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Polynomials is the chapter 2 of NCERT exemplar Class 10 Maths solutions. This chapter is restudied in Class 10 after Class 9. NCERT exemplar Class 10 Maths solutions chapter 2 provides a detailed understanding of Polynomials. These NCERT exemplar Class 10 Maths chapter 2 solutions are a result of the extensive subject matter experts of our mathematics team and are an excellent source to prepare for NCERT Class 10 Maths. The determinant of these NCERT exemplar Class 10 Maths chapter 2 solutions is a sound understanding of concepts of polynomials due to their comprehensive nature. The CBSE Syllabus Class 10 Maths is the reference point for NCERT exemplar Class 10 Maths solutions chapter 2.
Question:1
If one of the zeroes of the quadratic polynomial is –3, then the value of k is
(A)
(B)
(C)
(D)
Answer:
Answer. [A]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
Let
If –3 is one of the zeroes of p(x) then p(–3) = 0
put x = –3 in p(x)
Question:2
A quadratic polynomial, whose zeroes are –3 and 4, is
(A)
(B)
(C)
(D)
Answer:
Answer. [C]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
(A)
put x = –3 put x = 4
(B)
put x = –3 put x = 4
= 16 + 16 = 32 0
(C)
put x = –3 put x = 4
(D)
put x = –3 put x = 4
If –3, 4 is zeros of a polynomial p(x) then p(–3) = p(4) = 0
Here only (C) option satisfy p(–3) = p(4) = 0
Question:3
If the zeroes of the quadratic polynomial are 2 and –3, then
(A) a = –7, b = –1
(B) a = 5, b = –1
(C) a = 2, b = – 6
(D) a = 0, b = – 6
Answer:
Answer. [D]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
If 2 and –3 are the zero of then p(2) = p(–3) = 0.
….(1)
….(2)
Add equation (1) and (2)
2a + 3a = 0
5a = 0
a = 0
put a = 0 in (1)
2(0) + b = –6
b = –6
Hence a = 0, b = –6.
Question:4
The number of polynomials having zeroes as –2 and 5 is
(A) 1
(B) 2
(C) 3
(D) more than 3
Answer:
Answer. [D]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s).
Let the polynomial is ….(*)
We know that sum of zeroes
…..(1)
Multiplication of zeroes
…..(2)
Form equation (1) and (2) it is clear that
a = 1, b = –3, c = –10
put value of a, b and c in equation (*)
….(3)
But we can multiply of divide eqn. (3) by any real number except 0 and the zeroes remain same.
Hence, there are infinite number of polynomial exist with zeroes –2 and 5.
Hence the answer is more than 3.
Question:5
Given that one of the zeroes of the cubic polynomial is zero, the product of the other two zeroes is
(A)
(B)
(C) 0
(D)
Answer:
Answer. [B]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 3.
Here the given cubic polynomial is
Let three zeroes are
(given) …..(1)
we know that
Put
( using equation (1))
Hence the product of other two zeroes is .
Question:6
If one of the zeroes of the cubic polynomial is –1, then the product of the other two zeroes is
(A) b – a + 1
(B) b – a – 1
(C) a – b + 1
(D) a – b –1
Answer:
Answer. [A]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 3.
Here the given cubic polynomial is
Let are the zeroes of polynomial
(given) …..(1)
put x = –1 in
We know that
Here, a = 1, b = a, c = b, d = c
So,
( using equation (1))
Hence the product of other two is b – a + 1.
Question:7
The zeroes of the quadratic polynomial are
(A) both positive
(B) both negative
(C) one positive and one negative
(D) both equal
Answer:
Answer. [B]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
Here the given quadratic polynomial is
The value of both the zeroes are negative.
Question:8
The zeroes of the quadratic polynomial ,
(A) cannot both be positive
(B) cannot both be negative
(C) are always unequal
(D) are always equal
Answer:
Answer. [A]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
Here the given quadratic polynomial is
must be grater then 0
Hence the value of k is either less than 0 or greater than 4.
If value of k is less than 0 only one zero is positive.
If value of k is greater than 4 only one zero is positive.
