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# JEE Advanced Mock Test - 7

## 54 Questions MCQ Test National Level Test Series for JEE Advanced 2020 | JEE Advanced Mock Test - 7

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Attempt JEE Advanced Mock Test - 7 | 54 questions in 180 minutes | Mock test for JEE preparation | Free important questions MCQ to study National Level Test Series for JEE Advanced 2020 for JEE Exam | Download free PDF with solutions
QUESTION: 1

### A particle strikes a horizontal frictionless floor with a speed u at an angle φ with the vertical andrebounds with a speed v at an angle φ with the vertical. The co-efficient of restitution betweenthe particle and floor is e. The angle φ  is equal to

Solution:

C

∵ vertical component after collision = eucos θ
& Horizontal component = usin θ

QUESTION: 2

Solution:

C
Zero

QUESTION: 3

### A flat coil of area A and n turns is placed at the centre of a ring of radius r (r2 >> A) and resistance R. The two are co-planar when current in the coil increases from zero to i, the total charge circulating in the ring is

Solution:

QUESTION: 4

In the arrangement shown, all surfaces are frictionless. The rod R is constrained to move vertically. The vertical acceleration of R is a1 and the horizontal acceleration of the edge w is a2. The ratio a1/a2is equal to

Solution:

Relative acceleration of rod with respect to wedge is parallel to the inclined plane.

QUESTION: 5

Which of the following is the most accurate instrument for measuring length?

Solution:
QUESTION: 6

A block of mass m is placed on a wedge of mass 2m which rests on a rough horizontal surface. There is no friction between the block and the wedge. The minimum coefficient of friction between the wedge and the ground so that thewedge does not move is

Solution:
QUESTION: 7

A spherical object of mass 1 kg and radius 1 m is falling vertically downward inside a viscous liquid in a gravity free space. At a certain instant the velocity of the sphere is 2 m/s. If the coefficient of viscosity of the liquid is 1/18π n-s/m2, then velocity of ball will become 0.5 m/s after a time

Solution:
QUESTION: 8

Two identical simple pendulums A and B are fixed at same point. They are displaced by an angle α and β (α and β are very small and β > α) and released from rest. Find the time after which B reaches its initial position for the first time. Collisions are elastic and length of the strings is l.

Solution:
*Multiple options can be correct
QUESTION: 9

A photon collides with a stationary H – atom in ground state inelastically. Energy of the colliding photon is 10.2 eV. Almost instantaneously, another photon collides with same H – atom inelastically with an energy of 15 eV. What will be observed by the detector?

Solution:

*Multiple options can be correct
QUESTION: 10

An electron in H – atom is excited from ground state level to first excited level. Select the correct statements:

Solution:

A,B,C,D

*Multiple options can be correct
QUESTION: 11

In the given circuit, current in resistance R is 1A, then

Solution:

*Multiple options can be correct
QUESTION: 12

A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag + bullet)

Solution:

Apply conservation of linear momentum KE = P2/2 X mass

*Multiple options can be correct
QUESTION: 13

In the circuit diagram shown

Solution:

*Multiple options can be correct
QUESTION: 14

A particle starts SHM at time t = 0. Its amplitude is A and angular frequency isω. At time t = 0 its kinetic energy is 4/E , where E is total energy. Assuming potential energy to be zero at mean
position, the displacement-time equation of the particle can be written as

Solution:
QUESTION: 15

A disc having radius R is rolling without slipping on a horizontal plane as shown. Centre of the disc has a velocity v and acceleration a as shown.

Q. Speed of point P having coordinates (x, y) is

Solution:

A

QUESTION: 16

A disc having radius R is rolling without slipping on a horizontal plane as shown. Centre of the disc has a velocity v and acceleration a as shown.

Q. If V =  , the angle θ between acceleration of the top most point and the horizontal is

Solution:

B

QUESTION: 17

A certain substance has a mass of 50g/mol. When 300J of heat is added to 25 gm of sample of this material, its temperature rises from 25 to 45oC.

Q.. The thermal heat capacity of the substance is

Solution:

C
Thermal heat capacity,

*Answer can only contain numeric values
QUESTION: 18

Two thin symmetrical lenses of different nature have equal radii of curvature of all faces R = 20 cm. The lenses are put close together and immersed in water. The focal length of the system is 24 cm. The difference between refractive indices of the lenses is  Find n. The refractive index of water is

Solution:

QUESTION: 19

Which one of the following is not true about diborane?

Solution:

D

QUESTION: 20

For the reaction,

What is the product A?

