JEE Main Practice Test- 14

Question 1

Let f(x) be a one-to-one function such that f(1) = 3, f(3) = 1, f '(1) = – 4 and f '(3) = 2. If g = f ^–1, then the slope of the tangent line to 1/g at x = 1 is

Accepted Answer

-1/18

Answer

1/&radic;2

Answer

-1/9

Answer

1/32

Question 2

The value of is equal to

Accepted Answer

24

Answer

6

Answer

12

Answer

18

Question 3

If g (x³ + 1) = x⁶ + x³ + 2, then the value of g(x² – 1) is

Accepted Answer

x⁴ – 3x² + 4

Answer

x⁴ – 3x² + 3

Answer

x⁴ + x² + 4

Answer

x⁴ + x² + 2

Question 4

Suppose that f (0) = 0 and f ' (0) = 2, and let g (x) = f (- x + f (f (x))). The value of g ' (0) is equal to

Accepted Answer

6

Answer

0

Answer

1

Answer

8

Question 5

The value of the definite integral,

Accepted Answer

Answer

Answer

Answer

Question 6

A line L is perpendicular to the curve at its point P and passes through (10, –1). The coordinates of the point P are

Accepted Answer

(4, 2)

Answer

(2, &ndash;1)

Answer

(6, 7)

Answer

(0, &ndash;2)

Question 7

then the sum of the square of reciprocal of all the values of x where f(x) is non-differentiable, is equal to

Accepted Answer

82

Answer

1

Answer

81

Answer

82/81

Question 8

h(x) = {x},k(x) = 5^{log₂(x + 3)} then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to
[Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

Accepted Answer

f, g, h

Answer

h, k

Answer

f, g

Answer

g, h, k

Question 9

If the function f (x) = ax e^–bx has a local maximum at the point (2, 10), then

Accepted Answer

a = 5e, b = 1/2

Answer

a = 5; b = 0

Answer

a = 5e², b = 1

Answer

none

Question 10

then the value of x satisfying the equation f (x, 10) = f (x, 11), is

Accepted Answer

11

Answer

9

Answer

10

Answer

none

Question 11

Accepted Answer

1/10

Answer

1/35

Answer

1/14

Answer

1/5

Question 12

Number of integral solutions of the equation

[Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

Accepted Answer

2

Answer

3

Answer

5

Answer

7

Question 13

The area bounded by the curve y = x² + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

Accepted Answer

Answer

Answer

Answer

8/3

Question 14

Number of roots of the equation x² –2x–log₂ |1 – x | = 3 is

Accepted Answer

4

Answer

2

Answer

1

Answer

0

Question 15

Let F(x) be the primitive of w.r.t. x. If F(10) = 60 then the value of F(13), is

Accepted Answer

132

Answer

66

Answer

248

Answer

264

Question 16

is continuous at x = 0, then
[Note : {x} denotes fractional part of x.]

Accepted Answer

f(x) is differentiable at x = 0

Answer

k = 1

Answer

f(x) is continuous but not differentiable at x = 0

Answer

f(x) is continuous every where in its domain.

Question 17

[Note : where C is constant of integration.]

Accepted Answer

sin x - 2 (sin x)^-1 - 6 tan^-1 (sin x) + C

Answer

sin x - 6 tan^-1 (sin x) + C

Answer

sin x - 2 sin^-1 x + C

Answer

sin x - 2 (sin x)^-1 + 5 tan^-1 (sin x) + C

Question 18

Point 'A' lies on the curve and has the coordinate where x > 0. Point B has the coordinates (x, 0). If 'O' is the origin then the maximum area of the triangle AOB is

Accepted Answer

Answer

Answer

Answer

Question 19

Which one of the following statement is correct?

Accepted Answer

f (x) is continuous for all x = 2nπ – tan^–1 (3/4) , n ∈ I when a = 5.

Answer

f (x) is continuous for all x when a = 5.

