UGEE SUPR Mock Test- 6

Question 1

If a, b, c are in A.P., then the value of

Accepted Answer

0

Answer

3

Answer

-3

Answer

None of these

Answer

Cannot be determined

Question 2

The equation y² + 3 = 2(2x+y) represents a parabola with the vertex at

Accepted Answer

(1/2, 1) and focus at (3/2, 1)

Answer

(1/2, 1) and axis parallel to y-axis

Answer

(1, 1/2) and axis parallel to x-axis

Answer

(1, 1/2) and focus at (3/2, 1)

Answer

(0, 0) and axis parallel to x-axis

Question 3

∫ (27e^9x + e^12x)^1/3 dx is equal to

Accepted Answer

1/4(27 + e^3x)^4/3+ C

Answer

1/4(27 + e^3x)^1/3+ C

Answer

1/4(27 + e^3x)^2/3+ C

Answer

1/3(27 + e^3x)^4/3 + C

Answer

(27 + e³ˣ)^(1/3) + C

Question 4

The conic represented by x = 2(cos t + sin t), y = 5(cos t − sin t) is

Accepted Answer

an ellipse

Answer

a circle

Answer

a parabola

Answer

a hyperbola

Answer

a pair of straight lines

Question 5

The work done in ergs for the reversible expansion of one mole of an ideal gas from a volume of 10 litres to 20 litres at 25°C is

Accepted Answer

298 × 10⁷ × 8.31 × 2.303 log 2

Answer

2.303 × 298 × 0.082 log 2

Answer

2.303 × 298 × 0.082 log ⁡ 0.5

Answer

8.31 × 10⁷ × 298 × − 7log ⁡0.5

Answer

8.31 × 298 × ln 2

Question 6

Arrange the following particles in increasing order of values of e/m ratio: electron (e), proton (p), neutron (n) and α-particle (α) -

Accepted Answer

n, α, p, e

Answer

n, p, e, α

Answer

n, p, α, e

Answer

e, p, n, α

Answer

α, n, p, e

Question 7

For the reaction N₂ + 3H₂ → 2NH₃
if mol L⁻¹ s⁻¹, then value of would be

Accepted Answer

3 × 10⁻⁴mol L⁻¹s⁻¹

Answer

1 × 10⁻⁴mol L⁻¹s⁻¹

Answer

4 × 10⁻⁴ mol L⁻¹ s⁻¹

Answer

6 × 10⁻⁴mol L⁻¹s⁻¹

Answer

2 × 10⁻⁴ mol L⁻¹ s⁻¹

Question 8

The value of K_c for the reaction:
A + 3B ⇌ 2C at 400^∘C is 0.5. Calculate the value of K_p

Accepted Answer

1.64 × 10⁻⁴

Answer

1.64 × 10⁻⁶

Answer

1.64 × 10⁵

Answer

1.64 × 10³

Answer

0.5 × 10⁻⁴

Question 9

The electrode potentials for
Cu²⁺(aq) + e⁻ → Cu⁺(aq)
and Cu⁺(aq) + e⁻ → Cu(s)
are +0.15 V and +0.50 V, respectively.
The value of E°_Cu²⁺/Cu will be:

Accepted Answer

0.325 V

Answer

0.500 V

Answer

0.650 V

Answer

0.150 V

Answer

0.200 V

Question 10

The wavelengths of two photons are 2000Å and 4000Å respectively. What is the ratio of their energies?

Accepted Answer

2

Answer

1/4

Answer

4

Answer

1/2

Answer

3

Question 11

At low pressure, the van der Waals equation is reduced to

Accepted Answer

Answer

Answer

PVm = RT

Answer

Answer

PV = nRT − a/V²

Question 12

A direct current of 2A and an alternating current having a maximum value of 2A flow through two identical resistances. The ratio of heat produced in the two resistances will be

Accepted Answer

2 : 1

Answer

1 : 1

Answer

1 : 2

Answer

4 : 1

Answer

3 : 1

Question 13

A particle of mass m is under a potential v(x) = (1/2)k₁x² for x > 0 and v(x) = k₁x² for x < 0. When disturbed a little from the position x = 0, it will

