Optionals IAS Mains Mathematics: Questions 130 - 136 of 283

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Question 130

Appeared in Year: 2013

Describe in Detail

Essay▾

Solve

Where D and D՚ denote and . (CS Paper 2)

Explanation

Given

A. E is

Hence, complementary function

Now,

Hence, the solution of (1) is

Question 131

Appeared in Year: 2013

Describe in Detail

Essay▾

In an Examination, the number of students who obtained marks between certain limits were given in the following table:

Table Shows the Number of Students and Marks
Marks
No. of Students

Using Newton Forward interpolation formula, find the Number of Students whose marks lie between 45 and 50. (CS Paper 2)

Explanation

Rearranging the term of the table and preparing cumulative Frequency table, we have

Shows the Preparing Cumulative Frequency Table
Marks less thanNo. of Students

The forward Difference table is

Shows the Forward Difference Table

Here

By Newton՚s forward difference formula, we have,

Number of Students, getting works between

… (2 more words) …

Question 132

Appeared in Year: 2014

Describe in Detail

Essay▾

Solve the Partial Differential Equation

(CS Paper 2)

Explanation

Given Differential Equation is

Auxiliary equation is

C. F.

Where being arbitrary functions

Now P. I

Hence, the required solution is

Question 133

Edit

Appeared in Year: 2012

Describe in Detail

Essay▾

Solve the following system of simultaneous equations, using Gauss- Seidel Iterative method: (CS Paper 2)

Explanation

Sol: The Given system of linear equations is

According to Gauss – Seidel Method, the approximation to unknowns are given by

Let us take the initial approximation to each unknown as zero

i.e..

Iteration (1)

Iteration (2)

Iteration (3)

Iteration (4)

Iteration (5)

We observe in 4th and 5th iterations, there is no change in approximations, therefore we stop …

… (11 more words) …

Question 134

Appeared in Year: 2011

Describe in Detail

Essay▾

Using the method of variation of parameter, solve the second order differential

(CS Paper 1)

Explanation

Given,

Symbolic form is

Auxiliary equation of (2) is

Complementary function of (1) is

Where and being arbitrary constants

Let and

Here

Then, P. I

P. I

P. I

Hence, the general solution of (1) is

Question 135

Appeared in Year: 2012

Describe in Detail

Essay▾

Using Laplace transforms, solve the initial value

(CS Paper 1)

Explanation

Given Differential equation is

S. F is

Taking Laplace transform of the equation, we get

Putting

Now,

And

Question 136

Appeared in Year: 2015

Describe in Detail

Essay▾

Obtain the equation of the plane passing through the points and parallel to X axis. (CS Paper 1)

Explanation

The Equation of plane passing through is

This passes through the point

The plane (1) is parallel to the line

Therefore, normal to the plane is perpendicular to the line

Solving (2) and (3) we get

Substituting the value of in (1) , we get

This is the required equation of plane.