Answer

f (x) is discontinuous for all x.

Answer

f (x) is continuous for all x = 2nπ – tan^–1 (4/3) , n ∈ I when a = 5.

Question 20

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

If then the value of must be

Accepted Answer

Question 21

The sum of all the real roots of the equations
|x − 2|² + |x − 2| − 2 = 0 is …..

Accepted Answer

Question 22

If P_n = cosⁿ x + sinⁿ x, then 2.P₆ - 3.P₄ + 1 = ..

Accepted Answer

Question 23

If x = 2 + t³, y = 3t² and is a constant then the value of 343n must be

Accepted Answer

Question 24

The value of 49A + 5B, where A = 1 - log₇2 and B = - log₅ 4 is

Accepted Answer

Question 25

A transverse wave is travelling along a horizontal string. The first picture shows the shape of the string at an instant of time. This picture is superimposed on a coordinate system to help you make any necessary measurements. The second picture is a graph of the vertical displacement of one point along the string as a function of time. How far does this wave travel along the string in one second?

Accepted Answer

3.0 cm

Answer

0.3 cm

Answer

9.0 cm

Answer

27 cm

Question 26

A cyclic process of an enclosed gas of constant mass is represented by volume (V) against absolute temperature (T) as shown. If P represents pressure, the graph representing the same process can be

Accepted Answer

Answer

Answer

Answer

Question 27

A closed organ pipe is vibrating in its second overtone. The length of the pipe is 10cm and maximum amplitude of vibration of particles of the air in the pipe is 2mm. Then the amplitude of S.H.M. of the particles at 9cm from the open end is:

Accepted Answer

&radic;2 mm

Answer

&radic;3 mm

Answer

&radic;3/2 mm

Answer

none of these

Question 28

A sound source S and observers O₁, O₂ are placed as shown. S is always at rest and O₁, O₂ start moving with velocity v₀ at t = 0. At any later instant, let f₁ and f₂ represent apparent frequencies of sound received by O₁ and O₂, respectively. The ratio f₁/f₂ is

Accepted Answer

> 1

Answer

zero

Answer

between 0 and 1

Answer

1

Question 29

Equal masses of three liquids A, B and C have temperatures 10^oC, 25^oC and 40^oC respectively. If A and B are mixed, the mixture has a temperature of 15^oC. If B and C are mixed, the mixture has a temperature of 30^oC,. If A and C are mixed the mixture will have a temperature of

Accepted Answer

16oC

Answer

20oC

Answer

25oC

Answer

29oC

Question 30

A steel rod is 4.000 cm in diameter at 30ºC. A brass ring has an interior diameter of 3.992 cm at 30ºC. In order that the ring just slides onto the steel rod, the common temperature of the two should be nearly (α_steel= 11 × 10^-6/ºC and α_brass= 19 × 10^-6/ºC)

Accepted Answer

280&ordm;C

Answer

200&ordm;C

Answer

250&ordm;C

Answer

400&ordm;C

JEE Main & Advanced Practice Test- 14 Free Online Test 2026

MCQ Practice Test & Solutions: JEE Main Practice Test- 14 (75 Questions)

Let f(x) be a one-to-one function such that f(1) = 3, f(3) = 1, f '(1) = – 4 and f '(3) = 2. If g = f ^–1, then the slope of the tangent line to 1/g at x = 1 is

The value of is equal to

If g (x³ + 1) = x⁶ + x³ + 2, then the value of g(x² – 1) is

Suppose that f (0) = 0 and f ' (0) = 2, and let g (x) = f (- x + f (f (x))). The value of g ' (0) is equal to

The value of the definite integral,

A line L is perpendicular to the curve at its point P and passes through (10, –1). The coordinates of the point P are

then the sum of the square of reciprocal of all the values of x where f(x) is non-differentiable, is equal to

h(x) = {x},k(x) = 5^{log₂(x + 3)} then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to
[Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

If the function f (x) = ax e^–bx has a local maximum at the point (2, 10), then

then the value of x satisfying the equation f (x, 10) = f (x, 11), is

Number of integral solutions of the equation

[Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

The area bounded by the curve y = x² + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

Number of roots of the equation x² –2x–log₂ |1 – x | = 3 is

Let F(x) be the primitive of w.r.t. x. If F(10) = 60 then the value of F(13), is

is continuous at x = 0, then
[Note : {x} denotes fractional part of x.]

