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UGEE SUPR Mock Test-1 - JEE MCQ


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50 Questions MCQ Test UGEE Mock Test Series 2024 - UGEE SUPR Mock Test-1

UGEE SUPR Mock Test-1 for JEE 2024 is part of UGEE Mock Test Series 2024 preparation. The UGEE SUPR Mock Test-1 questions and answers have been prepared according to the JEE exam syllabus.The UGEE SUPR Mock Test-1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for UGEE SUPR Mock Test-1 below.
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UGEE SUPR Mock Test-1 - Question 1

A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a

Detailed Solution for UGEE SUPR Mock Test-1 - Question 1

Force due to electric field will make the charged particle released from rest to move in the straight line (that of electric field). Since the force due to magnetic field is zero, therefore, the charged particle will move in a straight line.

UGEE SUPR Mock Test-1 - Question 2

Accommodation of the human eye is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 2

The ability of the eye lens to adjust its focal length is called power of accommodation. This is done by the ciliary muscles by changing the focal length of the eye lens.

UGEE SUPR Mock Test-1 - Question 3

In the figure shown pulley is massless. Initially the blocks are held at a height such that spring is in its natural length. The amplitude and velocity amplitude of block Brespectively are (there is no slipping anywhere)

Detailed Solution for UGEE SUPR Mock Test-1 - Question 3

Decrease in GPE of B1 = Increase in Gravitational PE of B2 + Increase in elastic PE of spring. 

Again applying law of conservation of mechanical energy at the mean position we get 

UGEE SUPR Mock Test-1 - Question 4

A coil of inductance 0.20 H is connected in series with a switch and a cell of emf 1.6 V. The total resistance of the current is 4.0Ω. What is the initial rate of growth of the current when the switch is closed?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 4
When the switch is closed at(t = 0s), no current flows, voltage drop across the inductor is the same as the supply voltage of 1.6 V.

Voltage equation for the circuit, we have

Where i is the current drawn from the source , at t = 0s, i = 0, we thus have

UGEE SUPR Mock Test-1 - Question 5

Mass of the earth is 81 times the mass of the moon and the distance between the earth and moon is 60 times the radius of the earth. If R is the radius of the earth, then the distance between the moon and the point on the line joining the moon and earth where the gravitational force becomes zero is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 5

Let d be the distance between the moon and the point at force on mass m is zero then

UGEE SUPR Mock Test-1 - Question 6

A magnet of magnetic moment M and length 2l is bent at its mid-point such that the angle of bending is 60°. Now, the magnetic moment is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 6

In new situation we have

As the length of magnet is halved , Magnetic moment M’= m(l) = M/2

Resultant magnetic Moment

UGEE SUPR Mock Test-1 - Question 7

Three identical uniform rods of the same mass M and length L are arranged in xy plane as shown in the figure. A fourth uniform rod of mass 3 M has been placed as shown in the xy plane. What should be the value of the length of the fourth rod such that the centre of mass of all the four rods lie at the origin?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 7

Let 'x' be the length of the 4th rod and the centre of the mass of all the rods lies at origin then Xcm = 0

UGEE SUPR Mock Test-1 - Question 8

A metallic wire with tension T and at temperature 30°C vibrates with its fundamental frequency of 1 kHz. The same wire with the same tension but at 10°C temperature vibrates with a fundamental frequency of 1.001 kHz. The coefficient of linear expansion of the wire is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 8

UGEE SUPR Mock Test-1 - Question 9

For a gas, the difference between the two specific heats at constant pressure and constant volume is 4150 J kg-1 K-1 and their ratio is 1.4. What is the specific heat of the gas at constant volume in units of J kg-1 k-1?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 9

Given: Cp - Cv = 4150 Jkg-1K-1 and Cp/Cv = 1.4 Or Cp = 1.4 Cv.

Therefore,

1.4 Cv - Cv = 4150

Or CV = 4150/0.4 = 10375 J kg-1 K-1

UGEE SUPR Mock Test-1 - Question 10

Among the following pairs, which one does not have identical dimensions?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 10

Moment of inertia (I) = mr2

[I] = [ML2]

Moment of force (C) = rF

[C] = [r][F] = [L][MLT-2] or [C] = [ML2T-2]

Moment of inertia and moment of a force do not have identical dimensions.