Hence both the zeroes can not be positive.
Question:9
If the zeroes of the quadratic polynomial are equal, then
(A) c and a have opposite signs
(B) c and b have opposite signs
(C) c and a have the same sign
(D) c and b have the same sign
Answer:
Answer. [C]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
Here the given polynomial is
We know that if both the zeroes are equal there
….(1)
(A) c and a have opposite sign
If c and a have opposite sign then R.H.S. of equation (1) is negative but L.H.S. is always positive. So (A) is not a correct one.
(B) c and b have opposite sign
If c is negative and b is positive L.H.S. is positive but R.H.S. of eqn. (1) is negative. Hence (B) is not correct one.
(C) c and a have same sign
If c and a have same sign R.H.S. of eqn. (1) is positive and L.H.S. is always positive hence it is a correct one.
(D) c and b have same sign
If c and b both have negative sign then R.H.S. of eqn. (1) is negative and L.H.S. is positive. So this is not correct.
Only one option i.e. (c) is correct one.
Question:10
If one of the zeroes of a quadratic polynomial of the form is the negative of the other, then it
(A) has no linear term and the constant term is negative.
(B) has no linear term and the constant term is positive.
(C) can have a linear term but the constant term is negative.
(D) can have a linear term but the constant term is positive.
Answer:
Answer. [A]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
Here the given quadratic polynomial is …..(1)
a = 1, b = a, c = b
Let x_{1}, x_{2} are the zeroes of the equation (1)
According to question:
sum of zeroes =
( because x_{2} = - x_{1} )
( because b = a , a = 1)
Product of zeroes
( because c= b, a = 1)
Put value of a and b in (1)
Hence, it has no linear term and the constant term is negative.
Question:11
Which of the following is not the graph of a quadratic polynomial?
Answer:
Answer. [D]
Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.
If p(x) is quadratic polynomial then there are almost 2 values of x exists called roots.
Hence, the graph of p(x) cuts the x-axis almost 2 times.
But here we see that in option (D) the curve cuts the x-axis at 3 times
Hence, graph (D) is not a graph of a quadratic polynomial.
Question:1
Answer:
(i) Answer. [false]
Solution.
Let divisor of a polynomial in x of degree 5 is =
Quotient =
Dividend =
According to division algorithm if one polynomial p(x) is divided by the other polynomial , then the relation among p(x), g(x), quotient q(x) and remainder r(x) is given by
i,e. Dividend = Divisor × Quotient + Remainder
Remainder
Remainder
Here it is of degree seven but given dividend is of degree six.
Therefore can not be the quotient of because division algorithm is not satisfied.
Hence, given statement is false.
(ii) Here dividend is
and divisor is
According to division algorithm if one polynomial p(x) is divided by the other polynomial g(x) ¹ 0 then the relation among p(x), g(x) quotient q(x) and remainder r(x) is given by
where degree of r(x) < degree of g(x).
i.e. Dividend = Devisor × Quotient + Remainder
Here degree of divisor is greater than degree of dividend therefore.
According to division algorithm theorem is the remainder and quotient will be zero.
That is remainder =
Quotient = 0
(iii) Division algorithm theorem :- According to division algorithm if one polynomial p(x) is divided by the other polynomial g(x) is then the relation among p(x), g(x), quotient q(x) and remainder r(x) is given by
p(x) = g(x) × q(x) + r(x)
where degree of r(x) < degree of g(x)
i.e. Dividend = Division × Quotient + Remainder
In the given statement it is given that on division of a polynomial p(x) by a polynomial g(x), the quotient is zero.
The given condition is possible only when degree of divisor is greater than degree of dividend
i.e. degree of g(x) > degree of p(x).
(iv)
Division algorithm theorem :- According to division algorithm if one polynomial p(x) is divided by the other polynomial g(x) is then the relation among p(x), g(x), quotient q(x) and remainder r(x) is given by
p(x) = g(x) × q(x) + r(x) ….(1)
where degree of r(x) < degree of g(x)
According to given statement on division of a non-zero polynomial p(x) by a polynomial g(x) then remainder r(x) is zero then equation (1) becomes
p(x) = g(x) × q(x) ….(2)
From equation (2) we can say g(x) is a factor of p(x) and degree of g(x) may be less than or equal to p(x).