Solution:

D

QUESTION: 21

The wave function of atomic orbital of H-like atoms is given as under:

Given that the radius is in Å, then which of the following is radius for nodal surface for He+ ion

Solution:

QUESTION: 22

Solution:

Reimer – Tiemann’s reaction

QUESTION: 23

I2(s) | I- (0.1 M) half cell is connected to a H+ (aq.) | H2(1 bar) | Pt half cell and emf is found to be 0.7714 V. If  =  0.535 V,  find the pH of H+ |H half cell.

Solution:

QUESTION: 24

In the graph between √v and Z for the Mosley’s equation, theintercept OX is -1 on √v axis. What is the frequency whenatomic number (Z) is 51?

Solution:

QUESTION: 25

Which of the following equations must be used for the exact calculation of [H+] of an aqueous HCl solution at any concentration CHCl.[kw = 10-14 M2]

Solution:

QUESTION: 26

Which of the following salts give different result by the action of heat?

Solution:

(A) Both carbonates give oxides and CO2 gas.
(B) Both bicarbonates give carbonates, CO2 and H2O

(C)

(D) Both the sulphates give oxides and SO3

*Multiple options can be correct
QUESTION: 27

Which of the following is/are correct for the reaction with equilibrium constant K?

Solution:

A, B, C

are eq. constant
are rate cons tant

*Multiple options can be correct
QUESTION: 28

Which of the following reaction is incorrect regarding the formation of major product (alkene)?

Solution:

B

(Major product)

Due to greater probability of losing β-H (9 : 3 ratio).

*Multiple options can be correct
QUESTION: 29

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONE OR MORE is/are correct.

Select the correct statement(s) about the above compounds from the following:

Solution:

All reducing sugars are muatrotating. Although (IV) is an α -  hydroxy ketone and hence reducing but it can’t mutarotate as it not a carbohydrate, can’t form ring. In (II) the glycosidic linkage is in between two anomeric carbons and hence ring opening can’t occur, thus non – reducing as well as non – mutarotating.

*Multiple options can be correct
QUESTION: 30

HI cannot be prepared by the action of conc. H2SO4 on KI because

Solution:

fact

*Multiple options can be correct
QUESTION: 31

The correct statement(s) about solvent effect is/are

Solution:
*Multiple options can be correct
QUESTION: 32

Which of the following will not undergo aldol condensation?

Solution:
*Answer can only contain numeric values
QUESTION: 33

The number of bicarbonates that do not exist in solid form among the following is....................

Solution:

No bicarbonates exist in solid due to inefficient packing except Ammonium and Na+ to Cs+. Only NaHCO3 , KHCO3 , RbHCO3 , CsHCO3 and NH4HCO3 exist in solid.
So the correct answer is 4.

*Answer can only contain numeric values
QUESTION: 34

In Borax
(i) Number of B – O – B bond is x
(ii) Number of B – B bond is y
(iii) Number of sp2 hybridized B atom is z
Calculate the value of x + y + z

Solution:

*Answer can only contain numeric values
QUESTION: 35

Examine the structural formulas of following compounds and find out number of compounds
which show higher rate of nucleophilic addition than

Solution:

*Answer can only contain numeric values
QUESTION: 36

This section contains 6 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

Number of nuclear particles (Projectiles + ejectiles) involved in the conversion of the nuclide  92U238 into 94Pu239 by neutron – capture method is ..............

Solution:

QUESTION: 37

If   then  is equal to (where [•] and {•} denotes GIF and fraction parts of x),

n ∈ N

Solution:

QUESTION: 38

The solution of the differential equation y´y´´´=3(y´´)2 is

Solution:

QUESTION: 39

A point on the hypotenuse of a triangle is at distance a and b from the side of the triangle then minimum length of the hypotenuse is

Solution:

QUESTION: 40

This section contains 6 multiple choice questions numbered 1 to 6. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct

A(-2, 0), B(0, 4) . The point M on line y = x for which perimeter of ΔAMB is least is

Solution:

Use optimization technique

QUESTION: 41

Let where [.] denotes the greatest integer function. The value of S is

Solution:

Usemaxima minima concept

QUESTION: 42

The minimum value of

Solution:

It is the minimum distance between 2 curve

QUESTION: 43

Let 0 ≤  α < β < γ ≤ 2π and if cos(x + α) + cos (x + β) + cos (x + γ) = 0 ∀x∈R , then value of γ - α  is equal to

Solution:

Putting x = −α, x = −β, x = −γ in the equation

QUESTION: 44

Let the circles S1 ≡ x2 + y2 – 4x – 8y + 4 = 0 and S2 be its image in the line y = x, the equation of the circle touching y = x at (1, 1) and orthogonal to S2 is

Solution:

Centre of circle S1 = (2, 4)
Centre of circle S2 = (4, 2)
∴ equation of circle S2
(x – 4)2 + (y – 2)2 = 16
⇒ x2 + y2 – 8x – 4y + 4 = 0  . .  . (i)
Equation of circle touching y = x at (1, 1) can be taken as
(x – 1)2 + (y – 1)2 + λ(x – y) = 0
or, x2 + y2  + x (λ – 2) + y(– λ – 2) + 2 = 0  . . . (ii)
As this is orthogonal to S2

*Multiple options can be correct
QUESTION: 45

If f is a periodic function and g is a non–periodic function, then which of the following is not always a non–periodic function?

