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Differential Equations - 13 - Mathematics MCQ


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20 Questions MCQ Test - Differential Equations - 13

Differential Equations - 13 for Mathematics 2024 is part of Mathematics preparation. The Differential Equations - 13 questions and answers have been prepared according to the Mathematics exam syllabus.The Differential Equations - 13 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equations - 13 below.
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Differential Equations - 13 - Question 1

The function f defined by f(x) - x [1 + 1/3 sin (log x2)], a ≠ 0,/(0) = 0 ([] represents the greatest integer function) is

Detailed Solution for Differential Equations - 13 - Question 1


and sin (-∞) can be any value between - 1 and 1

The value of integral part can also become ∞, but in all cases
  due to factor x in it.
f'(x) does not exist because
f' (x) for x is 1 but integral value which is its coefficient changes to give different values.

Differential Equations - 13 - Question 2

If f is twice differentiable function such that f ''(x) = - f(x), f '(x) = g(x) and h(x) = [f(x)]2 + [g(x)]2, also if h(5) = 11, then h(10) is equal to

Detailed Solution for Differential Equations - 13 - Question 2



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Differential Equations - 13 - Question 3

The solution of the equation 

Detailed Solution for Differential Equations - 13 - Question 3

  ........(i)
Let 3x - 4y = v

Putting in given D.E. (i) we get 


Differential Equations - 13 - Question 4

The solution of 

Detailed Solution for Differential Equations - 13 - Question 4



  .....(i)




Differential Equations - 13 - Question 5

The solution of the differential equation 

Detailed Solution for Differential Equations - 13 - Question 5

 ....(i)

Differential Equations - 13 - Question 6

The solution of the differential equation y(2xy + ex)dx - exdy = 0 is

Detailed Solution for Differential Equations - 13 - Question 6

y(2xy + ex)dx - exdy = 0  ....(0i)





Differential Equations - 13 - Question 7

The solution of the differential equation 

Detailed Solution for Differential Equations - 13 - Question 7


Differential Equations - 13 - Question 8

The half-life of a radioactive substance is the time required for one-half of that substance to decay. The amount of 11C, an isotope of carbon present at a future time t (in months) is given by A(t) = 100 exp [- 0.0338 t]. The half life of the material in months is

Detailed Solution for Differential Equations - 13 - Question 8


Differential Equations - 13 - Question 9

Consider a pair of differential equations 
Eliminating t in the two equations results in 

Detailed Solution for Differential Equations - 13 - Question 9


Differential Equations - 13 - Question 10

Detailed Solution for Differential Equations - 13 - Question 10


Differential Equations - 13 - Question 11

The rare at which body changes temperature is proportional to the difference between its temperature and ihat of the surrounding medium. This is called Newton's law of cooling. If y = f{t} is the unknown temperature of The body at time t and M(t) denotes the known temperature of the surrounding medium, Newton's law' leads to the differential equation where k is a positive constant.

Detailed Solution for Differential Equations - 13 - Question 11

Differential Equations - 13 - Question 12

tan-1 x + tan-1 y = c is the general solution of the differential equation

Detailed Solution for Differential Equations - 13 - Question 12


(By differentiating)

Differential Equations - 13 - Question 13

The differential equation  represents

Detailed Solution for Differential Equations - 13 - Question 13


Differential Equations - 13 - Question 14

If u = log (x3 + y2 + z3 - 3xyz), then 

Detailed Solution for Differential Equations - 13 - Question 14

u = log(x3 + y3 + z3 - 3xyx)

As K is a homogeneous function of degree 3, So



As rest terms will cancel by symmetricity.

Differential Equations - 13 - Question 15

The solution of the differential equal ion (1 + x2) dy/dx = (1 + y2) is

Detailed Solution for Differential Equations - 13 - Question 15


   ......(i)
Integrating both sides of eq. (i) 

Differential Equations - 13 - Question 16

If a population grows at the rate of 5% per year, it will double (in years) after

Detailed Solution for Differential Equations - 13 - Question 16

After n years population will be

Differential Equations - 13 - Question 17

The differential equation of all circles passing through the origin and having their centres on the y-axis is

Detailed Solution for Differential Equations - 13 - Question 17


x2 + (y - a)2 = a2    .....(1)

Differential Equations - 13 - Question 18

The geometrical interpretation of the graph of the differential equation:  is a family of

Detailed Solution for Differential Equations - 13 - Question 18



Differential Equations - 13 - Question 19

The solution curves of the given differential equation: xdx - dy = 0 constitute a family of

Detailed Solution for Differential Equations - 13 - Question 19


Differential Equations - 13 - Question 20

If left to grow undisturbed, the fish population in a lake would be 50 per cent more than it was in the previous year. However, for research purposes 100 fishes are added to the population each year. If the initial population of fish in the pond was zero then how many years the slocking program should continue till the population increases to 2000?

Detailed Solution for Differential Equations - 13 - Question 20

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