let x be the 7
(3
1/3
1
+
4
1/3
th
n
)
term from the beginning and y be the 7
th
term from the end in the expansion of
. If y = 12x then the value of n is :
(1) 9
(2) 8
(3) 10
(4) 11
Q62
Let a and b are positive integers such that a < b < 2009. If a, b and 2009 form a geometric progression whose
common ratio is an integer then the sum of digits of a is
(1) 5
(2) 7
(3) 9
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(4) 11
Q63
Suppose a parabola has vertex (
1
4
,
−9
8
)
and equation y = a + bx + c (where a > 0 and a + b + c is integer).
2
Let 'a' takes its minimum possible value under given condition, then
Match List-I with List-II and select the correct answer using the code given below the list.
List-I
List-II
(P)2(latus rectum of parabola) is
(1) 9
(Q) If equation of directrix is 4y + λ = 0, then λ
(R) If the value of a is
p
q
(2)
(3)
(4)
P
Q
R
S
1
2
3
4
P
Q
R
S
3
1
2
4
P
Q
R
S
1
2
3
2
P
Q
R
S
4
1
2
3
is
(2) 81
(where p & q are relatively prime), then p + q is
(S) If (α, 0) lies on parabola, then 16(α −
(1)
2
1
4
(3) 11
2
)
is
(4) 36
Q64
An equilateral triangle is inscribed in an ellipse whose equation is x + 4y
2
(0, 1)
, then the length of each side is
(1)
8 √3
(2)
24√3
(3)
16√3
(4)
48√3
13
13
13
13
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2
= 4
. If one vertex of the triangle is
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Q65
Let a and b be two numbers such that f (x) = x + ax + b never equal to zero. Let A be a matrix of order
2
and B be a matrix such that B = f (A), then which of the following must be INCORRECT?
2 × 2
(1) B must be an invertible matrix
(2) B can be an invertible matrix but not always
(3) B can be a singular matrix
(4) B can be a null matrix
Q66
A light beam emanating from the point A(3, 10) reflects from the straight line 2x + y − 6 = 0 and then passes
through the point B(4, 3). The equation of the reflected beam is x + 3y − λ = 0, then find the value of λ.
(1) 22
(2) 11
(3) 9
(4) 13
Q67
Given |a
→| = |→b| = 1 and |a
→ + →b| = √3. If c→ be a vector such that c→ − a
→ − 2→b = 3(a
→ × →b), then c→ ⋅ →b is equal to
(1) −
(2)
1
(3)
3
(4)
5
1
2
2
2
2
Q68
The domain of f (x) = cos
(1) [3,
10
(2) [
10
2
3
,
3
3
−1
(
6−3x
4
) + cosec
−1
(
x−1
2
)
is
]
]
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(3) (−∞, 1] ∪ [3, ∞)
(4) None of these
Q69
In a right trapezium ABCD, the diagonals are perpendicular, and the ratio of the length of bases
AD : BC = 2 : 3
. Then the ratio of length of diagonals is
(1) 3 : 2
(2) 1 : 3
(3) 2 : √3
(4) √3 : √2
Q70
The number of integers in the range of 'c' such that there exists a line which intersects the curve
y = x
4
− 6x
3
+ 12x
2
+ cx + 1
at four distinct points is equal to
(1) 2
(2) 3
(3) 1
(4) 0
Q71
Let f be differentiable function such that (x − y)f (x + y) − (x + y)f (x − y) = 4xy (x − y ) and f (1) = 2.
2
Then area enclosed by
(1)
3f (4)
(2)
f (4)
(3)
f (4)
(4)
3f (4)
4
8
16
16
1
1
|f (x)−x| 3
|f (y)−y| 3
17
+
2
≤
1
4
, is
sq. units
sq. units
sq. units
sq. units
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MathonGo
Q72
Find the value of 96√3 ⋅ sin
π
48
⋅ cos
π
48
⋅ cos
π
24
cos
π
12
⋅ cos
π
6
.
(1) 6
(2) 18
(3) 12
(4) 9
Q73
The probability of solving a problem correctly by A and B are
1
8
and
1
12
respectively. Given that they obtain
the same answer after solving a problem and the probability of a common mistake by them is
1
1001
, then
probability that their solution is correct is (Assuming that if they commit different mistake then their answers
will differ)
(1)
77
(2)
14
(3)
2
(4)
13
96
15
5
14
Q74
Let f (x) be continuous function satisfying f (x) = ∫
x
0
e
x−y
′
f (y)dy − (x
which f (x) = 0, is:
(1)
1
2
(2) 1
(3)
1
(4)
1
4
8
Q75
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2
− x + 1) e
x
. The value of x for
AYJR 2024 (April) – Morning Shift
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Questions with Answer Keys
MathonGo
If the equation of the perpendicular bisector of the line joining two complex numbers P (z ) and Q (z ) in the
1
2
complex plane is ᾱz + αz + r = 0 then α and r are respectively are
¯
¯
¯
(1) z − z and |z | + |z |
2
(2) z − z and |z | − |z |
2
(3) z̄
2
2
2
1
1
2
2
1
2
2
− z̄ 1
1
2
and |z | + |z |
2
1
2
(4) z − z and |z | − |z |
2
2
1
1
2
2
Q76
Let f : R → R be a polynomial function satisfying f (f (x) − 2y) = 2x − 3y + f (f (y) − x), ∀x, y ∈ R then the
value of f (20) − f (14) is equal to
(1) 6
(2) 4
(3) 5
(4) 8
Q77
A be a square matrix of order 2 with |A| ≠ 0 such that |A| + |A adj(A)| = 0, where adj(A) is an adjoint of
matrix A, then the value of |A + |A| adj(A)| is
(1) 6
(2) 4
(3) 5
(4) 8
Q78
⎧
⎪
Let f (x) = ⎨
⎪
⎩
x[x] + 1
ax
2
+ x + b
sin(c(x − 3)) + d
,
x ∈ (0, 1)
,
x ∈ [1, 3)
,
x ∈ [3, ∞)
(where [.] denotes greatest integer function) be a continuous function in its domain.