Accepted Answer

not execute SHM

Answer

execute SHM with

Answer

execute SHM with T² = 2π²m/(k₁²)

Answer

execute SHM with

Answer

executes SHM with constant time period

Question 14

A far-sighted person can see clearly object beyond 100 cm distance. If he wants to see clearly an object at 40 cm distance, then the power of the lens he shall require is

Accepted Answer

+1.5 D

Answer

-1.5 D

Answer

+3.0 D

Answer

-3.0 D

Answer

None of these

Question 15

A hydrogen atom emits green light when it changes from n = 4 energy level to the n = 2 level. Which colour of light would the atom emit when it changes from n = 5 level to the n = 2 level?

Accepted Answer

violet

Answer

red

Answer

yellow

Answer

green

Answer

blue

Question 16

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be ______ cm.

Accepted Answer

20

Answer

15

Answer

30

Answer

40

Answer

8

Question 17

How many degree of freedom the gas molecules have if under STP the gas density ρ = 1.3 kg/m³ and the velocity of sound propagation in it is 330 m/sec?

Accepted Answer

5

Answer

10

Answer

15

Answer

12

Answer

3

Question 18

The work function of a metallic surface is 5.01 eV. Photoelectrons are emitted when light of wavelength 2000 Å falls on it. What is the minimum potential difference required to stop the fastest photoelectrons? (h = 4.14 × 10^-15 eV·s)

Accepted Answer

1.2

Answer

1.5

Answer

1.8

Answer

2

Answer

0.8

Question 19

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of 7M/8 and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I₁ be the moment of inertia of the new sphere about its axis. The ratio I₁/I₂ is 140/x. Find the value of x.
Note: I₁ is the inertia of the disk & I₂ is the inertia of the new sphere about the diameter.

Accepted Answer

1

Answer

10

Answer

5

Answer

3

Answer

2

Question 20

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P (in newton), such that the block does not move downward? (Take g = 10 m/s²)

Accepted Answer

32

Answer

21

Answer

45

Answer

26

Answer

15

Question 21

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, . The corresponding magnetic field , at that point is . Find the value of x.

Accepted Answer

2.1

Answer

3.2

Answer

1.5

Answer

3.5

Answer

4.2

Question 22

Two concentric coplanar circular loops made of wire, with resistance per unit length 10 Ω/m have diameters 0.2 m and 2 m. A time varying potential difference (4 + 2.5 t) volt is applied to the larger loop. Calculate the current (in A) in the smaller loop.

Accepted Answer

1.25

Answer

3.25

Answer

4.50

Answer

6.35

Answer

1/1

Question 23

Derivative of with respect to sin^-1(3x - 4x³) is

Accepted Answer

1/3

Answer

Answer

Answer

3

Answer

2/3

Question 24

a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ is equal to
Note: axy represents element whereas Axy represents Cofactor matrix.

Accepted Answer

0

Answer

1

Answer

-1

Answer

2

Answer

3

Question 25

If Rolle's theorem for
f(x) = e^x (sin x − cos x) is verified on [ then the value of c is

Accepted Answer

&pi;

Answer

&pi;/3

Answer

3&pi;/3

Answer

&pi;/2

Answer

π/2

Question 26

The joint equation of lines passing through the origin and trisecting the first quadrant is:

Accepted Answer

x² + √3xy - y² = 0

Answer

√3x² - 4xy + √3y² = 0

Answer

x² - √3xy - y² = 0

Answer

3x² - y² = 0

Answer

x² − √3xy + y² = 0

Question 27

If 2 tan^-1(cos x) = tan^-1(2 cosec x), then sin x + cos x is equal to:

Accepted Answer

&radic;2

Answer

2&radic;2

Answer

1/&radic;2

Answer

1/2

Answer

√3

Question 28

Direction cosines of the line , z = -1 are

Accepted Answer

Answer

Answer

Answer

Answer

(1/√3, 1/√3, 1/√3)

Question 29

is equal to

Accepted Answer

Answer

Answer

Answer

Answer

1

Question 30

The approximate value of f(x) = x³ + 5x² - 7x + 9at x = 1.1 is

Accepted Answer

8.6

Answer

8.5

Answer

8.4

Answer

8.3

Answer

8.7

UGEE SUPR Mock Test- 6 Free Online Test 2026

Full Mock Test & Solutions: UGEE SUPR Mock Test- 6 (40 Questions)