Solution:

Suppose period of f is T. Now fog may or may not be periodics. For example if f(x) = sin x and
g(x) = x + sin x, then fog is periodic of period 2π. On the other hand if f(x) = sin x and
g(x) = x2, then fog is a non–periodic function.
gof is always periodic of periodic T. Similarly fof is always periodic of period T.

*Multiple options can be correct
QUESTION: 46

A is 3 × 3 orthogonal matrix and if B = 5A5 , then det (B) must be equal to

Solution:

A is orthogonal matrix (3 × 3)
⇒ AAT = I3
det (AAT)  = det (I3)
det A. det AT = 1
(det A)2 = 1
det (A) = ±1  (1)
Q   B = 5A5
∴ det (B) = 53. (det A)5
⇒ det (B) = 125 (±1)5 = ±125

*Multiple options can be correct
QUESTION: 47

Which of the following is/are true for the equation e(k − x log x) = 1 ?

Solution:

Consider the eq uati onwhich represents point of intersection of  and y = x ln x. Clearly, no point of intersection if k < 0. One point of intersection if k = 0 and
Two points of intersection if

*Multiple options can be correct
QUESTION: 48

In triangle ABC, a = 4 and b = c =   A point P moves inside the triangle such that the square of its distance from BC is half of the area of rectangle contained by its distances from the other two sides. If D be the centre of locus of P, then

Solution:

PM = k
Equation of AB = −x + y = 2
Equation of AC = x + y = 2
According to equation

*Answer can only contain numeric values
QUESTION: 49

Consider a triangle ABC with BC = 3. Choose a point D on BC such that BD = 2. Find the value of AB2 + 2AC2− 3AD2 .

Solution:

Drop the perpendicular from A to BC and let F be its foot. Further more, suppose BF = x and AF = y.
Then, by Pyt hag orean theore m,

*Answer can only contain numeric values
QUESTION: 50

The equation of four circles are  Then the radius of a circle touching all the four circles internally is equal to

Solution:

Let radius of new circle = r
From symmetry centre of the required circle is (0, 0)

(Q  C1O is the distance from origin to centre of any of four circles).

*Answer can only contain numeric values
QUESTION: 51

If the coordinates (x, y, z) of the point S which is equidistant from the points O(0, 0, 0),  A(n5, 0, 0), B(0, n4, 0), C(0, 0, n) obey the relation 2(x + y + z) + 1 = 0. If n ∈ Z , then |n| = (| | is the modulus function)

Solution:

*Answer can only contain numeric values
QUESTION: 52

Minimum value of |z1 + 1| + |z2 + 1| + |z1z2 + 1|,   if |z1| = 1, |z2| = 1 is

Solution:

*Answer can only contain numeric values
QUESTION: 53

If x2 +  Px – 444P = 0 has integral roots (where P is a prime number) then the value of

Solution:

The equatio n x2 + Px  – 444P = 0 has integral roots.

Since P = 2 does not give the integral roots.
⇒ D must be perfect square of an odd integer.   i.e.
D2 = P(P + 1776) since perfect square.
⇒  P + 1776 must be multiple of P
⇒ 1776 must be a multiple of P
Now, 1776 = 24.3.37 when;   P = 2 or 3 or 37.
(i) P = 2 then P(P + 1776) = 2(2 + 1776) = 3556, not a perfect square.
(ii) P = 3 then P(P + 1776) = 3(3 + 1776) = 5337, not a perfect square.
(iii) P = 37 then P(P + 1776) = 37(37 + 1776) = 372.72 which is odd.
∴  P = 37

*Answer can only contain numeric values
QUESTION: 54

The number of integral values of  ‘a’ so that the point of local minima of f(x) = x3 – 3ax2 + 3(a2 – 1)x + 1 is less than 4 and point of local maximum is greater than −2, is/are

Solution:

f'(x) = 3(x2− 2ax + a2 −1)
f'(x) = 0 ⇒   (x − a)2 = 1, x = a + 1, a – 1
−2<a − 1, a + 1 < 4
⇒ −1<a , a < 3
⇒ a ∈ (−1, 3)

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