IAS (Admin.) Mains Mathematics: Questions 1 - 9 of 668
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Question 1
Explanation
- Here, from question given information is,
- As we know,
… (25 more equations) …
Question 2
Appeared in Year: 2003
Describe in Detail Subjective▾
Find the equations of the lines of intersection of the plane and the cone . (15 Marks)
EditExplanation
- Here, equations of the plane and cone are,
- Let the equation of the line of intersection of plan and the cone is…
… (237 more equations) …
Question 3
Describe in Detail Subjective▾
Prove that the plane cuts the cone in perpendicular lines, if . (15 marks)
EditExplanation
- Let the line of intersection of plane and cone is given as,
- Equation (1) lies on plane and cone,
… (77 more equations) …
Question 4
Explanation
- Given that
- Equation (1) can be simplified…
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Question 5
Explanation
- Here, given differential equation is,
… (79 more equations) …
Question 6
Appeared in Year: 2011
Describe in Detail Subjective▾
If be the potion vector of a point find the values of for which the vector is –
Irrotational
Solenoidal (15 marks)
EditExplanation
- Let, given position vector is,
… (266 more equations) …
Question 7
Appeared in Year: 2015
Describe in Detail Subjective▾
If is space of real matrices of order and is the space of real polynomials of degree at most 2, then find the matrix representation of , such that , with respect to the standard bases of and . Further find the null space of T. [CS (Main) Paper 1]
EditExplanation
- Standard basis of is
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Question 8
Appeared in Year: 2015
Describe in Detail Subjective▾
The vectors are linearly independent. Is it true? Justify your answer. [CS (Main) Paper 1]
EditExplanation
Given Vectors are
… (114 more equations) …
Question 9
Appeared in Year: 2016
Describe in Detail Subjective▾
Find the general integral of the partial differential equation
[CS (Main) Paper 2]
EditExplanation
- Given partial differential equation is
Auxiliary equations are
… (77 more equations) …