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NCERT exemplar Class 12 Maths solutions chapter 9 provides an understanding of equations that relate to one or more functions and their derivatives. In this continually changing world, describing how things change with respect to several factors is very important. The representation of this information is termed as a differential equation. A differential equation is a great way to express a set of information, but it can be hard to solve or formulate. One of the essential languages of Science is that of differential equations.
NCERT exemplar Class 12 Maths chapter 9 solutions provided on this page would help you gain academic success, ensure an efficient and easy way of clearing doubts, aid in preparation for 12 board exams, and shape your perspective about how the world works. Also, read NCERT Class 12 Maths Solutions
Question:1
Answer:
Given
To find: Solution of the given differential equation
Rewrite the equation as,
Integrating on both sides,
Formula:
Here c is some arbitrary constant
d is also some arbitrary constant = c In2
Question:2
Find the differential equation of all non-vertical lines in a plane.
Answer:
To find: Differential equation of all non vertical lines
The general form of equation of line is given by y=mx+c where, m is the slope of the line
The slope of the line cannot be or for the given condition because if it is so, the line will become perpendicular wihout any necessity.
So,
Differentiate the general form of equation of line
Formula:
Differentiating it again it becomes,
Thus we get the diferential euqation of all non vertical lines.
Question:3
Given that and y = 0 when x = 5. Find the value of x when y = 3.
Answer:
Given:
(5,0) is a solution of this equation
To find: Solution of the given differential equation
Rewriting the equation.
Integrate on both the sides,
Formula:
Given (5,0) is a solution so to get c, satisfying these values
Hence the solution is
e2y=2x + 9
when y=3,
e2(3) =2x + 9
e6=2x + 9
e6+ 9=2x
Question:4
Solve the differential equation
Answer:
Given:
To find: Solution of the given differential equation
Rewriting the equations as,
It is a first order liner differential equation Compare it with,
Calculate Integrating Factor,
Hence, solution of the differential equation is given by,
Question:5
Solve the differential equation
Answer:
To find: Solution of the given differential equation
Rewriting the given equation as,
Integrate on both the sides,
Question:6
Answer:
Given:
It is a first order differential equation. Comparing it with,
P(x) =a
Q(x)=exm
Calculating Integrating Factor
Hence the solution of the given differential equation is ,
Question:7
Solve the differential equation
Answer:
To find: Solution of the given differential equation
Assume x+y=t
Differentiate on both sides with respect to x
Substitute
in the above equation
Rewriting the equation,
Integrate on both the sides,
Is the solution of the differential equation
Question:8
Answer:
Given:
To find: solution of the differential equation
Rewriting the given equation,
Question:9
Solve the differential equation when y = 0, x = 0.
Answer:
Given:
and (0,0) is solution of the equation
To find: solution of the differential equation
Rewriting the given equation as,
Integrating on both the sides
Substitute(0,0) to find c’s value
0+0=c
c=0
Hence, the solution is
Question:10
Answer:
Given:
To find: Solution of the differential equation
Rewriting the equation as
It is a first order linear differential equation
Comparing it with
Calculation the integrating factor,
Therefore, the solution of the differential equation is
Question:11
If y(x) is a solution of and y(0) = 1, then find the value of
Answer:
Given:
To find: Solution of the differential equation
Rewriting the given equation as,
Integrating on both sides,
Let sinx=t and cos xdx= dt
ln(1+y)=-ln(2+t)+logc
ln(1+y)+ln(2++sinx)=logc
(1+y)(2+sinx)=c
When x=0 and y=1
c=4
Question:12
If y(t) is a solution of and y(0) = –1, then show that
Answer:
and (0,-1) is a solution
To find: Solution for the differential equation
Rewriting the given equation as,
It is a first order linear differential equation
Comparing it with,
Calculation Integrating Factor
Hence the solution for the differential equation is,
Substitution (0,-1) to find the value of c
The solution therefore y(1) is
Question:13
Answer:
Given:
To find: Solution of the differential equation
Differentiating on both the sides,
Differntiate again on both the sides
Hence the solution is
Question:14
Answer:
To find: Differential equations of all circles which pass though origin and centre lies on x axis
Assume a point (0,k) on y-axis
Radius of the circle is
General form of the equation of circle is,
Here a, c is the center and r is the radius.
