Coefficients

Q.

The value of $4^{\frac{1}{3}}.4^{\frac{1}{9}}.4^{\frac{1}{27}}..........\infty$ is

1. $2$

2. $3$

3. $4$

4. $9$

Q.

For $r=0,1,...,10$let $A_r,B_r$and $C_r$ denote, respectively the coefficient of $x_r$ in the expansion of${(1+x)}^{10},{(1+x)}^{20}$ and ${(1+x)}^{30}.$

Then $\sum _{r=1}^{10}{A}_r(B_{10}{B}_r-C_{10}{A}_r)=?$

1. $B_{10}–C_{10}$

2. $A_{10}({B_{10}}^2–C_{10}{A}_{10})$

3. $0$

4. $C_{10}–B_{10}$

Q.

To reduce the differential equation $\frac{dy}{dx}+P\left(x\right)·y=Q\left(x\right)·y^n$ to the linear form, the substitution is

1. $v=\frac{1}{y^n}$

2. $v=\frac{1}{y^{n-1}}$

3. $v=y^n$

4. $v=y^{n-1}$

Q.

Question 52

The numerical coefficient in $-37abc$ is ___

Q. Question 1(vi)
Identify the terms, their coefficients for the following expressions:
0.3a – 0.6ab + 0.5 b

Q.

Coefficient of $y$ in the term $-\frac{y}{3}$ is

1. $-1$

2. $-3$

3. $-\frac{1}{3}$

4. $\frac{1}{3}$

Q.

Coefficient of y in the term -$\frac{y}{9}$ is:

1. -3
   

2. -1
   

3. ​

4. -​

Q.

Write the coefficient of:

$\left(i\right)abin7abx,\left(ii\right)7ain7abx;\left(iii\right)5x^{2}in5x^2-5x;\left(iv\right)8in{a}^2-8ax+a;\left(v\right)4xyin{x}^2-4xy+y^2.$

Q. Write the coefficient of $x^2$ in $2+x^2+x$

1. $2$
2. $0$
3. $-1$
4. $1$

Q.

Question 1(iii)
Identify the terms, their coefficients for the following expression:
$4x^2{y}^2-4x^2{y}^2{z}^2+z^2$

Q.

Identify the terms, their co-efficients for each of the following expressions:

(i) $7x^{2}yz-5xy$ (ii) $x^2+x+1$ (iii) $3x^2{y}^2-5x^2{y}^2{z}^2+z^2$

(iv) $9-ab+bc-ca$ (v) $\frac{a}{2}+\frac{b}{2}-ab$ (vi) $0.2x-0.3xy+0.5y$

Q.

Write the degree of each of the following polynomials :

$1-x^8$

Q. $\text{The coefficient of 'y' in the term}-24x^{2}y\text{is}$ ________ .

1. $-24$
2. $-24x$
3. $-24x^2$
4. $-24x^{2}y$

Q. The coefficient of the term $x{y}^3$ in the expression $x{y}^4-x^{5}y-3x{y}^3$ is:

1. 3
2. -3
3. 1
4. -1

Q.

What is the condition for the quotient of two perfect squares to be also a perfect square?

Q. What is the sum of the coefficients of the variable terms of the polynomial

$5x^2$ + $4x$ + $10$ ?

1. 10
2. 14
3. 19
4. 9

Q.

Write the coefficient of $x^3$ in $-x^3$

Q.

What are Eigenvalues of a Matrix?

Q. If each side of a square is doubled, the factor by which area of the square will change is ___ times.

Q.

If each side of a square, of side a, is doubled, find the new area.

1. $a^2$

2. $a^4$

3. 4$a^2$

4. 4$a^4$

Q.

If $x^g$+$\frac{1}{x^a}$ is a polynomial in one variable and if it is given that g = a, the expression represents a constant polynomial for a = ___

Q.

Queston 1(i)
Identify the terms, their coefficients for the following expression:
$5xy{z}^2-3zy$

Q. Write the numerical coefficient of the following:
7xyz

Q.

Find the coefficient of ${\mathrm{y}}^2$ in the following algebraic expressions :

$22{\mathrm{y}}^2-{\mathrm{x}}^2$

Q. Write the coefficient of $x^2$ in $\sqrt{2}-1$

1. $\sqrt{2}$
2. $1$
3. $0$
4. $-1$

Q. Write down the coefficient of x in the following: $5xyz$

Q. Find the coefficient of $x^2$ in $2x^3+7x^2+6x+5$

1. $2$
2. $6$
3. $5$
4. $7$

Q. Write the coefficient of $x^2$ in $2-x^2+x^3$

1. $1$
2. $x$
3. $-1$
4. $2$

Q. Write the numerical coefficient of $ab.$

Q.

What is the coefficient of $x^2$ in the polynomial $5x^3-4x^2+3x+10$ ?

1. 3

2. -4

3. 5

4. 10