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Questions and Answers
What are the coordinates of point E based on the feasible solution graph?
What are the coordinates of point E based on the feasible solution graph?
What is the maximum value of Z if Z = 500x + 150y?
What is the maximum value of Z if Z = 500x + 150y?
If the function f(x) is differentiable in the interval (0, 12), what should hold true for its derivative?
If the function f(x) is differentiable in the interval (0, 12), what should hold true for its derivative?
Given that 6 is the critical point of the function, which condition must be satisfied for the constant m?
Given that 6 is the critical point of the function, which condition must be satisfied for the constant m?
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In the interval (0, 12), if a function is strictly increasing, what can be said about its derivative?
In the interval (0, 12), if a function is strictly increasing, what can be said about its derivative?
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Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}?
Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}?
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Identify the type of matrix represented by A = \[\begin{bmatrix} 1 & 2 \ 2 & 1 \end{bmatrix}\]?
Identify the type of matrix represented by A = \[\begin{bmatrix} 1 & 2 \ 2 & 1 \end{bmatrix}\]?
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Which of the following is not a possible ordered pair for a matrix of 6 elements?
Which of the following is not a possible ordered pair for a matrix of 6 elements?
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What is the formula for calculating the inverse of a matrix?
What is the formula for calculating the inverse of a matrix?
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Determine the nature of the function f(x) = x^3 - 3x^2 + 4x on R.
Determine the nature of the function f(x) = x^3 - 3x^2 + 4x on R.
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What is the probability of selecting a person who drives a scooter from the group of insured individuals?
What is the probability of selecting a person who drives a scooter from the group of insured individuals?
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Given the probabilities of accidents among drivers, which driver has the highest probability of meeting with an accident?
Given the probabilities of accidents among drivers, which driver has the highest probability of meeting with an accident?
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If both A and B independently attempt to solve a problem, what is the probability that at least one of them successfully solves it?
If both A and B independently attempt to solve a problem, what is the probability that at least one of them successfully solves it?
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From the given data, what is the probability that exactly one of A or B solves the problem?
From the given data, what is the probability that exactly one of A or B solves the problem?
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What is the needed semi-vertical angle of a cone with maximum volume given its slant height?
What is the needed semi-vertical angle of a cone with maximum volume given its slant height?
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How many people among the insured drive a car?
How many people among the insured drive a car?
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If the coordinates of a triangle's vertices are (1,0), (2,2), and (3,1), what is the area bounded by this triangle?
If the coordinates of a triangle's vertices are (1,0), (2,2), and (3,1), what is the area bounded by this triangle?
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Which matrix represents the coefficients of the system of equations related to A in the second part of the question?
Which matrix represents the coefficients of the system of equations related to A in the second part of the question?
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What is the value of P(X = 3) for the discrete random variable X where P(X = 0) = 0, P(X = 1) = \frac{1}{4}, and P(X = 2) = \frac{1}{4}?
What is the value of P(X = 3) for the discrete random variable X where P(X = 0) = 0, P(X = 1) = \frac{1}{4}, and P(X = 2) = \frac{1}{4}?
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What is the area of the triangle with vertices at (0, 1), (0, 2), and (1, 5)?
What is the area of the triangle with vertices at (0, 1), (0, 2), and (1, 5)?
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Which option correctly states the reverse law of transposes?
Which option correctly states the reverse law of transposes?
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If the objective function z = ax + by has the same maximum value at two corner points of a feasible region, how many points can Zmax occur?
If the objective function z = ax + by has the same maximum value at two corner points of a feasible region, how many points can Zmax occur?
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In the assertion A regarding the relation R in a set of human beings, what can be inferred about its symmetry?
In the assertion A regarding the relation R in a set of human beings, what can be inferred about its symmetry?
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What does it mean if a mapping is not surjective?
What does it mean if a mapping is not surjective?
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How do you differentiate sin^2 x with respect to e^cos x?
How do you differentiate sin^2 x with respect to e^cos x?
