MCQ 11 Mark
If we subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3,$ then the answer is:
- ✓
$8a - 2ab + 2b - 15$
- B
$8a + 2ab + 2b - 15$
- C
$8a - 2ab - 2b - 15$
- D
$8a + 2ab + 2b + 15$
AnswerCorrect option: A. $8a - 2ab + 2b - 15$
$(12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)$
$= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12$
$= (12 - 4)a - (9 - 7)ab + (5 - 3)b - 3 - 12$
$= 8a - 2ab + 2b - 15$
View full question & answer→MCQ 21 Mark
If we multiply $5x$ and $(-4xyz),$ then we get:
- A
$20x^2yz$
- ✓
$-20x^2yz$
- C
$x^2yz$
- D
$-2xyz$
AnswerCorrect option: B. $-20x^2yz$
B. $-20x^2yz$
Solution:
$(5x) \times (-4xyz)$
$= 5x \times (-4) \times x y \times z$
$= -20x^{1+1}yz$
$= -20^x2yz$
View full question & answer→MCQ 31 Mark
Tick $(\checkmark)$ the correct answer: $(x + 5)(x - 3) = ?$
- A
$x^2 + 5x - 15$
- B
$x^2 - 3x - 15$
- C
$x^2 + 2x + 15$
- ✓
$x^2 + 2x - 15$
AnswerCorrect option: D. $x^2 + 2x - 15$
D. $x^2 + 2x - 15$
Solution:
$(x + 5)(x - 3)$
$(x)^2 + (5 - 3)x + 5 \times (-3)$
$= x^2+ 2x - 15$
View full question & answer→MCQ 41 Mark
Which are the standard identities?
- A
$(a+b)^2=a^2+2 a b+b^2(a-b)^2=a^2-2 a b+b^2$ and $(x+a)(x+b)=x^2+(a-b) x+a b$
- B
$(a-b)^2=a^2-2 a b+b^2 a^2-b^2=(a+b)(a-b)$ and $(x+a)(x+b)=x^2+(a-b) x+a b$
- C
$(a+b)^2=a^2+2 a b+b^2 a^2-b^2=(a+b)(a-b)$ and $(x+a)(x+b)=x^2+(a-b) x+a b$
- ✓
$(a+b)^2=a^2+2 a b+b^2(a-b)^2 a^2 2 a b+b^2$ and $a^2-b^2=(a+b)(a-b)$
AnswerCorrect option: D. $(a+b)^2=a^2+2 a b+b^2(a-b)^2 a^2 2 a b+b^2$ and $a^2-b^2=(a+b)(a-b)$
D. $(a+b)^2=a^2+2 a b+b^2(a-b)^2 a^2 2 a b+b^2$ and $a^2-b^2=(a+b)(a-b)$
Solution:
$(a+b)^2=a^2+2 a b+b^2(a-b)^2=a^2-2 a b+b^2$ and $a^2-b^2=(a+b)(a-b)$ identities are known as standard identities.
View full question & answer→MCQ 51 Mark
Which of the following is a trinomial?
- A
$-7z$
- B
$z^2- 4y^2$
- ✓
$x^2y - xy^2 + y^2$
- D
$12a - 9ab + 5b - 3$
AnswerCorrect option: C. $x^2y - xy^2 + y^2$
C. $x^2y - xy^2 + y^2$
Solution:
$x^2y - xy^2 + y^2$ contains three terms
View full question & answer→MCQ 61 Mark
The value of $(-27x^2y) \div (-9xy)$ is:
AnswerD. $3x$
Solution:
We have, $(-27x^2y^2 ) \div (-9xy)$
$=\frac{-27\text{x}^2\text{y}^2}{-9\text{xy}}$
$=\frac{27\times\text{x}\times\text{x}\times\text{y}}{9\times\text{x}\times\text{y}}$
$=\frac{27}{9}\text{x}$
$=3\text{x}$
View full question & answer→MCQ 71 Mark
Product of $6a^2 - 7b + 5ab$ and $2ab$ is:
AnswerCorrect option: B. $12a^3b - 14ab^2 + 10a^2b^2$
B. $12a^3b - 14ab^2 + 10a^2b^2$
Solution:
Required product $= 2ab × (6a^2 - 7b + 5ab)$
This is the product of a trinomial by a monomial, so we multiply monomial with each term of the trinomial.