UGEE SUPR Mock Test-1 - Question 11

When the electron in the hydrogen atom jumps from the fourth Bohr orbit to the second Bohr orbit, one gets the

Detailed Solution for UGEE SUPR Mock Test-1 - Question 11

The wavelength of line in cased Baimer series is given by where n = 3,4,5 and R = Rydberg constant.

So, for the Balmer series, the transition takes from third orbit to second for first line spectrum, fourth orbit to second for second line spectrum, etc. Hence, the given transition represents the second line of the Balmer series.

UGEE SUPR Mock Test-1 - Question 12

In U.C.M, when time interval δt → 0, the angle between change in velocity (δv) and linear velocity (v) will be

Detailed Solution for UGEE SUPR Mock Test-1 - Question 12
The direction of change in velocity (δw) is given by

...(i)

This can be shown graphically as

For small time intervals, i,e„ δt →O, then the angle between v1 and v2 is very small i.e., θ ≈ 0°. So. from Eq. (i), we get ∅ = 900

UGEE SUPR Mock Test-1 - Question 13

A particle is performing a linear simple harmonic motion of amplitude 'A'. When it is midway between its mean and extreme position, the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 13
In linear simple harmonic motion, the velocity d particle is given by

…(i)

Where, ω = angular frequency

A = maximum displacement of amplitude

x = displacement from mean position,

The acceleration d a particle in simple harmonic motion, (SHM) is given by

a = ω2x …(iii)

Here, x = A/2

Also, v = a (given)

[from Eqs. (i) and (ii), we get]

⇒ 2π/T = √3 [∵ω = 2π/T]

⇒ T = (2π/√3)s

UGEE SUPR Mock Test-1 - Question 14

Three point masses each of mass ‘m’ are kept at the corners of an equilateral triangle of side ‘L’. The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to (cos 300 = sin600 √3/2)

Detailed Solution for UGEE SUPR Mock Test-1 - Question 14


UGEE SUPR Mock Test-1 - Question 15

When Light enters glass from the vacuum, then the wavelength of light

Detailed Solution for UGEE SUPR Mock Test-1 - Question 15

When light enters glass from the vacuum, its wavelength decreases. This is because the speed of light is slower in glass than in vacuum, due to the higher refractive index of glass. According to the formula c = λv, where c is the speed of light, λ is the wavelength, and v is the frequency, if the speed of light decreases (as it does in glass), then the wavelength must decrease proportionally to maintain a constant frequency.

UGEE SUPR Mock Test-1 - Question 16

What is the minimum energy required to launch a satellite of mass ‘m' from the surface of the earth of mass ‘M’ and radius ‘R’ at an altitude 2R?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 16

UGEE SUPR Mock Test-1 - Question 17

How many moles of magnesium phosphate, Mg3 (PO4)2 will contain 0.25 mole of oxygen atoms?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 17

Mg3(P04)→ 3Mg
→2 P
→ 8 mole oxygen
8 mole of oxygen - 1 mole Mg3 (P0)2
0.25 - ? 0.25/8 = 3 x 10-2

UGEE SUPR Mock Test-1 - Question 18

When an electron is added to neutral gaseous atom to convert it into a negative ion, the enthalpy change accompanying the process is called:

Detailed Solution for UGEE SUPR Mock Test-1 - Question 18

Electron affinity is defined as the change in energy (in kJ/mole) of a neutral atom (in the gaseous phase) when an electron is added to the atom to form a negative ion.

UGEE SUPR Mock Test-1 - Question 19

For emission line of atomic hydrogen from ni to nf = 8, the plot of wave number against is:

(The Rydberg constant, RH is in wave number unit).