Substituting the values in the above equation,
Differentiate the equation with respect to x
Substituting the value of k in (i)
Question:15
Find the equation of a curve passing through origin and satisfying the differential equation
Answer:
Given:
and (0,0) is a solution to the curve
To find: Equation of the curve satisfying the differential equation
Rewrite the given equation
Comparing with
Calculating Integrating Factor
Calculating
Assume
Hence the solution is
Satisfying (0,0) in the equation of the curve to find the value of c
0+0=c
c=0
therefore equation of the curve is
Question:16
Answer:
Given:
To find: solution for the differential equation
Rewriting the given equation as
Clearly it is a homogenous equation
Assume y=vx
Differentiate on both sides
Substituting dy/dx in the equation
Integrating on both the sides
is the solution for the differential equation
Question:17
Find the general solution of the differential equation
Answer:
Given
To find: Solution of the given differential equation
Rewrite the given equation as,
It is a first order differential equation
Comparing it with
Calculating Integrating Factor
Hence the solution of the given differential equation is
Differentiate on both the sides
Question:18
Answer:
Given:
To find: Solution for the given differential equation
Rewrite the given equation
It is a homogenous differential equation
Assume x=vy
Differentiating on both the sides
Substitute dy/dx in the given equation
Substitute v=x/y
Integrating on both the sides
Question:19
Solve: (x + y) (dx – dy) = dx + dy. [Hint: Substitute x + y = z after separating dx and dy].
Answer:
Given:
To find: Solution of the given differential equation
Rewriting the given equation
Assume x+y=z
Differentiate on both sides with respect to x
Substituting the values in the equation
Integrate on both the sides
Substitute v=xy
Question:20
Answer:
Given:
To Find: Solution of the differential equation
Integrating on both sides
Substitute (-2,1) to find value of c
Question:21
Solve the differential equation given that y = 2 when
Answer:
Given:
is a solution of the given differential equation
Rewriting the given equation
It is a first order differential equation
Calculate integrating factor
Therefore, the solution of the differential equation is
Substituting to find the value of c
Hence the solution is
Question:22
Form the differential equation by eliminating A and B in Ax2 + By2 = 1
Answer:
Given :
Ax2+By2=1
To find: Solution of the differential equation
Differentiate with respect to x
Differentiate the curve (i) again to get,
Substituting this in eq(i)
Question:23
Solve the differential equation (1+ y2) tan-1x dx + 2y (1 + x2) dy = 0
Answer:
Given:
To find: Solution for differential equation that s given
Rewriting the given equation as.
Integrate on the both sides
For LHS
Assume tan-1 =t
For RHS
Assume 1+y2=z
2ydy=dz
Substituting and integrating on both the sides
Substitute for t and z
Solution for the differential equation is
Question:24
Find the differential equation of system of concentric circles with centre (1, 2).
Answer:
To find: Differential equation of concentric circles whose center is (1,2)
Equation of the curve is given by
(x-a)2+(y-b)2=k2
Where (a,b) is the center and k, radius.
Subsitute the values now,
(x-1)2+(y-2)2=k2
Differentiate with respect to x
Question:25
Answer:
Now dx/dy (xy) refers to the differentiation of xy with respect to x
Using product rule
When we put it back originally in the differential equation given,
Divide by x
Compare
We get
The above equation is a linear differential equation with P and Q as functions of x
The first to find the solution of a linear differential equation is to find the integrating factor.
The solution of the linear differential equation is
Substituting values for Q and IF
Find the integrals individually,
Using uv for integration
Now
Use product rule
Substitute (i) and (ii) in (a)
Divide by
Question:26
Answer:
Divide throughout by dy
Divide by (1+tany)
Compare
We get
This is the linear differential equation with P and Q as functions of x
Put
Adding and subtracting siny in the numerator
Consider the integral
Let
Differentiate with respect to y
We get
The solution of the linear differential equation will be
Substitute values for Q and IF
Put and differentiate with respect to y
We get
Which means
Hence
Substitute t again
Question:27
Solve: [Hint: Substitute x + y = z]
Answer:
Using the given hint substitute x+y=z
Differentiate z- x with respect to x
Integrate
As we know
And
Differentiate with respect to z
We get
hence
Again substitute t
Similarly substitute z
Question:28
Answer:
We get, P= -3 and Q= sin2x
The equation is a linear differential equation where P and Q are functions of x
For the solution of the linear differential equation, we need to find Integrating factor,
The solution of the linear differential equation is
Substitute values for Q and IF
Let
If are two functions, then by integration by parts.
