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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
e^{2y}=2x + 9
when y=3,
e^{2(3)} =2x + 9
e^{6}=2x + 9
e^{6}+ 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)=e^{xm}
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 Ax^{2} + By^{2} = 1
Answer:
Given :
Ax^{2}+By^{2}=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+ y^{2}) tan^{-1}x dx + 2y (1 + x^{2}) 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+y^{2}=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}=k^{2}
Where (a,b) is the center and k, radius.
Subsitute the values now,
(x-1)^{2}+(y-2)^{2}=k^{2}
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 + A^{3} 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:09 September,2024 - 14 November,2024
Application Date:09 September,2024 - 14 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Hello there! Thanks for reaching out to us at Careers360.
Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.
Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!
Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.
If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.
Let me know if you need any other tips for your math prep. Good luck with your studies!
It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.
Possible steps:
Re-evaluate Your Study Strategies:
Consider Professional Help:
Explore Alternative Options:
Focus on NEET 2025 Preparation:
Seek Support:
Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.
I hope this information helps you.
Hi,
Qualifications:
Age: As of the last registration date, you must be between the ages of 16 and 40.
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Scholarships can range from Rs. 2,000 to Rs. 18,000 per month, depending on the marks obtained and the type of scholarship exam (SAKSHAM, SWABHIMAN, SAMADHAN, etc.).
Since you already have a 12th grade qualification with 84%, you meet the qualification criteria and are eligible to apply for the Medhavi Scholarship exam. Make sure to prepare well for the exam to maximize your chances of receiving a higher scholarship.
Hope you find this useful!
hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
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