ICSE Class 12 Maths by Pavan | Practice Test to Test Your Knowledge
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

  2. Practice Tests
  3. ICSE Class 12 Maths
ICSE Class 12 Maths

ICSE Class 12 Maths

Thorough mock test covering Calculus, Probability, Linear Programming, and Coordinate Geometry. Contains both objective and subjective questions with varying difficulty levels.

2025-07-19
Pavan Pavan
ICSE Class 12 Grade 12 Mathematics

Duration

30 min

Questions

30

Marking

Negative

You've not yet enrolled in this practice test. Please login to start practice test.

Questions Preview

Which of the following is a reflexive relation?

A
For every element x in set A, (x, x) is in the relation
B
For every element x in set A, (x, y) is in the relation for some y
C
For every element x in set A, (y, x) is in the relation for some y
D
There is no relation between any pair of elements

Which of the following is an example of a symmetric relation?

A
If (a, b) is in the relation, then (b, a) is also in the relation
B
For all x, (x, x) is in the relation
C
If (a, b) is in the relation, then (a, c) is also in the relation
D
If (a, b) is in the relation, then (c, b) is also in the relation

Which of the following is a transitive relation?

A
If (a, b) and (b, c) are in the relation, then (a, c) must also be in the relation
B
If (a, b) is in the relation, then (b, a) is also in the relation
C
If (a, b) is in the relation, then (b, c) is in the relation
D
There is no relation between any pair of elements

Which of the following is an equivalence relation?

A
A relation that is reflexive, symmetric, and transitive
B
A relation that is only reflexive
C
A relation that is only symmetric
D
A relation that is only transitive

Which of the following is an onto function?

A
For every element in the range, there is at least one element in the domain that maps to it
B
Each element in the domain maps to exactly one element in the range
C
The function is not defined for some elements in the domain
D
None of the above

What is the inverse of the function f(x) = 2x + 3?

A
f⁻¹(x) = (x - 3) / 2
B
f⁻¹(x) = (x + 3) / 2
C
f⁻¹(x) = 2(x - 3)
D
f⁻¹(x) = 3(x - 2)

Which of the following is a characteristic of a one-to-one function?

A
Each element in the range is mapped by exactly one element in the domain
B
Each element in the domain is mapped to multiple elements in the range
C
There is no mapping between the domain and the range
D
Some elements in the range are not mapped by any element in the domain

Which of the following is an example of a binary operation?

A
Addition of two real numbers
B
Subtraction of a real number from an imaginary number
C
Finding the modulus of a complex number
D
Division of a number by zero

What is the domain of the inverse trigonometric function sin⁻¹(x)?

A
-1 ≤ x ≤ 1
B
-∞ < x < ∞
C
0 ≤ x ≤ π
D
0 ≤ x ≤ 2π

What is the range of the inverse trigonometric function tan⁻¹(x)?

A
-π/2 ≤ y ≤ π/2
B
0 ≤ y ≤ π
C
-π ≤ y ≤ π
D
-π/4 ≤ y ≤ π/4

Which of the following is true for the graph of the inverse function sin⁻¹(x)?

A
It is a reflection of the sine graph over the line y = x
B
It is a reflection of the cosine graph over the line y = x
C
It is a shifted version of the sine graph
D
It is an exponential function

What is the principal value branch of tan⁻¹(x)?

A
-π/2 ≤ y ≤ π/2
B
-π ≤ y ≤ π
C
0 ≤ y ≤ π
D
0 ≤ y ≤ 2π

Which of the following is the inverse trigonometric function of cos(x)?

A
cos⁻¹(x)
B
sin⁻¹(x)
C
tan⁻¹(x)
D
sec⁻¹(x)

What is the formula for the range of the inverse function cos⁻¹(x)?

A
0 ≤ y ≤ π
B
-π/2 ≤ y ≤ π/2
C
-π ≤ y ≤ π
D
0 ≤ y ≤ 2π

What is the range of the inverse trigonometric function sin⁻¹(x)?

A
-π/2 ≤ y ≤ π/2
B
-π ≤ y ≤ π
C
0 ≤ y ≤ π
D
0 ≤ y ≤ 2π

What is the value of sin⁻¹(1)?

A
π/2
B
0
C
π
D
-π/2

The inverse of sin(x) is defined for which values of x?

A
-1 ≤ x ≤ 1
B
-∞ < x < ∞
C
0 ≤ x ≤ 2π
D
0 ≤ x ≤ π

Which of the following is true for inverse trigonometric functions?

A
They are defined only for certain ranges of x
B
They are not continuous
C
They are only defined for angles between 0 and 360 degrees
D
They are not differentiable

What is the range of the inverse function tan⁻¹(x)?

A
-π/2 ≤ y ≤ π/2
B
0 ≤ y ≤ π
C
0 ≤ y ≤ 2π
D
-π ≤ y ≤ π

Which of the following is the inverse trigonometric function of cos(x)?

A
cos⁻¹(x)
B
sin⁻¹(x)
C
tan⁻¹(x)
D
sec⁻¹(x)

What is the range of the function cos⁻¹(x)?

A
0 ≤ y ≤ π
B
-π/2 ≤ y ≤ π/2
C
0 ≤ y ≤ 2π
D
-π ≤ y ≤ π

What is the formula for the inverse of cos(x)?

A
cos⁻¹(x) = π/2 - sin⁻¹(x)
B
cos⁻¹(x) = tan⁻¹(x)
C
cos⁻¹(x) = π/2 - tan⁻¹(x)
D
cos⁻¹(x) = π - sin⁻¹(x)

What is the formula for the inverse of tan(x)?

A
tan⁻¹(x) = π/2 - cos⁻¹(x)
B
tan⁻¹(x) = sin⁻¹(x)
C
tan⁻¹(x) = cos⁻¹(x)
D
tan⁻¹(x) = tan⁻¹(x)

What is the range of the inverse sine function sin⁻¹(x)?

A
-π/2 ≤ y ≤ π/2
B
0 ≤ y ≤ π
C
0 ≤ y ≤ 2π
D
-π ≤ y ≤ π

What is the principal value branch for sin⁻¹(x)?

A
-π/2 ≤ y ≤ π/2
B
0 ≤ y ≤ π
C
-π ≤ y ≤ π
D
0 ≤ y ≤ 2π

What is the value of cos⁻¹(0)?

A
π/2
B
π
C
0
D
1

What is the domain of the inverse function sec⁻¹(x)?

A
x ≥ 1 or x ≤ -1
B
0 ≤ x ≤ 1
C
-1 ≤ x ≤ 1
D
0 ≤ x ≤ 2π

What is the range of sec⁻¹(x)?

A
0 ≤ y ≤ π/2, π ≤ y ≤ 3π/2
B
0 ≤ y ≤ 2π
C
-π/2 ≤ y ≤ π/2
D
0 ≤ y ≤ π

What is the value of cos⁻¹(1)?

A
0
B
π/2
C
π
D
1

What is the value of sin⁻¹(1)?

A
π/2
B
0
C
1
D
π