after applying the formula we get,
Again, applying the above stated rule in
Put this value in (1) to get
Question:29
Answer:
Slope of the tangent is given by
Slope of the tangent of the curve
Put y=VX
Using product rule differentiate vx
Integrate
Put
Resubstitute 1
Resubstitute v
The curve is passing through (2,1)
Hence (2,1) will satisfy the equation (a)
Put x=1 and y=2 in (a)
Use loga+logb=logab
Put c in equation (a)
Question:30
Given: Slope of the tangent is
Slope of tangent of a curve
Integrate
Use partial fraction for
Equate the numerator
Put x=0
A=1
Put x=-1
B=-1
Hence
Hence equation (a) becomes,
Now it is given that the curve is passing through (1,0)
Hence (1,0) will satisfy the equation (b)
Put x=1 and y=0 in b
When we put y=0 in equation b the result is which is undefined
hence, we must simplify equation (b) further
using loga-logb=loga/b
Constant c must be taken as log c to eliminate undefined elements in the
equation.(log cand not any other terms because taking logc completely
eliminates the log terms and we don't have to worry about undefined terms
in the equation)
Eliminate log
Substitute x=1 and y=0
c=-2
put back c=-2 in (c)
Question:31
Answer:
Abscissa refers to the x coordinate and ordinate refers to the y coordinate.
Slope of the tangent is the square of the difference of the abscissa and the ordinate.
Difference of the abscissa and ordinate is (x-y) and its square is
Hence the Slope of the tangent is
The curve passes through the (0,0)
Question:32
Answer:
Points on the y axis and x axis are namely A(0,a), B(b,0). The midpoint of AB is P(x,y).
The x coordinate of the points is given by the addition of the x coordinates of A and B divided by 2.
Therefore, the coordinates of A and B are (0,2y) and (2x,0) respectively.
AB is the tangent to curve where P is the point of contact.
Slope of the line given with two points
Here respectively.
Slope of the tangent AB is
Hence the slope of the tangent is -y/x
Slope of the tangent curve is given by,
Integrate
using logat logb=logab.
as given curve is passing through(1,a)
Hence (1,1) will satisfy the equation of the curve(a)
Putting
put c back in (a)
Hence the equation of the curve is
Question:33
Answer:
Using loga-logb =loga/b
Put y=v x
Differentiate yx with respect to x using product rule
Now Integrate
Substitute log v =t
Differentiate with respect to v.
logt= logx + logc
Resubstitute value of t
log(log v)=log x + logc.
Resubstitute v
Therefore the solution of the differential equation is
Question:34
The degree of the differential equation is:
A. 1
B. 2
C. 3
D. Not defined
Answer:
Degree of differential equation is defined as the highest integer power of the highest order derivative in the equation.
Here’s the differential equation
Now for the degree to exit the differential equation must be a polynomial in some differentials.
Differential means
The given differential equation is not a polynomial because of the term sin dy/dx and therefore degree of such a differential equation is not defined.
Option D is correct.
Question:35
The degree of the differential equation is:
A. 4
B. 3/4
C. not defined
D. 2
Answer:
Generally, for a polynomial degree is the highest power.
Differential equation is Squaring both the sides,
Now for the degree to exit the differential equation must be a polynomial in
some differentials.
The given differential equation is polynomial in differential is
Degree of differential equation is the highest integer power of the highest order
derivative in the equation.
Highest derivative is
There is only one term of the highest order derivative in the equation which is
Whose power is 2 hence the degree is 2
Option D is correct.
Question:36
The order and degree of the differential equation respectively, are
A. 2 and 4
B. 2 and 2
C. 2 and 3
D. 3 and 3
Answer:
The differential equation is
Order is defined as the number which represents the highest derivative in a differential equation.
Is the highest derivative in the given equation is second order hence the degree of the equation is 2 .
Integer powers on the differentials,
Now for the degree to exit the differential equation must be a polynomial in some differentials.
Here differentials means
The given differential equation is polynomial in differentials
Degree of differential equation is the highest integer power of the highest
order derivative in the equation.
Observe that
Of differential equation (a) the maximum power
Highest order is and highest power is 4
Degree of the given differential equation is 4 .
Hence order is 2 and degree is 4
Option A is correct.
