English mein solve karo

Here are the solutions to your questions:

1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

• 1(i) $4x^2 - 3x + 7$ This is a polynomial in one variable. Reason: The expression has only one variable $x$, and the powers of $x$ ($2, 1, 0$) are all whole numbers.

• 1(ii) $y^2 + \sqrt{2}$ This is a polynomial in one variable. Reason: The expression has only one variable $y$, and the powers of $y$ ($2, 0$) are all whole numbers.

• 1(iii) $3\sqrt{t} + t\sqrt{2}$ This is not a polynomial. Reason: The expression can be written as $3t^{1/2} + t\sqrt{2}$. Here, the power of the variable $t$ is $1/2$, which is not a whole number.

• 1(iv) $y + \frac{2}{y}$ This is not a polynomial. Reason: The expression can be written as $y + 2y^{-1}$. Here, the power of the variable $y$ is $-1$, which is not a whole number.

• 1(v) $x^{10} + y^3 + t^{50}$ This is not a polynomial in one variable. Reason: The expression has three different variables $x, y,$ and $t$.

2. Write the coefficients of $x^2$ in each of the following.

• 2(i) $2 + x^2 + x$ The coefficient of $x^2$ is $\boxed{1}$.

• 2(ii) $2 - x^2 + x^3$ The coefficient of $x^2$ is $\boxed{-1}$.

• 2(iii) $\frac{\pi}{2}x^2 + x$ The coefficient of $x^2$ is $\boxed{\frac{\pi}{2}}$.

• 2(iv) $\sqrt{2}x - 1$ There is no $x^2$ term, so its coefficient is $\boxed{0}$.

3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

• Binomial of degree 35: A binomial has two terms, and the degree 35 means the highest power of the variable is 35. Example: $\boxed{x^{35} + 9}$

• Monomial of degree 100: A monomial has one term, and the degree 100 means the power of the variable is 100. Example: $\boxed{4y^{100}}$

4. Write the degree of each of the following polynomials.

• 4(i) $5x^3 + 4x^2 + 7x$ The degree of a polynomial is the highest power of the variable. Here, the highest power is 3. Degree: $\boxed{3}$

• 4(ii) $4 - y^2$ Here, the highest power is 2. Degree: $\boxed{2}$

• 4(iii) $5t - \sqrt{7}$ Here, the highest power is 1. Degree: $\boxed{1}$

• 4(iv) 3 This is a constant polynomial, which can be written as $3x^0$. Degree: $\boxed{0}$

5. Classify the following as linear, quadratic and cubic polynomials.

• 5(i) $x^2 + x$ The degree of this polynomial is 2. It is a $\boxed{\text{quadratic polynomial}}$.

• 5(ii) $x - x^3$ The degree of this polynomial is 3. It is a $\boxed{\text{cubic polynomial}}$.

• 5(iii) $y + y^2 + 4$ The degree of this polynomial is 2. It is a $\boxed{\text{quadratic polynomial}}$.

• 5(iv) $1 + x$ The degree of this polynomial is 1. It is a $\boxed{\text{linear polynomial}}$.

• 5(v) $3t$ The degree of this polynomial is 1. It is a $\boxed{\text{linear polynomial}}$.

• 5(vi) $r^2$ The degree of this polynomial is 2. It is a $\boxed{\text{quadratic polynomial}}$.

• 5(vii) $7x^3$ The degree of this polynomial is 3. It is a $\boxed{\text{cubic polynomial}}$.