[Note : where C is constant of integration.]

Point 'A' lies on the curve and has the coordinate where x > 0. Point B has the coordinates (x, 0). If 'O' is the origin then the maximum area of the triangle AOB is

Which one of the following statement is correct?

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)
If then the value of must be

The sum of all the real roots of the equations
|x − 2|² + |x − 2| − 2 = 0 is …..

If P_n = cosⁿ x + sinⁿ x, then 2.P₆ - 3.P₄ + 1 = ..

If x = 2 + t³, y = 3t² and is a constant then the value of 343n must be

The value of 49A + 5B, where A = 1 - log₇2 and B = - log₅ 4 is

A cyclic process of an enclosed gas of constant mass is represented by volume (V) against absolute temperature (T) as shown. If P represents pressure, the graph representing the same process can be

A closed organ pipe is vibrating in its second overtone. The length of the pipe is 10cm and maximum amplitude of vibration of particles of the air in the pipe is 2mm. Then the amplitude of S.H.M. of the particles at 9cm from the open end is:

A sound source S and observers O₁, O₂ are placed as shown. S is always at rest and O₁, O₂ start moving with velocity v₀ at t = 0. At any later instant, let f₁ and f₂ represent apparent frequencies of sound received by O₁ and O₂, respectively. The ratio f₁/f₂ is

Equal masses of three liquids A, B and C have temperatures 10^oC, 25^oC and 40^oC respectively. If A and B are mixed, the mixture has a temperature of 15^oC. If B and C are mixed, the mixture has a temperature of 30^oC,. If A and C are mixed the mixture will have a temperature of

A steel rod is 4.000 cm in diameter at 30ºC. A brass ring has an interior diameter of 3.992 cm at 30ºC. In order that the ring just slides onto the steel rod, the common temperature of the two should be nearly (α_steel= 11 × 10^-6/ºC and α_brass= 19 × 10^-6/ºC)

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JEE Main & Advanced Practice Test- 14 Free Online Test 2026

MCQ Practice Test & Solutions: JEE Main Practice Test- 14 (75 Questions)

Let f(x) be a one-to-one function such that f(1) = 3, f(3) = 1, f '(1) = – 4 and f '(3) = 2. If g = f –1, then the slope of the tangent line to 1/g at x = 1 is

The value of is equal to

If g (x3 + 1) = x6 + x3 + 2, then the value of g(x2 – 1) is

Suppose that f (0) = 0 and f ' (0) = 2, and let g (x) = f (- x + f (f (x))). The value of g ' (0) is equal to

The value of the definite integral,

A line L is perpendicular to the curve at its point P and passes through (10, –1). The coordinates of the point P are

then the sum of the square of reciprocal of all the values of x where f(x) is non-differentiable, is equal to

h(x) = {x},k(x) = 5log2 (x + 3) then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to [Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

If the function f (x) = ax e–bx has a local maximum at the point (2, 10), then

then the value of x satisfying the equation f (x, 10) = f (x, 11), is

Number of integral solutions of the equation [Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

The area bounded by the curve y = x2 + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

Number of roots of the equation x2 –2x–log2 |1 – x | = 3 is

Let F(x) be the primitive of w.r.t. x. If F(10) = 60 then the value of F(13), is

is continuous at x = 0, then [Note : {x} denotes fractional part of x.]

[Note : where C is constant of integration.]

