Examination Overview and Instructions

Let f: R → R be the functions defined by f(x) = x³ + 5. Then f⁻¹(x) is

The domain of the function defined by f(x) = Sin(√x − 1) is

Find the positive integer n in lim (x→3) (x−3)/((x²−9)) = 108. a)

Find the value of sec²(tan⁻¹(2)) + cosec²(cot⁻¹(3))

If tan⁻¹(2x) + tan⁻¹(3x) = π/4, then x is

If 0 |x y z| 5 = 6 |0 0 w|, then the values of x, y, z and w respectively are

If A² – A + I = O, then the inverse of A is

If the points (3, -2), (x, 2), (8, 8) are co-linear, find the value of x.

Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).

If xy + yx = 16, then the value of d/dx at (2, 2) is

If y = (tan x)sin x, then dy/dx is equal to

It is given that at x = 1, the function x⁴ – 62x² + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a.

The area of a right-angled triangle with a given hypotenuse is maximum when the triangle is

Examination Overview

Examination Date: October 6, 2023
Total Marks: 100
Examination Duration: 90 minutes (1.5 hours)
Initial Reading Time: 15 minutes (not allowed to write)

General Instructions

Clearly write Registration Number on the Answer Booklet.
First 15 minutes reserved for reviewing the question paper and instructions; no writing permitted.
Structure of Paper:
- Part I: 70 multiple choice questions (1 mark each).
- Part II: 10 short answer questions (3 marks each).
All questions are compulsory.
Responses must be exclusively on the provided Answer Booklet; writing on question papers is prohibited.
Correct numbering for Part, Section, and Question is necessary for evaluation.
Start each Part on a new page of the Answer Booklet.
Avoid tearing off any pages from the Answer Booklet or Question Paper.
Hand in the Answer Booklet to the Invigilator before leaving.

Structure of Part I: Multiple Choice Questions

Contains 70 questions specifically focused on Mathematics.
Each question requires selection of the correct answer, to be noted in the Answer Booklet.
Incorrect formatting, such as double writing or smudged answers, may lead to non-evaluation.

Mathematics Questions Preview

Examples of types of questions include function inverses, limits, trigonometric identities, systems of equations, determinant applications, and properties of geometric shapes.
Key mathematical concepts include:
- Functions: Understanding of inverses and domains.
- Limits: Calculation and determination of specific variable values.
- Trigonometry: Evaluation of angles and identities.
- Geometry: Application of concepts such as area in relation to triangle types.

Important Reminder

The paper consists of 13 printed pages in total, including instruction and question sections.

Closing Note

Good luck to all candidates! Prepare thoroughly, focusing on key mathematical principles and problem-solving techniques.

This quiz provides an overview of the upcoming examination scheduled for October 6, 2023. It outlines the structure, types of questions, and important instructions to ensure proper conduct during the exam. Familiarize yourself with the guidelines to maximize your performance.