Class 12 Maths Most Expected Questions; Download PDF Here

CBSE Class 12 Maths Most Expected Questions presents a true representation of the exam pattern for the students going to appear in the final examination. As per the CBSE Date Sheet 2025 released by the Central Board of Secondary Education at its official website, the CBSE Class 12 Mathematics Exam 2025 is scheduled to be conducted on March 08, 2025.

All the students who are to appear in the Mathematics exam must now complete their preparations for the exam by going through the CBSE Class 12 Mathematics Most Expected Questions mentioned in the article below.

CBSE Class 12 Maths Exam Pattern 2025

The CBSE Class 12 Mths Exam Pattern 2025 is listed below in the table so that all the students who are to appear in the final exam can complete their preparations and have a better understanding of the exam. Check the Class 12 Mathematics Exam Pattern 2025 here:

CBSE Class 12 Maths Marking Scheme 2024-25

The students who are to appear in the Class 12 Mathematics exam need to have an understanding of the CBSE Class 12 Maths Making Scheme 2024-25 as detailed below:

Class 12 Mathematics Most Expected Questions

Q1. A function 𝒇:𝑹→R defined as 𝒇(𝒙)= x²−𝟒𝒙+𝟓 is :
(a) injective but not surjective
(b) surjective but not injective
(c) both injective and surjective
(d) neither injective nor surjective
S1. Ans.(d)
Sol. Given, 𝑓(𝑥)= x²−4𝑥+5
Here 𝑓(0)=𝑓(4)=5
Hence, 𝑓(𝑥) is not one-one.
To check whether the function is onto or not, we have to find range of function.
Let 𝑦= x²−4𝑥+5⇒ x²−4𝑥+5−𝑦=0
∴𝐷=(4)²−4(1)(5−𝑦)≥0 ∀𝑥∈𝑅
⇒16−20+4𝑦≥0⇒4𝑦−4≥0
⇒4(𝑦−1)≥0⇒𝑦≥1
Here, range =(1,∞)
Here, Co-domain ≠ Range
So, 𝑓(𝑥) is not onto.
{∵ If for a function co-domain ≠ range, then the function is not onto.}

Q2. Check if the relation R in the set ℝ 𝐨𝐟 𝐫𝐞𝐚𝐥 𝐧𝐮𝐦𝐛𝐞𝐫𝐬 𝐝𝐞𝐟𝐢𝐧𝐞𝐝 𝐚𝐬 𝑹={(𝒂,𝒃):𝒂<𝒃} is (i) symmetric,
(ii) transitive
Sol. We have, 𝑅={(𝑎,𝑏):𝑎<𝑏}, where 𝑎,𝑏∈ℝ
(i) Symmetric: Let (𝑥,𝑦)∈𝑅,𝑖.𝑒.,𝑥𝑅𝑦.
⇒𝑥<𝑦
But 𝑦≮𝑥,so(𝑥,𝑦)∈𝑅⇒(𝑦,𝑥)∉𝑅
Thus, 𝑅 is not symmetric.
(ii) Transitive: Let (𝑥,𝑦),(𝑦,𝑧)∈𝑅
⇒𝑥<𝑦 and 𝑦<𝑧⇒𝑥<𝑧
⇒(𝑥,𝑧)∈𝑅. Thus, 𝑅 is transitive.

Q3. If A is a square matrix such that A²=𝑰, then find the simplified value 𝐨𝐟 (𝑨−𝑰)³+(𝑨+𝑰)³−𝟕𝑨.

Sol. Given, A²=𝑰
∴ The simplified value of (𝐴−𝐼)³+(𝐴+𝐼)³−7𝐴
=𝐴³−𝐼³−3𝐴²𝐼+3𝐴𝐼²+𝐴³+𝐼³+3𝐴²𝐼+3𝐴𝐼²−7𝐴
=2𝐴³+6𝐴𝐼²−7𝐴=2𝐴𝐴²+6𝐴𝐼−7𝐴
=2𝐴𝐼+6𝐴−7𝐴=2𝐴−𝐴=𝐴
{∵𝐼⋅𝐴=𝐴⋅𝐼=𝐴 and 𝐴²=𝐼}

CBSE Class 12 Mathematics Most Expected Questions – Click to Download

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