Question:37
Answer:
If is a solution of differential equation, then differentiating it will give the same differential equation.
Differentiate the differential equation twice. Twice because all the options have order as 2 and also because there are two constants A and B
Differentiating using product rule
But
Differentiating again with respect to x,
But
Also,
Means,
Question:38
The differential equation for are arbitrary constants is
Answer:
Let us find the differential equation by differentiating y with respect to x twice
Twice because we have to eliminate two constants .
Differentiating,
Differentiating again
Option B is correct.
Question:39
Solution of differential equation xdy – ydx = 0 represents:
A. a rectangular hyperbola
B. parabola whose vertex is at origin
C. straight line passing through origin
D. a circle whose centre is at origin
Answer:
is constant because e is a constant and c is the integration constant let it be denoted as k hence
is the equation of straight line and (0,0) satisfies the equation.
Option C is correct.
Question:40
Integrating factor of the differential equation is:
A. cosx
B. tanx
C. sec x
D. sinx
Answer:
Differential equation is
Compare
With
The IF integrating factor is given by
Substitute hence
Resubstitute the value of t
hence IF is sec x
Option C is correct.
Question:41
Solution of the differential equation is:
A. tanx + tany = k
B. tanx – tan y = k
C.
D. tanx . tany = k
Answer:
The given differential equation is
Divide it by tanx tany
Integrate
Put tanx=t hence,
Put tany =z hence
That is
Resubstitue t and z
is constant because e is a constant and c is the integration constant let it be denoted as
Option D is correct.
Question:42
Family of curves is represented by the differential equation of degree:
A. 1
B. 2
C. 3
D. 4
Answer:
let us find the differential equation representing it so we have to eliminate
the constant A
Differentiate with respect to x
Put back value of A in y
Now for the degree to exit the differential equation must be a polynomial in some differentials.
Here the differentials mean
The given differential equation is polynomial in differentials
Degree of differential equation is the highest integer power of the highest order derivative in the equation.
Highest derivative is
And highest power to it is 3 . Hence degree is 3 .
Option C is correct.
Question:43
Integrating factor of is:
A. x
B. logx
C.
D. –x
Answer:
Given differential equation
Divide though by x
Compare
We get
The IF integrating factor is given by el $^{\mathrm{iPdx}}$
Option C is correct.
Question:44
B.
C.
D.
Answer:
Integrate
now it is given that y(0)=1 which means when x=0, y=1 hence substitute x=0 and y=0 in (a)
put back in (a)
using
Hence solution of differential equation is
Option D is correct.
Question:45
The number of solutions of when y(1) = 2 is:
A. none
B. one
C. two
D. infinite
Answer:
using
Now as given y(1)=2 which means when x=1, y=2 Substitute x=1 and y=2 in (a)
So only one solution exists.
Option B is correct.
Question:46
Which of the following is a second order differential equation?
Answer:
Order is defined as the number which defines the highest derivative in a differential equation
Second order means the order should be 2 which means the highest
derivative in the equation should be or y Let's examine each of the option given
A.
The highest order derivative is is in first order.
B.
The highest order derivative is is in second order
C.
The highest order derivative is is in third order
D.
The highest order derivative is is in first order
Option B is correct.
Question:47
Integrating factor of the differential equation is:
A. -x
B.
C.
D.
Answer:
Divide through by
Compare
We get
The IF factor is given by
Substitute hence
Which means
Resubstitute
Hence the IF integrating factor is
Option C is correct.
Question:48
is the general solution of the differential equation:
A.
B.
C.
D.
Answer:
If is a solution of differential equation then differentiating it will give the same differential equation.
To find the differential equation differentiate with respect to x.
Option C is correct..
Question:49
The differential equation represents:
A. Family of hyperbolas
B. Family of parabolas
C. Family of ellipses
D. Family of circles
Answer:
integrate
k is the integration constant
This is the equation of circle because there is no ‘xy’ term and and have the same coefficient.
This equation represents the family of circles because for different values of c and k we will get different circles.
Option D is correct.
Question:50
The general solution of is:
A.
B.
C.
D.
Answer:
Integrate
substitute cosy =t hence
Which means sinydy=-dt
Option A is correct.
Question:51
The degree of the differential equation is
(a) 1
(b) 2
(c) 3
(d) 5
Answer:
The answer is the option (a) 1 as the degree of a differential equation is the highest exponent of the order derivative.