If a, b, c are in A.P., then the value of

The equation y² + 3 = 2(2x+y) represents a parabola with the vertex at

∫ (27e^9x + e^12x)^1/3 dx is equal to

The conic represented by x = 2(cos t + sin t), y = 5(cos t − sin t) is

The work done in ergs for the reversible expansion of one mole of an ideal gas from a volume of 10 litres to 20 litres at 25°C is

Arrange the following particles in increasing order of values of e/m ratio: electron (e), proton (p), neutron (n) and α-particle (α) -

For the reaction N₂ + 3H₂ → 2NH₃
if mol L⁻¹ s⁻¹, then value of would be

The value of K_c for the reaction:
A + 3B ⇌ 2C at 400^∘C is 0.5. Calculate the value of K_p

The electrode potentials for
Cu²⁺(aq) + e⁻ → Cu⁺(aq)
and Cu⁺(aq) + e⁻ → Cu(s)
are +0.15 V and +0.50 V, respectively.
The value of E°_Cu²⁺/Cu will be:

The wavelengths of two photons are 2000Å and 4000Å respectively. What is the ratio of their energies?

At low pressure, the van der Waals equation is reduced to

A direct current of 2A and an alternating current having a maximum value of 2A flow through two identical resistances. The ratio of heat produced in the two resistances will be

A particle of mass m is under a potential v(x) = (1/2)k₁x² for x > 0 and v(x) = k₁x² for x < 0. When disturbed a little from the position x = 0, it will

A far-sighted person can see clearly object beyond 100 cm distance. If he wants to see clearly an object at 40 cm distance, then the power of the lens he shall require is

A hydrogen atom emits green light when it changes from n = 4 energy level to the n = 2 level. Which colour of light would the atom emit when it changes from n = 5 level to the n = 2 level?

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be ______ cm.

How many degree of freedom the gas molecules have if under STP the gas density ρ = 1.3 kg/m³ and the velocity of sound propagation in it is 330 m/sec?

The work function of a metallic surface is 5.01 eV. Photoelectrons are emitted when light of wavelength 2000 Å falls on it. What is the minimum potential difference required to stop the fastest photoelectrons? (h = 4.14 × 10^-15 eV·s)

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, . The corresponding magnetic field , at that point is . Find the value of x.

Two concentric coplanar circular loops made of wire, with resistance per unit length 10 Ω/m have diameters 0.2 m and 2 m. A time varying potential difference (4 + 2.5 t) volt is applied to the larger loop. Calculate the current (in A) in the smaller loop.

Derivative of with respect to sin^-1(3x - 4x³) is

a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ is equal to
Note: axy represents element whereas Axy represents Cofactor matrix.

If Rolle's theorem for
f(x) = e^x (sin x − cos x) is verified on [ then the value of c is

The joint equation of lines passing through the origin and trisecting the first quadrant is:

If 2 tan^-1(cos x) = tan^-1(2 cosec x), then sin x + cos x is equal to:

Direction cosines of the line , z = -1 are

is equal to

The approximate value of f(x) = x³ + 5x² - 7x + 9at x = 1.1 is

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UGEE SUPR Mock Test- 6 Free Online Test 2026

Full Mock Test & Solutions: UGEE SUPR Mock Test- 6 (40 Questions)

If a, b, c are in A.P., then the value of

The equation y2 + 3 = 2(2x+y) represents a parabola with the vertex at

∫ (27e9x + e12x)1/3 dx is equal to

The conic represented by x = 2(cos t + sin t), y = 5(cos t − sin t) is

The work done in ergs for the reversible expansion of one mole of an ideal gas from a volume of 10 litres to 20 litres at 25°C is

Arrange the following particles in increasing order of values of e/m ratio: electron (e), proton (p), neutron (n) and α-particle (α) -

For the reaction N2 + 3H2 → 2NH3 if mol L−1 s−1, then value of would be

The value of Kc ​for the reaction: A + 3B ⇌ 2C at 400∘C is 0.5. Calculate the value of Kp ​

The electrode potentials for Cu²⁺(aq) + e⁻ → Cu⁺(aq) and Cu⁺(aq) + e⁻ → Cu(s) are +0.15 V and +0.50 V, respectively. The value of E°Cu²⁺/Cu will be:

The wavelengths of two photons are 2000Å and 4000Å respectively. What is the ratio of their energies?