(v)
Answer. [false]
Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s)
Quadratic polynomial : when the degree of polynomial is two then the polynomial is called quadratic polynomial.
Let
It is given that zeroes of p(x) has equal and we know that when any polynomial having equal zeroes than their discriminate is equal to zero
i.e.
here, a = 1, b = k, c = k
Hence, the given quadratic polynomial have equal zeroes only when the values of k will be 0 and 4.
Hence, given statement is not correct.
Question:2
Answer:
(i) Answer. [false]
Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Quadratic polynomial : when the degree of polynomial is two then the polynomial is called quadratic polynomial.
If a quadratic polynomial is then
Sum of zeroes
Product of zeroes
Here two possibilities can occurs:
b > 0 and a < 0, c < 0
OR b < 0 and a > 0, c > 0
Here we conclude that a, b and c all have nor same sign is given statement is false.
(ii) Answer. [False]
Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Quadratic polynomial : when the degree of polynomial is two then the polynomial is called quadratic polynomial.
We know that the roots of a quadratic polynomial is almost 2, Hence the graph of a quadratic polynomial intersects the x-axis at 2 point, 1 point or 0 point.
For example :
(a quadratic polynomial)
Here only one value of x exist which is –2.
Hence the graph of the quadratic polynomial intersect the x-axis at x = –2.
Hence, we can say that if the graph of a polynomial intersect the x-axis at only one point can be a quadratic polynomial.
Hence the given statement is false.
(iii)
Answer. [True]
Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Quadratic polynomial : when the degree of polynomial is two then the polynomial is called quadratic polynomial.
Let us take an example :-
It is a cubic polynomial
If we find its roots then x = 1, 2
Hence, there are only 2 roots of cubic polynomial exist.
In other words we can say that the graph of this cubic polynomial intersect x-axis at two points x = 1, 2.
Hence we can say that if the graph of a polynomial intersect the x-axis at exactly two points, it need not to be a quadratic polynomial it may be a polynomial of higher degree.
Hence the given statement is true.
(iv)
Answer. [True]
Polynomial: It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Cubic polynomial: when the degree of polynomial is three then the polynomial is called cubic polynomial.
Let be the zeroes of a cubic polynomial.
It is given that two of the given zeroes have value zero.
i.e.
Let
Here, we conclude that if two zeroes of a cubic polynomial are zero than the polynomial does not have linear and constant terms.
Hence, given statement is true.
(v)
Answer. [True]
Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Cubic polynomial : when the degree of polynomial is three then the polynomial is called cubic polynomial.
Let the standard equation of cubic polynomial is:
Let and be the roots of p(x)
It is given that all the zeroes of a cubic polynomial are negative
i.e
Sum of zeroes
It is given that zeroes are negative then
…….(1)
That is
Sum of the products of two zeroes at a time
Replace
…..(2)
That is
Product of all zeroes
Replace
……(3)
That is
From equation (1), (2) and (3) we conclude that all the coefficient and the constant term of the polynomial have the same sign.
Hence, given statement is true.
(vi)
Answer. [False]
Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Cubic polynomial : when the degree of polynomial is three then the polynomial is called cubic polynomial.
The given cubic polynomial is
Let a, b and g are the roots of the given polynomial
Sum of zeroes
We know that when all zeroes of a given polynomial are positive then their sum is also positive
But here a is negative
Sum of the product of two zeroes at a time
Also here b is negative
Product of all zeroes
Also c is negative
Hence if all three zeroes of a cubic polynomial are positive then a, b and c must be negative.
Hence given statement is false.
(vii)
Answer. [False]
Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).
Quadratic polynomial : when the degree of polynomial is two then the polynomial is called cubic polynomial.
Let
Here it is gives that zeroes of p(x) are equal and we know that when any polynomial having equal zeroes then their discriminate will be equal to zero.
i.e. d = 0
(Q d = b2 – 4ac)
Here, a = k, b = 1, c = k
When and then the given quadratic polynomial has equal zeroes.