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What is the area of the region bounded by the curve y = x^2 and the line y = 2 in the first quadrant?
What is the area of the region bounded by the curve y = x^2 and the line y = 2 in the first quadrant?
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What is the value of k for the function f(x) to be continuous at x = \frac{\pi}{2}?
What is the value of k for the function f(x) to be continuous at x = \frac{\pi}{2}?
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What is the correct integral of the expression 3e^{x} + 2\frac{(\log x)}{3x}?
What is the correct integral of the expression 3e^{x} + 2\frac{(\log x)}{3x}?
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In the expression ∫a^b^f(y), what is y referred to?
In the expression ∫a^b^f(y), what is y referred to?
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What is the result of the integral provided by \int_{3}^{7}{\sin t - 2\cos t\text{ dt}}?
What is the result of the integral provided by \int_{3}^{7}{\sin t - 2\cos t\text{ dt}}?
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What is the general solution of the differential equation \frac{dy}{dx} = \frac{3secy}{2\text{cosec} x}?
What is the general solution of the differential equation \frac{dy}{dx} = \frac{3secy}{2\text{cosec} x}?
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What is the degree of the differential equation \frac{d^{2}y}{dx^{2}} + 5\cot\left( \frac{dy}{dx} \right)?
What is the degree of the differential equation \frac{d^{2}y}{dx^{2}} + 5\cot\left( \frac{dy}{dx} \right)?
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What is the magnitude of the vector \overset{\rightarrow}{a} = \overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k}?
What is the magnitude of the vector \overset{\rightarrow}{a} = \overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k}?
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Which of the following statements regarding direction ratios and direction cosines of a line is incorrect?
Which of the following statements regarding direction ratios and direction cosines of a line is incorrect?
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Evaluate the integral $\int \tan^4 x , dx$. What is the general representation for the result?
Evaluate the integral $\int \tan^4 x , dx$. What is the general representation for the result?
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What is the area of a parallelogram with adjacent sides represented by the vectors $\overset{\land}{i} + 2\overset{\land}{j} - \overset{\land}{k}$ and $2\overset{\land}{j} + \overset{\land}{k}$?
What is the area of a parallelogram with adjacent sides represented by the vectors $\overset{\land}{i} + 2\overset{\land}{j} - \overset{\land}{k}$ and $2\overset{\land}{j} + \overset{\land}{k}$?
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Determine the value of $p$ that makes the lines $\frac{1 - x}{3} = \frac{7y - 14}{2p} = \frac{z - 3}{2}$ and $\frac{7 - 7x}{3p} = \frac{y - 5}{1} = \frac{6 - z}{5}$ orthogonal.
Determine the value of $p$ that makes the lines $\frac{1 - x}{3} = \frac{7y - 14}{2p} = \frac{z - 3}{2}$ and $\frac{7 - 7x}{3p} = \frac{y - 5}{1} = \frac{6 - z}{5}$ orthogonal.
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Solve the differential equation $\frac{dy}{dx} = x^5 \tan^{-1}(x^3)$. What is its general solution?
Solve the differential equation $\frac{dy}{dx} = x^5 \tan^{-1}(x^3)$. What is its general solution?
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Evaluate $\int_{0}^{\frac{\pi}{4}} \log(1 + \tan x) , dx$. What is the expected result?
Evaluate $\int_{0}^{\frac{\pi}{4}} \log(1 + \tan x) , dx$. What is the expected result?
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What area does the parabola $y^2 = 4ax$ and the line $y = mx$ enclose?
What area does the parabola $y^2 = 4ax$ and the line $y = mx$ enclose?
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Determine if the relation $R = {(a, b): a \in \mathbb{Z},, (a - b) \text{ is divisible by } 5}$ is an equivalence relation. What property does it not satisfy?
Determine if the relation $R = {(a, b): a \in \mathbb{Z},, (a - b) \text{ is divisible by } 5}$ is an equivalence relation. What property does it not satisfy?