At low pressure, the van der Waals equation is reduced to

A direct current of 2A and an alternating current having a maximum value of 2A flow through two identical resistances. The ratio of heat produced in the two resistances will be

A particle of mass m is under a potential v(x) = (1/2)k1x2 for x > 0 and v(x) = k1x2 for x < 0. When disturbed a little from the position x = 0, it will

A far-sighted person can see clearly object beyond 100 cm distance. If he wants to see clearly an object at 40 cm distance, then the power of the lens he shall require is

A hydrogen atom emits green light when it changes from n = 4 energy level to the n = 2 level. Which colour of light would the atom emit when it changes from n = 5 level to the n = 2 level?

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be ______ cm.

How many degree of freedom the gas molecules have if under STP the gas density ρ = 1.3 kg/m3 and the velocity of sound propagation in it is 330 m/sec?

The work function of a metallic surface is 5.01 eV. Photoelectrons are emitted when light of wavelength 2000 Å falls on it. What is the minimum potential difference required to stop the fastest photoelectrons? (h = 4.14 × 10-15 eV·s)

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, . The corresponding magnetic field , at that point is . Find the value of x.

Two concentric coplanar circular loops made of wire, with resistance per unit length 10 Ω/m have diameters 0.2 m and 2 m. A time varying potential difference (4 + 2.5 t) volt is applied to the larger loop. Calculate the current (in A) in the smaller loop.

Derivative of with respect to sin-1(3x - 4x3) is

a11A21 + a12A22 + a13A23 is equal to Note: axy represents element whereas Axy represents Cofactor matrix.

If Rolle's theorem for f(x) = ex (sin x − cos x) is verified on [ then the value of c is

The joint equation of lines passing through the origin and trisecting the first quadrant is:

If 2 tan-1(cos x) = tan-1(2 cosec x), then sin x + cos x is equal to:

Direction cosines of the line , z = -1 are

is equal to

The approximate value of f(x) = x3 + 5x2 - 7x + 9at x = 1.1 is

UGEE Mock Test Series 2026

UGEE Mock Test Series 2026

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About this JEE Mock Test

Explore more JEE Resources

The equation y² + 3 = 2(2x+y) represents a parabola with the vertex at

∫ (27e^9x + e^12x)^1/3 dx is equal to

For the reaction N₂ + 3H₂ → 2NH₃
if mol L⁻¹ s⁻¹, then value of would be

The value of K_c for the reaction:
A + 3B ⇌ 2C at 400^∘C is 0.5. Calculate the value of K_p

The electrode potentials for
Cu²⁺(aq) + e⁻ → Cu⁺(aq)
and Cu⁺(aq) + e⁻ → Cu(s)
are +0.15 V and +0.50 V, respectively.
The value of E°_Cu²⁺/Cu will be:

A particle of mass m is under a potential v(x) = (1/2)k₁x² for x > 0 and v(x) = k₁x² for x < 0. When disturbed a little from the position x = 0, it will

How many degree of freedom the gas molecules have if under STP the gas density ρ = 1.3 kg/m³ and the velocity of sound propagation in it is 330 m/sec?

The work function of a metallic surface is 5.01 eV. Photoelectrons are emitted when light of wavelength 2000 Å falls on it. What is the minimum potential difference required to stop the fastest photoelectrons? (h = 4.14 × 10^-15 eV·s)

Derivative of with respect to sin^-1(3x - 4x³) is

a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ is equal to
Note: axy represents element whereas Axy represents Cofactor matrix.

If Rolle's theorem for
f(x) = e^x (sin x − cos x) is verified on [ then the value of c is

If 2 tan^-1(cos x) = tan^-1(2 cosec x), then sin x + cos x is equal to:

The approximate value of f(x) = x³ + 5x² - 7x + 9at x = 1.1 is