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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 câs 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) = â1, 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 â 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
Solve: given that y (1) = â2
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.
Hereâs 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 â 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 â 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. âx
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 âxyâ 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 â 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
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.
Application Date:20 November,2023 - 19 December,2023
Application Date:20 November,2023 - 19 December,2023
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.
If you'll do hard work then by hard work of 6 months you can achieve your goal but you have to start studying for it dont waste your time its a very important year so please dont waste it otherwise you'll regret.
Yes, you can take admission in class 12th privately there are many colleges in which you can give 12th privately.
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.
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.
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.
The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction.
The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions.
How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.
A career as Bank Probationary Officer (PO) is seen as a promising career opportunity and a white-collar career. Each year aspirants take the Bank PO exam. This career provides plenty of career development and opportunities for a successful banking future. If you have more questions about a career as Bank Probationary Officer (PO), what is probationary officer or how to become a Bank Probationary Officer (PO) then you can read the article and clear all your doubts.
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.
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.
A career as a Finance Executive requires one to be responsible for monitoring an organisation's income, investments and expenses to create and evaluate financial reports. His or her role involves performing audits, invoices, and budget preparations. He or she manages accounting activities, bank reconciliations, and payable and receivable accounts.
An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.
Bank Branch Managers work in a specific section of banking related to the invention and generation of capital for other organisations, governments, and other entities. Bank Branch Managers work for the organisations and underwrite new debts and equity securities for all type of companies, aid in the sale of securities, as well as help to facilitate mergers and acquisitions, reorganisations, and broker trades for both institutions and private investors.
Treasury analyst career path is often regarded as certified treasury specialist in some business situations, is a finance expert who specifically manages a company or organisation's long-term and short-term financial targets. Treasurer synonym could be a financial officer, which is one of the reputed positions in the corporate world. In a large company, the corporate treasury jobs hold power over the financial decision-making of the total investment and development strategy of the organisation.
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 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.
A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability.
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.
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.
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.
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 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 Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.
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 veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.
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.
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.
When it comes to an operation theatre, there are several tasks that are to be carried out before as well as after the operation or surgery has taken place. Such tasks are not possible without surgical tech and surgical tech tools. A single surgeon cannot do it all alone. It’s like for a footballer he needs his team’s support to score a goal the same goes for a surgeon. It is here, when a surgical technologist comes into the picture. It is the job of a surgical technologist to prepare the operation theatre with all the required equipment before the surgery. Not only that, once an operation is done it is the job of the surgical technologist to clean all the equipment. One has to fulfil the minimum requirements of surgical tech qualifications.
Also Read: Career as Nurse
A Maxillofacial Surgeon is a medical professional who performs facial surgeries that include tooth implant, neck, head or other surgeries such as removal of tumours, cosmetic surgeries and treatment of injuries on the face.
Surgical assistants are professionals in the service of saving others’ lives. They perform various medical procedures. In a career as a surgical assistant, one works in a team and contributes to the success of operations. Surgical assistants learn new procedures and update their knowledge of new medical technology and equipment. Surgical assistants clean and sterilize the tools used in surgery. In a career as a surgical assistant, individuals perform all the basic duties that allow surgeons to keep their focus on essential technical functions.
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.
The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.
If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.
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.
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.
Fashion bloggers use multiple social media platforms to recommend or share ideas related to fashion. A fashion blogger is a person who writes about fashion, publishes pictures of outfits, jewellery, accessories. Fashion blogger works as a model, journalist, and a stylist in the fashion industry. In current fashion times, these bloggers have crossed into becoming a star in fashion magazines, commercials, or campaigns.
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.
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.
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.
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.
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 cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.
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.
Content writing is meant to speak directly with a particular audience, such as customers, potential customers, investors, employees, or other stakeholders. The main aim of professional content writers is to speak to their targeted audience and if it is not then it is not doing its job. There are numerous kinds of the content present on the website and each is different based on the service or the product it is used for.
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.
Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning).
Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian.
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 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.
Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.
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A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.
A Quality Systems Manager is a professional responsible for developing strategies, processes, policies, standards and systems concerning the company as well as operations of its supply chain. It includes auditing to ensure compliance. It could also be carried out by a third party.
A career as a merchandiser requires one to promote specific products and services of one or different brands, to increase the in-house sales of the store. Merchandising job focuses on enticing the customers to enter the store and hence increasing their chances of buying a product. Although the buyer is the one who selects the lines, it all depends on the merchandiser on how much money a buyer will spend, how many lines will be purchased, and what will be the quantity of those lines. In a career as merchandiser, one is required to closely work with the display staff in order to decide in what way a product would be displayed so that sales can be maximised. In small brands or local retail stores, a merchandiser is responsible for both merchandising and buying.
The procurement Manager is also known as Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness.
Individuals who opt for a career as a production planner are professionals who are responsible for ensuring goods manufactured by the employing company are cost-effective and meets quality specifications including ensuring the availability of ready to distribute stock in a timely fashion manner.
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.
ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.
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
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.
Individuals in the computer systems analyst career path study the hardware and applications that are part of an organization's computer systems, as well as how they are used. They collaborate closely with managers and end-users to identify system specifications and business priorities, as well as to assess the efficiency of computer systems and create techniques to boost IT efficiency. Individuals who opt for a career as a computer system analyst support the implementation, modification, and debugging of new systems after they have been installed.
A Test Manager is a professional responsible for planning, coordinating and controlling test activities. He or she develops test processes and strategies to analyse and determine test methods and tools for test activities. The test manager jobs involve documenting tests that have been carried out, analysing and evaluating software quality to determine further recommended procedures.
A career as Azure Developer comes with the responsibility of designing and developing cloud-based applications and maintaining software components. He or she possesses an in-depth knowledge of cloud computing and Azure app service.
A Deep Learning Engineer is an IT professional who is responsible for developing and managing data pipelines. He or she is knowledgeable about analyzing and storing data collected from various sources. A Career as a Deep Learning Engineer needs to help the data scientists and analysts to create effective data sets.
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