Question:52
The solution of is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (b)
Explanation: -
This is a linear differential equation.
On comparing it with , we get
So, the general solution is:
Given that when x=0 and y=0
Eq. (i) becomes
Question:53
Integrating factor of the differential equation
(a)
(b)
(c)
(d)
Answer:
The answer is the option (b) Sec x
Explanation: -
Question:54
The solution of the differential equation is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (b) y – x = k(1 + xy)
Explanation: -
Question:55
The integrating factor of the differential equation is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (b)
Explanation: -
This is a linear differential equation.
On comparing it with we get
Question:58
The solution of is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (a)
Explanation: -
This is a linear differential equation. Dn comparing it with $\frac{d y}{d x}+P y=Q$, we get
So, the general solution is:
Question:59
The differential equation of the family of curves where a is arbitrary constant, is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (a)
Given:
Question:60
Family y = Ax + A3 of curves will correspond to a differential equation of order ,
(a) 3 (b) 2 (c) 1 (d) not defined.
Answer:
The answer is the option (c) 1.
Explanation: -
Putting the value of A in Eq. (i), we gt
Question:61
The general solution of is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (c)
Explanation: -
Question:62
The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is
(a) an ellipse (b) parabola (c) circle (d) rectangular hyperbola
Answer:
The answer is the option (d) Rectangular Hyperbola
Explanation: -
According to the question,
On integrating both sides, we get
which is an equation of rectangular hyperbola.
Question:63
The general solution of differential equation is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (c)
Explanation: -
This is a linear differential equation. On comparing it with we get
So, the general solution is:
Question:64
The solution of equation is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (c)
Explanation: -
Question:65
The differential equation for which is a solution, is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (a)
Explanation: -
On differentiating both sides w.r.t. x, we get
Again, differentiating w.r.t. x, we get
Question:66
The solution of is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (d)
Explanation: -
Here,
Given, when x=0 and y=0
Eq. (i) reduces to
Question:67
The order and degree of the differential equation
(a) 1,4
(b) 3,4
(c) 2,4
(d) 3,2
Answer:
Ans: - The answer is the option (d) 3, 2
Question:68
The order and degree of the differential equation are
(a)
(b) 2,3
(c) 2,1
(d) 3,4
Answer:
Ans: -
The answer is the option (c) 2, 1.
Question:69
The differential equation of family of curves is
(a)
(b)
(c)
(d)
Answer:
Ans: - The answer is the option (d)
Explanation: -
On differentiating both sides w.r.t. x, we get
On putting the value of a in Eq. (i), we get
Question:70
Which of the following is the general solution of ?
(a)
(b)
(c)
(d)
Answer:
Ans: -
The answer is the option (a)
Explanation: -
Question:71
General solution of is
(a)
(b)
(c)
(d)
Answer:
Ans: - The answer is the option (a) y sec x = tan x + C
Explanation: -
Here,
Question:72
Solution of the differential equation is
(a)
(b)
(c)
(d)
Answer:
Ans: - The answer is the option (a) x(y + cos x) = sin x + C
Explanation: -
Here,
Question:73
The general solution of differential equation is
(a)
(b)
(c)
(d)
Answer:
Ans: - The answer is the option (c)
Explanation: -
Question:74
The solution of the differential equation is
(a)
(b)
(c)
(d)
Answer:
The answer is the option (b)
Explaination:
Question:75
The solution of the differential equation
(a)
(b)
(c)
(d)
Answer:
Ans: - The answer is the option (a)
Explanation: -
Here,
Question:76
Answer:
(i) Given differential equation is
Degree of this equation is not defined as it cannot be expresses as polynomial of derivatives.
(ii) We have
So, degree of this equation is two.
(iii) Given that the general solution of a differential equation has three arbitrary constants. So we require three more equations to eliminate these three constants. We can get three more equations by differentiating given equation three times. So, the order of the differential equation is three.
(iv) We have
The equation is of the type
Hence it is linear differential equation.
(v) We have
For solving such equation we multiply both sides by
So we get
This is the required solution of the given differential equation.
(vi) We have,
This equation of the form
The general solution is
(vii) We have
This equation is of the form
So, the general solution is:
(viii) We have, $
(ix) We have,
Which is of the form
So, the general solution is:
(x) Given differential equation is
(xi) Given differential equation is
Which is linear differential equation.
