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100+ Free Kerala Plus Two Mathematics (DHSE) Practice Questions

Kerala Higher Secondary (Plus Two / Class 12) Mathematics under the Directorate of Higher Secondary Education (DHSE), Kerala practice questions are available now; exam metadata is being verified.

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2026 Statistics

Key Facts: Kerala Plus Two Mathematics (DHSE) Exam

100 marks

Subject total via TE + CE (typically no PE; exact splits as notified)

DHSE Kerala Plus Two assessment pattern

~2.5 h + cool-off

Typical Mathematics theory duration for non-practical subjects

DHSE Plus Two timetable logistics

D+ / ~30%

Common pass grade/aggregate with separate TE floor

Kerala Plus Two grading / pass criteria reporting

TE + CE

Official format is mixed written TE plus CE, not pure MCQ

DHSE Kerala Plus Two Mathematics assessment pattern

English MCQ adaptation

This free local bank is not the official mixed paper format

OpenExamPrep practice policy

DHSE Kerala

Administrator: Directorate of Higher Secondary Education

Government of Kerala Higher Secondary system

Kerala Plus Two Mathematics (DHSE) totals 100 marks via TE + CE (typically no PE); theory is commonly ~2.5 h plus cool-off. Pass is commonly D+/~30% aggregate with ~30% in TE separately as notified. Fees are paid through schools. This free 2026 bank is an English MCQ study adaptation — not an official paper simulation.

Sample Kerala Plus Two Mathematics (DHSE) Practice Questions

Try these sample questions to test your Kerala Plus Two Mathematics (DHSE) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Let A = {1, 2, 3, 4} and R = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1)}. Then R is:
A.reflexive only
B.symmetric only
C.reflexive and symmetric but not transitive
D.an equivalence relation
Explanation: R includes all diagonal pairs, so it is reflexive. (1,3) and (3,1) are both present, so it is symmetric. Compositions involving only 1 and 3 stay in R, so R is transitive — an equivalence relation with classes {1,3}, {2}, {4}.
2The number of binary relations on a set with 2 elements is:
A.4
B.8
C.16
D.32
Explanation: A set with n elements has n squared ordered pairs. Each may or may not belong to a relation, so there are 2 to the power n squared relations. For n=2, 2^4 = 16.
3Let f: R to R be defined by f(x) = 2x + 5. Then f is:
A.one-one but not onto
B.onto but not one-one
C.both one-one and onto
D.neither one-one nor onto
Explanation: If f(x1)=f(x2) then 2x1+5=2x2+5 implies x1=x2, so one-one. For any y in R, x=(y-5)/2 is a preimage, so onto. Hence f is bijective.
4If f(x) = 3x + 1 and g(x) = x squared - 2, then (g compose f)(1) equals:
A.7
B.14
C.2
D.-1
Explanation: f(1)=3(1)+1=4. Then g(f(1))=g(4)=16-2=14.
5Let A = {1, 2, 3, 4} and B = {a, b, c}. The number of onto functions from A to B is:
A.24
B.81
C.36
D.6
Explanation: By inclusion-exclusion: 3^4 - C(3,1)*2^4 + C(3,2)*1^4 = 81 - 48 + 3 = 36. Equivalently 3! * S(4,3) = 6*6 = 36.
6If f: R to R is defined by f(x) = 4x - 7, then f inverse of x is:
A.(x - 7)/4
B.4x + 7
C.(7 - x)/4
D.(x + 7)/4
Explanation: Set y = 4x - 7 so x = (y+7)/4. Swapping variables, f inverse(x) = (x+7)/4.
7A relation R on Z defined by a R b iff a - b is divisible by 3 is:
A.reflexive only
B.symmetric only
C.an equivalence relation
D.neither reflexive nor symmetric
Explanation: a-a=0 is divisible by 3 so reflexive. If 3 divides (a-b) then 3 divides (b-a) so symmetric. If 3 divides (a-b) and (b-c) then 3 divides (a-c) so transitive. Congruence mod 3 is an equivalence relation.
8If f(x) = cos x and g(x) = x/2, then (f compose g)(pi/3) equals:
A.1/2
B.sqrt(3)/2
C.0
D.1
Explanation: g(pi/3)=pi/6. Then f(g(pi/3))=cos(pi/6)=sqrt(3)/2.
9The principal value of cos inverse(1/2) is:
A.pi/6
B.pi/3
C.pi/4
D.2pi/3
Explanation: cos inverse maps [-1,1] to [0,pi]. cos(pi/3)=1/2, so cos inverse(1/2)=pi/3.
10The domain of f(x) = sin inverse(2x - 3) is:
A.[0, 1]
B.[1, 2]
C.[-1, 1]
D.[2, 3]
Explanation: Need -1 <= 2x-3 <= 1 so 2 <= 2x <= 4 so 1 <= x <= 2. Domain is [1,2].

About the Kerala Plus Two Mathematics (DHSE) Practice Questions

Verified exam format metadata for Kerala Higher Secondary (Plus Two / Class 12) Mathematics under the Directorate of Higher Secondary Education (DHSE), Kerala is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.