9th Maths 2.1

NCERT Class 9th solution of Exercise 2.2

NCERT Class 9th solution of Exercise 2.3

NCERT Class 9th solution of Exercise 2.4

NCERT Class 9th solution of Exercise 2.5

NCERT Class 9th solution of Exercise 1.1

NCERT Class 9th Projects

Exercise 2.1

Q1. Which of the following expression are polynomials in one variable and which are not? State reason for your answer :

i) `4x^2 - 3x + 7`   ii) `y^2 + sqrt2`

iii)  `3sqrtt + tsqrt2`   iv)  `y + frac{2}{y}`

v)  `x^(10) + y^3 + t^(50)`

Answer :

i) A polynomial in one variable because there is only one variable with each exponent a whole number.

ii) A polynomial in one variable because there is only one variable with each exponent a whole number.

iii) Not a polynomial because every exponent of the variable is not a whole number.

iv) Not a polynomial because every exponent of the variable is not a whole number.

v) A polynomial in three variables because there are three variables with each exponent a whole number.

Q2. Write the coefficient of `x^2` in each of the following:

i) `2+x^2+x`   ii) `2 - x^2 + x^3`  

iii) `frac{π}{2}x^2 + x`  iv) `sqrt2x - 1`

Answer :

i) `1`  ii) `-1`  iii) `frac{π}{2}`  iv) `0`

Q3. Give one example of each of a binomial of degree `35` and of a monomial of degree `100`.

Answer :

Binomial of degree `35 = x^35 + 100`

Monomial of degree `100 = 10x^100`. 

Q4. Write the degree of each of the following polynomial:

i) `5x^3 + 4x^2 + 7x`  ii) `4 - y^2`

ii) `5t - sqrt7`  v) `3`.

Answer :

i) `3`  ii) `2`  iii) `1`  iv) `0`

Q5. Classify the following as linear, quadratic and polynomial :

i) `x^2 + x`  ii) `x - x^2`

iii) `y+y^2+4`  iv) `1 + x`

v) `3t`  vi) `r^2`   vii) `7x^3`.

Answer :

Linear:  iv),  v)

Quadratic: i),  iii),  vi)

Cubic: ii),  vii)