Detailed Solution for UGEE SUPR Mock Test-1 - Question 19

m = RH

Linear with slope RH

UGEE SUPR Mock Test-1 - Question 20

Two pi and half sigma bonds are present in:

Detailed Solution for UGEE SUPR Mock Test-1 - Question 20

UGEE SUPR Mock Test-1 - Question 21

Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p. x/m is proportional to

Detailed Solution for UGEE SUPR Mock Test-1 - Question 21

Slope =

⇒ n = 2

So,

UGEE SUPR Mock Test-1 - Question 22

The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are:

Detailed Solution for UGEE SUPR Mock Test-1 - Question 22
Total number of isotopes of hydrogen is 3

and only 13H or 13T is an Radioactive element.

UGEE SUPR Mock Test-1 - Question 23

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m3 at 1000 K. given R is the gas constant in JK-1 mol-1 m, x is :

Detailed Solution for UGEE SUPR Mock Test-1 - Question 23

nT = (0.5 + x)

PV = n × R × T

200 × 10 = (0.5 + x) × R × 1000

2 = (0.5 + x) R

UGEE SUPR Mock Test-1 - Question 24

In general, the properties that decrease and increase down a group in the periodic table, respectively, are:

Detailed Solution for UGEE SUPR Mock Test-1 - Question 24
The value of effective nuclear charge decreases down the group.

Hence, the electronegativity decreases and atomic radius increases on moving down the group.

UGEE SUPR Mock Test-1 - Question 25

Phenyl diazonium salts form azo dye with

(1) Aniline

(2) Phenol

(3) N, N–dimethylaniline

(4) Anisole (methoxybenzene)

Of these statements :

Detailed Solution for UGEE SUPR Mock Test-1 - Question 25
PhN+ ≡ N is a weak electrophile that undergoes diazocoupling only with rings activated by −OH,−NH2,−NHR or−NR2. The ring is not sufficiently activated by -OCH3 and hence, anisole does not form azodye.
UGEE SUPR Mock Test-1 - Question 26

Low spin complex is formed by

Detailed Solution for UGEE SUPR Mock Test-1 - Question 26
Low spin complex utilises (n−1) d-orbital for hybridisation and thus the low spin complex is formed with d2sp3 hybridisation. Inner d-orbital complex is formed.
UGEE SUPR Mock Test-1 - Question 27

Which of the following hybridization pattern best describes the carbon atom in NCO?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 27
NCO. is isoelectronic with CO2, which has a linear geometry in which C−atom is sp-hybridized.

UGEE SUPR Mock Test-1 - Question 28

What is the shape and magnetic nature of permanganate ions?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 28

The permanganate ions are tetrahedral. The π-bonding takes place by the overlap of p-orbitals of oxygen with d-orbitals of manganese. It is also diamagnetic due to the absence of an unpaired electron. The structure of permanganate ion is given below

UGEE SUPR Mock Test-1 - Question 29

“The mass and energy both are conserved in an isolated system”, is the statement of

Detailed Solution for UGEE SUPR Mock Test-1 - Question 29
"The mass and energy both are conserved in an isolated system*, is the statement at modified first law of thermodynamics. According to this law, if a certain amount of one kind of energy is produced, an equal amount of some other kind of energy is consumed so that the total energy in the universe remains constant.
UGEE SUPR Mock Test-1 - Question 30

The number of π-bonds present in benzoic acid molecule are

Detailed Solution for UGEE SUPR Mock Test-1 - Question 30
The number of π-bonds present in benzoic acid molecule are 4 (four). The structure of benzoic acid is as follows

UGEE SUPR Mock Test-1 - Question 31

The combining ratios of hydrogen and oxygen in water and hydrogen peroxide are 1: 8 and 1 : 16. Which law is illustrated in this example?

Detailed Solution for UGEE SUPR Mock Test-1 - Question 31
The combining ratios of hydrogen and oxygen . In water and hydrogen peroxide are 1 : 8 and 1 : 16. It is an example of a law of multiple proportions. According to this law, if two elements combine together to form several compounds then the weight of one of those elements, which combines with a fixed weight of the other, are in the ratio of simple whole numbers.
UGEE SUPR Mock Test-1 - Question 32

The precipitation power of an electrolyte increases with

Detailed Solution for UGEE SUPR Mock Test-1 - Question 32
The precipitation power of an electrolyte increases with the charge of an ion. It can be explained on the basis of Hardy-Schulze rule. Greater the valence of the flocculating ion added, the greater is its power to cause precipitation.
UGEE SUPR Mock Test-1 - Question 33

The highest oxidation state in plutonium (At. no. = 94) is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 33

The highest oxidation state in plutonium (Atomic numbers = 94) is +7. It can show a greater range of oxidation states which (in part) is attributed to the fact that 5l, 6d and 7s teveisare of comparable energies. Plutonium (Pu) can show an oxidation state of +3, +4, +5, +6 and +7 in its compound.

