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Consider the following statements
I. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.
II. If T(x, y) = 0 is the equation of the tac-locus, then
T(x, y ) is a factor of the P-discriminant.
III. T(x, y ) is a factor of a c-discriminant.
IV. Cusp-locus has two distinct tangent.
Choose the correct answer.
I. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.
II. If T(x, y) = 0 is the equation of the tac-locus, then
T(x, y ) is a factor of the P-discriminant.
III. T(x, y ) is a factor of a c-discriminant.
IV. Cusp-locus has two distinct tangent.
Choose the correct answer.
- a)Only I is true
- b)I, II and IV are true
- c)All are true
- d)No one is true
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider the following statementsI. A singular solution of differentia...
I. A singular solution of a differential equation satisfies the differential equation but is not a particular solution of the equation.
A singular solution of a differential equation is a solution that cannot be obtained from the general solution by specifying values for any arbitrary constants. It satisfies the differential equation, but it is not a particular solution because it does not correspond to any specific initial conditions or boundary conditions. Therefore, statement I is true.
II. If T(x, y) = 0 is the equation of the tac-locus, then T(x, y) is a factor of the P-discriminant.
The tac-locus is the locus of points where the tangent to a given curve is parallel to a given line. If T(x, y) = 0 is the equation of the tac-locus, it means that the curve satisfies the condition of having a parallel tangent to the given line. The P-discriminant is a discriminant that determines the nature of the points on a curve. If T(x, y) = 0 is the equation of the tac-locus, then T(x, y) must be a factor of the P-discriminant. Therefore, statement II is true.
III. T(x, y) is a factor of a c-discriminant.
The c-discriminant is a discriminant that determines the nature of the critical points on a curve. There is no direct relationship between the tac-locus equation T(x, y) = 0 and the c-discriminant. Therefore, statement III is false.
IV. Cusp-locus has two distinct tangents.
A cusp is a point on a curve where the curve has a sharp corner or a point of self-intersection. At the cusp point, the curve has two distinct tangents that are not parallel to each other. Therefore, statement IV is true.
Based on the explanations above, we can conclude that statements I, II, and IV are true. Therefore, the correct answer is option 'B'.
A singular solution of a differential equation is a solution that cannot be obtained from the general solution by specifying values for any arbitrary constants. It satisfies the differential equation, but it is not a particular solution because it does not correspond to any specific initial conditions or boundary conditions. Therefore, statement I is true.
II. If T(x, y) = 0 is the equation of the tac-locus, then T(x, y) is a factor of the P-discriminant.
The tac-locus is the locus of points where the tangent to a given curve is parallel to a given line. If T(x, y) = 0 is the equation of the tac-locus, it means that the curve satisfies the condition of having a parallel tangent to the given line. The P-discriminant is a discriminant that determines the nature of the points on a curve. If T(x, y) = 0 is the equation of the tac-locus, then T(x, y) must be a factor of the P-discriminant. Therefore, statement II is true.
III. T(x, y) is a factor of a c-discriminant.
The c-discriminant is a discriminant that determines the nature of the critical points on a curve. There is no direct relationship between the tac-locus equation T(x, y) = 0 and the c-discriminant. Therefore, statement III is false.
IV. Cusp-locus has two distinct tangents.
A cusp is a point on a curve where the curve has a sharp corner or a point of self-intersection. At the cusp point, the curve has two distinct tangents that are not parallel to each other. Therefore, statement IV is true.
Based on the explanations above, we can conclude that statements I, II, and IV are true. Therefore, the correct answer is option 'B'.
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Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer?
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Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer?.
Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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ample number of questions to practice Consider the following statementsI. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.II. If T(x, y) = 0 is the equation of the tac-locus, thenT(x, y ) is a factor of the P-discriminant.III. T(x, y ) is a factor of a c-discriminant.IV. Cusp-locus has two distinct tangent.Choose the correct answer.a)Only I is trueb)I, II and IV are truec)All are trued)No one is trueCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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