Question:1
Answer:
Answer.
Zeroes : zeroes of polynomial are the value(s) that makes it equal to 0.
x – 1 = 0 4x + 1 = 0
x = 1 4x = –1
Hence, 1, are the zeroes of the polynomials
We know that
Sum of the zeroes
Here,
Which is equal to
Product of zeroes
Here
Question:2
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
Hence, are the zeroes of the polynomial
a = 3, b = 4, c = –4
Sum of the zeroes
Here,
Product of the zeroes
Here,
Question:3
Answer:
Answer.
Zeroes : zeroes of the polynomial are the values(s) the makes it equal to 0
t + 1 = 0 5t + 7 = 0
t = –1
Hence, are the zeroes of polynomial
Sum of zeroes
Here,
Product of zeroes
Here,
Question:4
Answer:
Answer.
Zeroes : zeroes of the polynomial area the value(s) that makes it equal to 0.
=0 (a = 1, b = –2, c = –15, d = 0)
=0
=0
=0
=0
t = 0 t – 5 = 0 t + 3 = 0
t = 5 t = –3
Hence, 0, 5, –3 are the zeroes of the polynomial
Sum of zeroes
Here,
Product of zeroes
Here,
If are three roots the
Hence proved.
Question:5
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
Multiply by 4
=0
=0
=0
=0
Hence, are the zeroes of the polynomial
Here,
Sum of zeroes
Here,
Product of zeroes
Here,
Question:6
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
= 0
Hence, are the zeroes of the polynomial
Here, a = 4, b = , c = –3
Sum of zeroes
Here,
Product of zeroes
Here,
Question:7
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
= 0
=0
=0
=0
2s – 1 = 0
Hence, are the zeroes of the polynomial
Here, a = 2,
Sum of zeroes
Here,
Product of zeroes
Here,
Question:8
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
=0
=0
=0
=0
Hence, are the zeroes of the polynomial
Here, a = 1, b = , c = –15
Sum of zeroes
Here,
Product of zeroes
Here,
Question:9
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
=0
Multiply by 2
=0
=0
=0
=0
Hence, are the zeroes of the polynomial
Here, a = 2, b = , c = –10
Sum of zeroes
Here,
Product of zeroes
Here,
Question:10
Which of the following equations has no real roots ?
Answer:
(A)
Solution
We know that if the equation has no real roots, then
(A)
Compare with where
Here
(no real roots)
(B)
Compare with where
Here
(two distinct real roots)
(C)
Compare with where
Here
(two distinct real roots)
(D)
Compare with where
Here
(two equal real roots)
Here only has no real roots.
Question:10
Answer:
Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
=0
Multiply by 3
=0
=0
=0
=0
Hence, are the zeroes of the polynomial
Here, a = 21, b = –11, c = –2
Sum of zeroes
Here,
Product of zeroes
Here,
Question:1
For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
(i)
(ii)
(iii)
(iv)
Answer:
(i) Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
Here, sum of zeroes
Product of zeroes
Let p(x) is the required polynomial
p(x) = x^{2} – (sum of zeroes)x + (product of zeroes)
Multiply by 3
Hence, is the required polynomial
=0
are the zeroes of p(x).
(ii) Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
Here, sum of zeroes
Product of zeroes
Let p(x) is the required polynomial
p(x) = x^{2} – (sum of zeroes)x + (product of zeroes)
Multiply by 16 we get
Hence, is the required polynomial
=
==0
are the zeroes of p(x).
(iii) Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
Here, sum of zeroes
Product of zeroes = –9
Let p(x) is required polynomial
p(x) = x^{2} – (sum of zeroes)x + (product of zeroes)
Hence, is the required polynomial
=
=
==0
are the zeroes of p(x)
(iv) Answer.
Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.
Here sum of zeroes
Product of zeroes
Let p(x) is the required polynomial
p(x) = x^{2} – (sum of zeroes)x + (product of zeros)
Multiplying by we get
Hence, is the required polynomial
=
=
are the zeroes of p(x).