UGEE SUPR Mock Test-1 - Question 34

Let a, b and c be such that b(a + c) ≠ 0. If , then the value of n is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 34

This is equal to zero only if n + 2 is odd i.e. n is odd integer.

UGEE SUPR Mock Test-1 - Question 35

Find .

Detailed Solution for UGEE SUPR Mock Test-1 - Question 35

UGEE SUPR Mock Test-1 - Question 36

If a1, a2, a3,....,a20 are the arithmetic means between 13 and 67, then the maximum value of the product a1⋅a2⋅a3⋅....a20 is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 36

13, a1, a2, a3, ....a20, 67 are in AP

= 800

Now, AM ≥ GM

∴∴The maximum value of a1⋅a2⋅a3⋅....a20 is (40)20

UGEE SUPR Mock Test-1 - Question 37

The locus of the mid point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Detailed Solution for UGEE SUPR Mock Test-1 - Question 37
Let p(h,k) be the mid point of the line segment joining the focus (a,0) and a general point Q(x, y) on the parabola. Then,

⇒ x = 2h − a, y = 2k

Put these values of x and y in y2 = 4ax to get

4k2 = 4a(2h − a)

⇒ 4k2 = 8ah − 4a2

⇒ k2 = 2ah − a2

So, the locus of P(h, k) is y2 = 2ax − a2

Its directrix is x − a/2 = −a/2

⇒ x = 0.

UGEE SUPR Mock Test-1 - Question 38

The length of the diameter of the circle which touches the X-axis at the point (1, 0) and passes through the point (2, 3) is

Detailed Solution for UGEE SUPR Mock Test-1 - Question 38

Let, the centre of the required circle is (1, k) and radius |k|

So, the equation of the required circles is

(x−1)2 +(y − k)2 = k2

Given, it passes through (2, 3)

Thus diameter = 10/3

UGEE SUPR Mock Test-1 - Question 39

If line and intersect, then k=

Detailed Solution for UGEE SUPR Mock Test-1 - Question 39

UGEE SUPR Mock Test-1 - Question 40

The p.d.f of a random variable x is given by f(x) = 1/4a, 0<x<4a , (a>0) = 0, otherwise and P then k = ...

Detailed Solution for UGEE SUPR Mock Test-1 - Question 40

We have p.d.f of a random variable x is given by

f(x)= 1/4a, 0<x<4a,(a>0) and also,

⇒ k = 1

UGEE SUPR Mock Test-1 - Question 41

The solution of the differential equation ydx - xdy = xy dx is ...

Detailed Solution for UGEE SUPR Mock Test-1 - Question 41
We have differential equation ydx - xdy = xydx

On integrating both sides, we get

log(x/y) = x ⇒ x/y = ex

⇒ x = yex

UGEE SUPR Mock Test-1 - Question 42

If , then n = ........

Detailed Solution for UGEE SUPR Mock Test-1 - Question 42
We have,

⇒ 3 + 5 + 7 … + (2n + 1) = 440

⇒ n/2[2 x 3 + (n-1)(2) = 440

⇒ n(3 + n - 1) = 440

⇒ n(n + 2) = 440

⇒ n = 20

UGEE SUPR Mock Test-1 - Question 43

If the standard deviation of the random variable X is and mean is 3p then E(x2) = ...

