Multiplication of Monomials

Q.

Find the HCF of 1260 and 7344 using Euclids algorithm?

Q. Express the following in exponential form:
(i) 5 × 5 × 5 × 5 × 5
(ii) 4 × 4 × 4 × 5 × 5 × 5
(iii) (-1) × (-1) × (-1) × (-1) × (-1)
(iv) a × a × a × b × c × c × c × d × d

Q.

What is the result if a monomial is multiplied by a monomial?

1. Monomial

2. Binomial

3. Trinomial

4. Constant

Q. Prove that $a^2+b^2+c^2-ab-bc-ca=\frac{1}{2}\left[{\left(b-c\right)}^2+{\left(c-a\right)}^2+{\left(a-b\right)}^2\right]$

Q. How many terms are obtained on simplifying $(3x+5)(x-4)$?

Q. If X = 5 x 5 x 7 x 11 x 13 x 13 x Y, find the value of Y that makes X a perfect square.​

1. 7
2. 35
3. 91
4. 77

Q. If $(x^2+y^2=58)$ and $(x+y=10)$, then find the value of $(x^3+y^3)$.

Q. If the area of a rectangle is a${}^2$ + 5ab + 6b${}^2$, what will be its perimeter? (2 marks)

Q. If $a+b=7$ and $ab=12$, find the value of $(a^2-ab+b^2)$.

Q.

Which of the following is equal to $(x+2)(x+3)?$

1. $x^2+5x+6$

2. $x^2+4x+6$

3. $x^2+3x+6$

4. $x^2+2x+6$

Q. $\frac{8^{3a}\times 2^5\times 2^{2a}}{4\times 2^{11a}\times 2^{-2a}}$ is $2^{2a+3}$
State true or false:

1. True
2. False

Q. Prove independently that
$\frac{C_0}{1}-\frac{C_1}{4}+\frac{C_2}{7}-.......+(-1{)}^n\frac{C_n}{3n+1}=\frac{3^n\cdot n!}{\mathrm{1.4.7.....}(3n+1)}$

Q.

The product of $(x+7y)and(7x-y)$ is

1. $7x^2-48xy+7y^2$

2. $7x^2-48xy-7y^2$

3. $7x^2+48xy+7y^2$

4. $7x^2+48xy-7y^2$

Q. Find the squares of the following binomials:

(1) x + 4
(2) 3 + m
(3) 3x + 1
(4) p + 2q
(5) x + 2y

Q. Multiply : (i) $3x^2$ + 4xy by 2x (ii) – 4a [a + 3b]

Q. Simplify:
$[{(5z-2)}^2+40z]÷(5z+2)$

Q. $x^2+6xy-z^2+9y^2$=

1. $(x+3y-z)(x+3y-z)$
2. $(x-3y+z)(x-3y+z)$
3. $(x-3y-z)(x-3y-z)$
4. $(x+3y+z)(x+3y-z)$

Q. For real number $a,b,c$ and $d$ , if $a^2+b^2=4$ and $c^2+d^2=1$, then possible value of $ac+bd$ is / are

1. $2$
2. $3$
3. $1$
4. $\frac{1}{4}$

Q. Simplify: $(3x-2y)(3x+4y)-(3x+2y)(3x-2y)$$\left[3Marks\right]$

Q. Expanded form of $(-ab{)}^4$ is

1. $(-ab)\times (-ab)\times (-ab)\times (-ab)$
2. $4\times (-ab)$
3. $(-ab)\times (-ab)$
4. $(-ab)\times (-ab)\times (-ab)$

Q. The product of $(x+7y)and(7x-y)$ is

Q. The value of $x$, if $\frac{11}{17}\times x=1$, is

1. $1$
2. $\frac{17}{11}$
3. $\frac{11}{17}$
4. $0$

Q. If $3a+5b+4c=0$, then

1. True
2. False

Q. Find the missing term in the

1. 16
2. 19
3. 15
4. None of these

Q. Factorise the following expression using algebraic identities.
$9y^2+66xy+121y^2$

Q.

Find the product of $\frac{4}{6}ab$ and $\frac{-3}{10}{x}^{2}y$.

1. $\frac{1}{5}abxy$
   

2. $\frac{-1}{5}abxy$

3. $\frac{-1}{5}ab{x}^{2}y$

4. $\frac{1}{5}ab{x}^{2}y$
   

Q. At $25,\left[H_3{O}^{+}\right]=1\times {10}^{-7}M$ in water, hence, $K_a$ is:

1. $1\times {10}^{-14}$
2. $5.55\times {10}^{-15}$
3. $1.8\times {10}^{-16}$
4. $55.5\times {10}^{-10}$

Q.