IAS (Admin.) Mains Mathematics: Questions 1 - 9 of 668

Choose Programs:

📹 Video Course 2024 (36 Lectures [25 hrs : 50 mins]): Offline Support

Rs. 160.00 -OR-

1 Month Validity (Multiple Devices)

Preview All LecturesDetails

🎓 Study Material (212 Notes): 2024-2025 Syllabus

Rs. 250.00 -OR-

3 Year Validity (Multiple Devices)

Topic-wise Notes & SampleDetails

🎯 668 Questions (& PYQs) with Full Explanations (2024-2025 Exam)

Rs. 1150.00 -OR-

3 Year Validity (Multiple Devices)

CoverageDetailsSample Explanation

Help me Choose & Register (Watch Video) Already Subscribed?

Question 1

Describe in Detail Subjective▾

If . Then find

Edit

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)

Edit

Explanation

  • 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)

Edit

Explanation

  • Let the line of intersection of plane and cone is given as,

  • Equation (1) lies on plane and cone,

… (77 more equations) …

Question 4

Describe in Detail Subjective▾

Solve Differential Equation:

Edit

Explanation

  • Given that

  • Equation (1) can be simplified…

… (35 more equations) …

Question 5

Describe in Detail Subjective▾

Solve:

Edit

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)

Edit

Explanation

  • 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]

Edit

Explanation

  • Standard basis of is

… (141 more equations) …

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]

Edit

Explanation

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]

Edit

Explanation

  • Given partial differential equation is

    Auxiliary equations are

… (77 more equations) …