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If f (x) is continuous but non-differentiable at exactly two points in its domain, then(1) a ≠ −
1
2
, c ≠ 2, a = −b =
(2) a ≠ −2, c ≠ −
(3) a = −
1
(4) a ≠ −
1
2
2
1
2
d−3
6
d+3
, a = −b =
, c ≠ −2, a = b =
8
d−3
6
d−3
, c ≠ −2, a = −b =
8
Q79
If I = ∫
1
(1)
π
(2)
π
(3)
3π
(4)
π
4
π/2
−π/2
cos
2
xdx
1+3
x
and I = ∫
2
π
0
x
2
sin x cos(
π
2
cos x)dx
(2x−π)
, then (I + I ) equals
1
2
+ 1
2
4
4
+ 2
Q80
^ to the straight line through R(2, 3, −4)
The distance from the point P whose position vector is −^i + 2^j + 6k
^ is ______.
and parallel to the vector 6^i + 3^j − 4k
(1) 6
(2) 7
(3) 5
(4) 8
Q81
If a point P (x, y) moves such that |x − y| + |x + y| = 2, then the area bounded by the locus of the point P is
equal to
Q82
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AB
is a chord of x + y
2
2
MathonGo
= 4
and P (1, 1) trisects AB. If C is the centre of the circle then the length of the
chord AB is
Q83
A relation R is defined on set A = {a, b, c} such that R ≡ {(a, a), (b, b), (b, c), (c, b)}, then minimum
number of additional elements required in R so that R becomes an equivalance relation, is
Q84
In an experiment with 10 observations on x, ∑ x = 60, ∑ x = 1000 one observation that was 20 was found
2
to be wrong and was replaced by the correct value 30 then the corrected variance is
Q85
Find the remainder, when 5
5
5
.
.
.
5
(24 times 5) is divided by 24.
Q86
The number of four digit numbers abcd where a, b, c, d ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9} such that a > b, a > c and
c > d
, is
Q87
^ and r
^
→ = −^i + μ(2^i + ^j + k)
A line with direction ratios (2, 1, 2) intersects the lines r→ = −^j + λ(^i + ^j + k)
at A and B, respectively, then length of AB is equal to
Q88
If AM, GM and HM of the first and last terms of series 100, 101, 102, … … (n − 1), n are the terms of series
itself, then value of
n
100
(100 < n ≤ 500)
is
Q89
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MathonGo
For a positive constant t, let α, β be the roots of the quadratic equation x + t x − 2t = 0. If the minimum
2
value of ∫
2
−1
(a − b + c)
((x +
1
α
2
) (x +
1
β
2
) +
1
αβ
) dx
is √
a
b
+ c
2
where a, b, c ∈ N , then the least value of
is
Q90
If the area bounded by y = f (x) and the curve y =
2
1+x
2
where f is a continuous function satisfying the
conditions f (x) ⋅ f (y) = f (xy). ∀ x, y, ∈ R and f (1) = 2, f (1) = 1 is (π −
′
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a
3
)
, then a =
AYJR 2024 (April) – Morning Shift
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Questions with Answer Keys
MathonGo
Answer Key
Q1 (2)
Q2 (4)
Q3 (4)
Q4 (2)
Q5 (3)
Q6 (1)
Q7 (1)
Q8 (3)
Q9 (3)
Q10 (3)
Q11 (2)
Q12 (1)
Q13 (2)
Q14 (1)
Q15 (2)
Q16 (3)
Q17 (3)
Q18 (3)
Q19 (3)
Q20 (4)
Q21 (100)
Q22 (2)
Q23 (4)
Q24 (7)
Q25 (2)
Q26 (10)
Q27 (1)
Q28 (200)
Q29 (18)
Q30 (28)
Q31 (3)
Q32 (1)
Q33 (4)
Q34 (3)
Q35 (4)
Q36 (1)
Q37 (2)
Q38 (2)
Q39 (1)
Q40 (3)
Q41 (4)
Q42 (4)
Q43 (3)
Q44 (4)
Q45 (1)
Q46 (3)
Q47 (2)
Q48 (3)
Q49 (4)
Q50 (3)
Q51 (5)
Q52 (37)
Q53 (4)
Q54 (3)
Q55 (30)
Q56 (4)
Q57 (5)
Q58 (3)
Q59 (4)
Q60 (200)
Q61 (1)
Q62 (1)
Q63 (3)
Q64 (3)
Q65 (1)
Q66 (4)
Q67 (4)
Q68 (1)
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AYJR 2024 (April) – Morning Shift
Are You JEE Ready (AYJR)
Questions with Answer Keys
MathonGo
Q69 (4)
Q70 (3)
Q71 (3)
Q72 (4)
Q73 (4)
Q74 (1)
Q75 (4)
Q76 (1)
Q77 (2)
Q78 (4)
Q79 (4)
Q80 (2)
Q81 (4)
Q82 (3)
Q83 (1)
Q84 (101)
Q85 (5)
Q86 (546)
Q87 (3)
Q88 (4)
Q89 (4)
Q90 (2)
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