Question:77
Answer:
i) Integrating factor of the differential of the form is given by . Hence given statement is true.
(ii) Solution of the differential equation of the type is given by .
Hence given statement is true.
iii) Correct substitution for the solution of the differential equation of the type is a homogeneous function of zero degree is y=v x.
Hence given statement is true.
(iv) Correct substitution for the solution of the differential equation of the type where g(x, y) is a homogeneous function of the degree zero is x=v y.
Hence given statement is true.
(V) There is no arbitrary constants in the particular solution of a differential equation. Hence given statement is Flase.
(vi) In thegiven equation the number of arbitrary constant is one. So the order order will be one.
Hence given statement is False.
(vii)
Hence the given statement is true.
(viii)
.
Hence the given statement is true.
ix) Given:
Compare with
Here ,
General solution
Hence the given statement is true.
x) Given:
Let y =vx
Hence the given statement is true.
xi) Assume equation of a non-horizontal line in the plane
y = mx +c
Hence the given statement is true.
Question:56
satisfies which of the following differential equation.
Answer:
given
upon differentiation, we get
after differentiation again we get
Option c is correct
Below is the list of topics which are covered in Class 12 Maths NCERT exemplar solutions chapter 9
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In NCERT exemplar Class 12 Maths solutions chapter 9 pdf download, we would also look at the graphical aspects of differential equations, including a family of straight lines and curves, and have a look at the devised solutions and mathematical tools to solve the most complex equations over time.
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | Differential Equations |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 |
Yes, these NCERT exemplar Class 12 Maths solutions chapter 9 can be highly useful in understanding the way the questions should be solved in entrance exams.
These solutions can be used for both getting used to the chapter and its topics and to also get an idea about how to solve questions in exams.
One can understand how to stepwise solve these questions through NCERT exemplar Class 12 Maths solutions chapter 9 and how the CBSE expects a student to solve in their final paper.
We have the best maths teachers onboard to solve the questions as per the students understanding and also CBSE standards. These teachers prepare the NCERT exemplar solutions for Class 12 Maths chapter 9.
Hello aspirant,
The purpose of graphic design extends beyond the brand's look. Nevertheless, by conveying what the brand stands for, it significantly aids in the development of a sense of understanding between a company and its audience. The future in the field of graphic designing is very promising.
There are various courses available for graphic designing. To know more information about these courses and much more details, you can visit our website by clicking on the link given below.
https://www.careers360.com/courses/graphic-designing-course
Thank you
Hope this information helps you.
hello,
Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.
I hope this was helpful!
Good Luck
Hello dear,
If you was not able to clear 1st compartment and now you giving second compartment so YES, you can go for your improvement exam next year but if a student receives an improvement, they are given the opportunity to retake the boards as a private candidate the following year, but there are some requirements. First, the student must pass all of their subjects; if they received a compartment in any subject, they must then pass the compartment exam before being eligible for the improvement.
As you can registered yourself as private candidate for giving your improvement exam of 12 standard CBSE(Central Board of Secondary Education).For that you have to wait for a whole year which is bit difficult for you.
Positive side of waiting for whole year is you have a whole year to preparing yourself for your examination. You have no distraction or something which may causes your failure in the exams. In whole year you have to stay focused on your 12 standard examination for doing well in it. By this you get a highest marks as a comparison of others.
Believe in Yourself! You can make anything happen
All the very best.
Hello Student,
I appreciate your Interest in education. See the improvement is not restricted to one subject or multiple subjects and we cannot say if improvement in one subject in one year leads to improvement in more subjects in coming year.
You just need to have a revision of all subjects what you have completed in the school. have a revision and practice of subjects and concepts helps you better.
All the best.
Hi,
You just need to give the exams for the concerned two subjects in which you have got RT. There is no need to give exam for all of your subjects, you can just fill the form for the two subjects only.
Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.
The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.
A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.
GIS officer work on various GIS software to conduct a study and gather spatial and non-spatial information. GIS experts update the GIS data and maintain it. The databases include aerial or satellite imagery, latitudinal and longitudinal coordinates, and manually digitized images of maps. In a career as GIS expert, one is responsible for creating online and mobile maps.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.
If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi.
Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.
Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.
Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.
Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.
A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.
A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.
Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.
Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.
A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.
Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.
The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.
An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.
Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.
For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.
An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.
They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.
Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.
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