Detailed Solution for UGEE SUPR Mock Test-1 - Question 43

We have standard deviation of X =

⇒Vai(X) = 3pq

and mean, E(X) = 3p

Now, 3pq = E(x2)-(3p2)

(∵ Var(X) = E(x2) - (E(x)2))

⇒ E(x2) = 3pq + 9p2

= 3p(1-p) + 9p2 (∵p+q = 1)

= 3p - 3p2 + 9p2

⇒ 3p + 6p2 ⇒ 3p(1 + 2p)

UGEE SUPR Mock Test-1 - Question 44

If this represented by (1 + sin2θ)x2 + 2hxy + 2sin(θ)y2 = 0, θ ∈ [0, 2π] are perpendicular to each other then θ = .......

Detailed Solution for UGEE SUPR Mock Test-1 - Question 44

Key Idea Given, ax2 + 2hxy + by2 = 0 represents perpendicular pair of straight lines then a + b = 0

we have, pair of Snes represented by (1+sin2θ)x2 + 2hxy + 2sinθy2 =0, θ ∈(0, 2π)

∴ (1 + sin2θ) + 2Sinθ = 0

⇒ (1+ sinθ)2 = 0

⇒1 + sinθ = 0

UGEE SUPR Mock Test-1 - Question 45

If R is the circum radius of ΔABC, then A (ΔABC) = .......

Detailed Solution for UGEE SUPR Mock Test-1 - Question 45
In any ΔABC we know that Area of Δ = ½(bc sinA)

⇒ sin A = 2Δ/bc …(i)

also, R = a/2sinA …(ii)

From Eqs. (i) and (ii), we have

⇒ R = abc/4Δ

⇒ Δ = A(ΔABC) = abc/4R

UGEE SUPR Mock Test-1 - Question 46

If (-√2, √2) are cartesian co-ordinates of the point, then its polar co-ordinates are......

Detailed Solution for UGEE SUPR Mock Test-1 - Question 46
We have rcos θ = -√2 and r sinθ = √2

∴ r2 cos2θ + r2 sin2θ = 2 + 2 = 4

⇒ r2(cos2θ + sin2θ) = 4

⇒ r = ±2 and θ = tan-1

θ = tan-1(-1) ⇒ θ = 3π/4

∴ Required polar co-ordinate is (r, θ) = (2, 3π/4)

UGEE SUPR Mock Test-1 - Question 47

II A is non-singular matrix and (A + l) (A - l) = 0 then A + A-1 = ....

Detailed Solution for UGEE SUPR Mock Test-1 - Question 47

We have, A is non-singular matrix

∴ |A| = 0

and (A + l)(A - l) = 0

⇒ A2 - I2 = 0

⇒ A2 = I2 = I

⇒ A·A = I

⇒ A-1 = A

∴ A + A-1 = A + A = 2A

UGEE SUPR Mock Test-1 - Question 48

The y-intercept of the line passing through A(6, 1) and perpendicular to the line x - 2y = 4 is ........

Detailed Solution for UGEE SUPR Mock Test-1 - Question 48
Slope of the given line, x - 2y = 4 is ½

Equation of a line passing through 4(6, 1) and perpendicular to given line is y - 1 = (-2)(x - 6)

⇒ y - 1 = -2x + 12

⇒ 2x + y = 13

∴ the y-intercept of slope (i) is 13.

UGEE SUPR Mock Test-1 - Question 49

In ΔABC, if tan A +tan B + tan C = 6 and tanA.tanB = 2 then tan C = ......

Detailed Solution for UGEE SUPR Mock Test-1 - Question 49

Key Idea Use Identity. In ΔABC tanA + tanB + tanC = tanA tanB tanC

We have, tanA + tanB + tanC = 6

⇒ tanA tanB tanC = 6 …(i)

and tanA.tanB = 2 …(ii)

From Eqs. (i) and (ii) we get, tanC = 3

UGEE SUPR Mock Test-1 - Question 50

For LP.P, maximize z = 4x, + 2x2 subject to 3x1 + 2x2 ≥ 9, x1 - x2 3, x1 ≥ 0, x2 ≥ 0 has...

Detailed Solution for UGEE SUPR Mock Test-1 - Question 50
We have, maximise z = 4x1 + 2x2

Subject to contracts, 3x1 + 2x2 ≥ 9, x1 - x2 ≤ 3, x1 ≥ 0, x2 ≥ 0

On taking given constraints as equation, we get the following graphs

Here, we get feasible region is unbounded.

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