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Find the shortest distance between the lines represented by the vector equations $\overset{\rightarrow}{r} = (1 - t)\overset{\land}{i} + (t - 2)\overset{\land}{j} + (3 - 2t)\overset{\land}{k}$ and $\overset{\rightarrow}{r} = (s + 1)\overset{\land}{i} + (2s - 1)\overset{\land}{j} + (2s + 1)\overset{\land}{k}$.
Find the shortest distance between the lines represented by the vector equations $\overset{\rightarrow}{r} = (1 - t)\overset{\land}{i} + (t - 2)\overset{\land}{j} + (3 - 2t)\overset{\land}{k}$ and $\overset{\rightarrow}{r} = (s + 1)\overset{\land}{i} + (2s - 1)\overset{\land}{j} + (2s + 1)\overset{\land}{k}$.
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Study Notes
Section A - Multiple Choice Questions
- Question 1: Which relation is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}? Options provided.
- Question 2: The matrix A = [[2, 1], [1, 2]] is a/an... Options provided. (Symmetric matrix)
- Question 3: Which ordered pair is not possible for a 6-element matrix? Options provided.
- Question 4: The formula for calculating the inverse of a matrix.
- Question 5: The value of ∫2sin(cosx) dx. Options provided.
- Question 6: The nature of the function f(x) = x³ - 3x² + 4x on R. Options provided. (Increasing and decreasing)
- Question 7: A function f(x) is continuous at x = π/2. Given f(x) is defined. Options provided.
- Question 8: The integral of 3ex+2(logx). Options provided.
- Question 9: Definition of a term in a math equation. Options provided.
- Question 10: Integral of a trigonometric function. Options provided.
- Question 11: General solution of a differential equation. Options provided.
- Question 12: Degree of a differential equation. Options provided.
- Question 13: Magnitude of a vector. Options provided.
- Question 14: A math relationship concerning direction ratios. Options provided.
- Question 15: The value of P(X = 3) with discrete random variable data. Options provided.
- Question 16: Area of a triangle with given vertices. Options provided.
- Question 17: The reverse law of transposes. Options provided.
- Question 18: The number of corner points in an LP problem where objective function has the same maximum value. Options provided.
Section B - Very Short Answer Questions
- Question 21: Differentiate sin²x w.r.t. ecosx.
- Question 22: Find the area bounded by y = x² and y = 2 (first quadrant).
- Question 23: Evaluate ∫tanx dx.
- Question 24: Calculate the area of a parallelogram with given vectors.
- Question 25: Find 'p' so that two lines are orthogonal.
Section C - Short Answer Questions
- Question 26: Solve the differential equation related to tan⁻¹(x³). OR Solve the differential equation dy - (1-2y)/ (3x+1) = 0
- (More questions likely on derivatives, integrals, geometry of curves, calculus, and differential equations.)
Section D - Long Answer Questions
- Question 32: Show that the semi-vertical angle of a cone is tan⁻¹√2.
- Question 33: Find the inverse of matrix A. [Matrix given].
- Question 34: Find the area of a triangle with given vertices.
- Question 35: Problem related to probability - find the probability.... OR Find the distance.... (More questions on calculus, probability, matrices, etc.). (Options provided)
Section E - Case Study Questions
- Question 36: Problem on the probabilities of accidents based on people with different modes of transport. Subparts related to car drivers, scooter drivers etc. probability of accident in a specific type of driver.
- Question 37: Feasible solutions of an LP problem based on graph. Finding equations, coordinates, and maximum value. OR finding probability - problem based on probability of events.
- Question 38: Temperature function problem in a given interval using calculus. Finding the intervals where the function is increasing or decreasing. (Options provided)
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Test your knowledge on various mathematical concepts including symmetric relations, matrices, integrals, and function behavior. This quiz covers essential topics and will help reinforce your understanding of math. Dive in to see how well you can answer these challenging questions!