Question:2
Answer:
Answer. [5, 2, –1]
Solution. Here the given cubic polynomial is
A = 1, B = –6, C = 3, D = 10
Given that,
We know that,
3(a + b) = 6
a + b = 2 …..(1)
(Q a + b = 2)
(Q a + b = 2)
a = 5, –1
Put a = 5 in (1) put a = –1 in (1)
5 + b = 2 –1 + b = 2
b = –3 b = 3
Hence, value of a = 5, b = –3 and a = –1, b = 3
put a = 5, b = –3 and we get zeroes
a = 5
a + b = 5 – 3 = 2
a + 2b = 5 + 2(–3) = –1
Hence, zeroes are 5, 2, –1.
Question:3
Given that is a zero of the cubic polynomial , find its other two zeroes.
Answer:
Answer.
Given cubic polynomial is
If is a zero of the polynomial then (x – ) is a factor of
=0
Hence, are the other two zeroes.
Question:4
Find k so that is a factor of . Also find all the zeroes of the two polynomials.
Answer:
The given polynomial is
Here, is a factor of
Use division algorithm
Here, is remainder
It is given that is a factor hence remainder = 0
By comparing L.H.S. and R.H.S.
7k + 21 = 0
k = – 3 ….(1)
2k(k + 1) + 6(k + 1) = 0
(k + 1) (2k + 6) = 0
k = –1, –3 …..(2)
From (1) and (2)
k = –3
Hence,
Put k = –3
x + 3 = 0 x – 1 = 0 x – 2 = 0 2x + 1 = 0
x = –3 x = 1 x = 2 2x = – 1
Here zeroes of is –3, 1
Zeroes of
Question:5
Given that is a factor of the cubic polynomial ,find all the zeroes of the polynomial.
Answer:
Answer.
Solution.
The given cubic polynomial is
Hence is a factor
Use divided algorithm
a = 1, b = , c = 3
Hence, are the zeroes of the polynomial.
Question:6
Answer:
Answer. [2, 1]
Solution.
Given :-
,
Hence, q(x) is a factor of p(x) use divided algorithm
Since is a factor hence remainder = 0
By comparing
– 1 – a = 0 b – 2a = 0
a = – 1 2a = b
put a = –1
2(–1) = b
b = –2
Hence, a = –1, b = –2
x – 2 = 0 x – 1 = 0
x = 2 x = 1
Hence, 2, 1 are the zeroes of p(x) which are not the zeroes of q(x).
These Class 10 Maths NCERT exemplar chapter 2 solutions provide a detailed knowledge of polynomials.
The basics of this chapter are covered in Class 9. If any student wants to pursue mathematics in higher classes and appear for competitive exams like JEE Advanced, this chapter holds great importance.
All sets of problems related to Class 10 Polynomials can be studied and practiced through these Class 10 Maths NCERT exemplar solutions chapter 2 Polynomials and are sufficient to solve books such as RS Aggarwal Class 10 Maths, RD Sharma Class 10 Maths, NCERT Class 10 Maths.
NCERT exemplar Class 10 Maths solutions chapter 2 pdf download can be used by the students to refer to the solutions in offline scenarios and sail smoothly through the doubts faced in the NCERT exemplar Class 10 Maths chapter 2.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
The chapter of Polynomials is important for Board examinations as it holds around 5-6% weightage of the whole paper.
The chapter on Polynomials serves as a key topic for JEE Advanced and clarity of concepts beginning from lower classes such as Class 10 can help the students to build a strong foundation for competitive exams as well as higher classes.
NCERT exemplar Class 10 Maths solutions chapter 2 delivers very descriptive solutions to the student and can be referred while facing any issues in solving the problems of exemplar.
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The Sadhu Ashram in Aligarh is located in Chhalesar . The ashram is open every day of the week, except for Thursdays . On Mondays, Wednesdays, and Saturdays, it's open from 8:00 a.m. to 7:30 p.m., while on Tuesdays and Fridays, it's open from 7:30 a.m. to 7:30 p.m. and 7:30 a.m. to 6:00 a.m., respectively . Sundays have varying hours from 7:00 a.m. to 8:30 p.m. . You can find it at Chhalesar, Aligarh - 202127 .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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