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Questions and Answers
Which of the following statements is true for the function (f(x) = \begin{cases} x^2 + 3, & x \neq 0 \\ 1, & x = 0 \end{cases}) ?
Which of the following statements is true for the function (f(x) = \begin{cases} x^2 + 3, & x \neq 0 \\ 1, & x = 0 \end{cases}) ?
Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Then, this function f(x) is strictly increasing in (a, b) if
Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Then, this function f(x) is strictly increasing in (a, b) if
If (\begin{bmatrix} x + 5y & 2 \\ x & y \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}), then the value of (\left(\frac{24}{x} + \frac{24}{y}\right)) is:
If (\begin{bmatrix} x + 5y & 2 \\ x & y \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}), then the value of (\left(\frac{24}{x} + \frac{24}{y}\right)) is:
If a matrix has 36 elements, the number of possible orders it can have, is:
If a matrix has 36 elements, the number of possible orders it can have, is:
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The integrating factor of the differential equation ((1-x^2)\frac{dy}{dx} + xy = ax, -1 < x < 1), is:
The integrating factor of the differential equation ((1-x^2)\frac{dy}{dx} + xy = ax, -1 < x < 1), is:
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If the direction cosines of a line are (\sqrt{3}k, \sqrt{3}k, \sqrt{3}k), then the value of k is:
If the direction cosines of a line are (\sqrt{3}k, \sqrt{3}k, \sqrt{3}k), then the value of k is:
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A linear programming problem deals with the optimization of a/an:
A linear programming problem deals with the optimization of a/an:
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If (P(A|B) = P(A'|B)), then which of the following statements is true?
If (P(A|B) = P(A'|B)), then which of the following statements is true?
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The order and degree of the differential equation (\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}} = \frac{d^2y}{dx^2}) are:
The order and degree of the differential equation (\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}} = \frac{d^2y}{dx^2}) are:
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The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is:
The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is:
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The distance of point P(a, b, c) from y-axis is:
The distance of point P(a, b, c) from y-axis is:
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The number of corner points of the feasible region determined by constraints (x \ge 0, y \ge 0, x + y \ge 4) is:
The number of corner points of the feasible region determined by constraints (x \ge 0, y \ge 0, x + y \ge 4) is:
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If A and B are two non-zero square matrices of the same order such that ((A + B)^2 = A^2 + B^2), then:
If A and B are two non-zero square matrices of the same order such that ((A + B)^2 = A^2 + B^2), then:
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Study Notes
General Instructions
- This document contains 38 compulsory questions
- The document is divided into 5 sections (A, B, C, D, and E)
- Section A consists of multiple choice questions (MCQs) and Assertion-Reason based questions
- Section B consists of very short answer (VSA) type questions
- Section C consists of short answer (SA) type questions
- Section D consists of long answer (LA) type questions
- Section E consists of case study based questions
- No overall choice is provided
- Internal choices are provided in some questions within each section
- Calculators are not allowed
Section A - Multiple Choice Questions
- Questions 1-18 are multiple choice questions (MCQs) with 1 mark each
- Question 1: A function f: Rn → R (Rn = set of non-negative real numbers) defined by f(x) = 4x+3 is one-one and onto
- Question 2: If a matrix has 36 elements, its possible orders are 3 × 12, 4 × 9 or 6 × 6
- Multiple problems follow with options
Section B - Very Short Answer Questions
- Questions 21-25 are very short answer (VSA) type questions, carrying 2 marks each
- Internal choices are provided
Section C - Short Answer Questions
- Questions 26-31 are short answer (SA) type questions, carrying 3 marks each
- Internal choices are provided
Section D - Long Answer Questions
- Questions 32-35 are long answer (LA) type questions, carrying 5 marks each
- Internal choices are provided
Section E - Case Study Questions
- Questions 36-38 are case study questions, carrying 4 marks each
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Description
This quiz comprises 38 compulsory questions, divided into five sections: MCQs, very short answers, short answers, long answers, and case studies. It covers various mathematical concepts, testing understanding and application across different question formats. Calculators are not allowed, emphasizing the need for mental agility.