Point 'A' lies on the curve and has the coordinate where x > 0. Point B has the coordinates (x, 0). If 'O' is the origin then the maximum area of the triangle AOB is

Which one of the following statement is correct?

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)If then the value of must be

The sum of all the real roots of the equations |x − 2|2 + |x − 2| − 2 = 0 is …..

If Pn = cosn x + sinn x, then 2.P6 - 3.P4 + 1 = ..

If x = 2 + t3, y = 3t2 and is a constant then the value of 343n must be

The value of 49A + 5B, where A = 1 - log72 and B = - log5 4 is

A cyclic process of an enclosed gas of constant mass is represented by volume (V) against absolute temperature (T) as shown. If P represents pressure, the graph representing the same process can be

A closed organ pipe is vibrating in its second overtone. The length of the pipe is 10cm and maximum amplitude of vibration of particles of the air in the pipe is 2mm. Then the amplitude of S.H.M. of the particles at 9cm from the open end is:

A sound source S and observers O1, O2 are placed as shown. S is always at rest and O1, O2 start moving with velocity v0 at t = 0. At any later instant, let f1 and f2 represent apparent frequencies of sound received by O1 and O2, respectively. The ratio f1/f2 is

Equal masses of three liquids A, B and C have temperatures 10oC, 25oC and 40oC respectively. If A and B are mixed, the mixture has a temperature of 15oC. If B and C are mixed, the mixture has a temperature of 30oC,. If A and C are mixed the mixture will have a temperature of

A steel rod is 4.000 cm in diameter at 30ºC. A brass ring has an interior diameter of 3.992 cm at 30ºC. In order that the ring just slides onto the steel rod, the common temperature of the two should be nearly (αsteel = 11 × 10-6/ºC and αbrass = 19 × 10-6/ºC)

JEE Main & Advanced Mock Test Series 2026

JEE Main & Advanced Mock Test Series 2026

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

Let f(x) be a one-to-one function such that f(1) = 3, f(3) = 1, f '(1) = – 4 and f '(3) = 2. If g = f ^–1, then the slope of the tangent line to 1/g at x = 1 is

If g (x³ + 1) = x⁶ + x³ + 2, then the value of g(x² – 1) is

h(x) = {x},k(x) = 5^{log₂(x + 3)} then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to
[Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

If the function f (x) = ax e^–bx has a local maximum at the point (2, 10), then

Number of integral solutions of the equation

[Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

The area bounded by the curve y = x² + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

Number of roots of the equation x² –2x–log₂ |1 – x | = 3 is

is continuous at x = 0, then
[Note : {x} denotes fractional part of x.]

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)
If then the value of must be

The sum of all the real roots of the equations
|x − 2|² + |x − 2| − 2 = 0 is …..

If P_n = cosⁿ x + sinⁿ x, then 2.P₆ - 3.P₄ + 1 = ..

If x = 2 + t³, y = 3t² and is a constant then the value of 343n must be

The value of 49A + 5B, where A = 1 - log₇2 and B = - log₅ 4 is

A sound source S and observers O₁, O₂ are placed as shown. S is always at rest and O₁, O₂ start moving with velocity v₀ at t = 0. At any later instant, let f₁ and f₂ represent apparent frequencies of sound received by O₁ and O₂, respectively. The ratio f₁/f₂ is

Equal masses of three liquids A, B and C have temperatures 10^oC, 25^oC and 40^oC respectively. If A and B are mixed, the mixture has a temperature of 15^oC. If B and C are mixed, the mixture has a temperature of 30^oC,. If A and C are mixed the mixture will have a temperature of

A steel rod is 4.000 cm in diameter at 30ºC. A brass ring has an interior diameter of 3.992 cm at 30ºC. In order that the ring just slides onto the steel rod, the common temperature of the two should be nearly (α_steel= 11 × 10^-6/ºC and α_brass= 19 × 10^-6/ºC)