$= 2ab \times (6a^2 - 7b + 5ab) = 2ab \times 6a^2 + 2ab(-7b) + 2ab \times 5ab$
$= 12a^3b - 14ab^2 + 10a^2b^2$
View full question & answer→MCQ 81 Mark
Which of the following is like term as $3xy^2?$
- A
$7xy$
- ✓
$7xy^2$
- C
$7x$
- D
$7y^2$
AnswerCorrect option: B. $7xy^2$
B. $7xy^2$
View full question & answer→MCQ 91 Mark
The product of $6x$ and $-11x$ is:
- ✓
$-66x^2$
- B
$-x^2$
- C
$x^2$
- D
$66x^2$
AnswerCorrect option: A. $-66x^2$
A. $-66x^2$
Solution:
$(6x)(-11x) = -66x^2$
View full question & answer→MCQ 101 Mark
The coefficient in the term $-20$ is:
View full question & answer→MCQ 111 Mark
Tick $(\checkmark)$ the correct answer: If $\Big(\text{x}+\frac{1}{\text{x}}\Big)=5,$ then $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)=?$
- A
$25$
- B
$27$
- ✓
$23$
- D
$25\frac{1}{25}$
Answer$\Big(\text{x}+\frac{1}{\text{x}}\Big)=5,$
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=(5)^2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+2=25$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+25-2=23$
View full question & answer→MCQ 121 Mark
If $3x - 7y = 10$ and $xy = -1$ then the value of $9x^2 + 49y^2$ is:
- ✓
$58$
- B
$-104$
- C
$104$
- D
$\frac{14}{2}$
View full question & answer→MCQ 131 Mark
What degree does $x^3- x^2y^2 - 8y^2 + 2$ have?
View full question & answer→MCQ 141 Mark
If $2x + y = 5$ then $4x + 2y$ is equal to:
View full question & answer→MCQ 151 Mark
($a + b)^2$ is equal to:
- A
$a^2 + b^2 - 2ab$
- ✓
$a^2 + b^2 + 2ab$
- C
$a^2 + b^2$
- D
$2ab$
AnswerCorrect option: B. $a^2 + b^2 + 2ab$
B. $a^2 + b^2 + 2ab$
Solution:
$(a + b)^2 = a^2 + b^2 + 2 ab$
View full question & answer→MCQ 161 Mark
If $x + y = 6$ and $3x - y = 4$ then $x - y$ is equal to:
View full question & answer→MCQ 171 Mark
What is the value of the expression $2ab + 3bc + 4ac$, when $a = b = c = 1?$
View full question & answer→MCQ 181 Mark
What is the simplified form of $(a^2 - b^2)^2?$
- A
$a^4 + 2a^2b^2 + b^4$
- ✓
$a^4- 2a^2b^2 + b^4$
- C
$a^4 - 2a^2b^2 - b^4$
- D
$a^4 + a^2b^2 + b^4$
AnswerCorrect option: B. $a^4- 2a^2b^2 + b^4$
B. $a^4- 2a^2b^2 + b^4$
View full question & answer→MCQ 191 Mark
What is the value of $5x^{25} - 3x^{32} + 2x^{-12}$ at $x = 1?$
AnswerC. $4$
Solution:
$5x^{25} - 3x^{32} + 2x^{-12}$
$5 \times (1) - 3 \times (1) + 2 \times (1)$
If we give 1 any raised power the answer is always $1.$
$[e.g 1^4 = 1 \times 1 \times 1 \times 1 = 1]$
$= 5 - 3 + 2$
$= 2 + 2 = 4$
View full question & answer→MCQ 201 Mark
What is the sum of $7xy + 5yz - 3xz$ & $2xy + 4yz + 2xz?$
- A
$8xy + yz - xz$
- ✓
$9xy + 9yz + xz$
- C
$9xy + 9yz - xz$
- D
$9xy + 9yz + 5xz$
AnswerCorrect option: B. $9xy + 9yz + xz$
$9xy + 9yz + xz$
View full question & answer→MCQ 211 Mark
Sum of $a - b + ab, b + c - bc$ and $c - a - ac$ is:
- ✓
$2c + ab - ac - bc$
- B
$2c - ab - ac - bc$
- C
$2c + ab + ac + bc$
- D
$2c - ab + ac + bc$
AnswerCorrect option: A. $2c + ab - ac - bc$
Required sum $= (a - b + ab) + (b + c - bc) + (c - a - ac)$
$= a - b + ab + b + c - bc + c - a - ac$
$= 2c + ab - ac - bc$
View full question & answer→MCQ 221 Mark
The sum of $8pq$ and $-17\ pq$ is:
AnswerCorrect option: C. $-9pq$
Sum $= \{8 + (-17)\} pq = -9pq$
View full question & answer→MCQ 231 Mark
Simplify $\Bigg(\frac{4\text{x}}{\text{y}}-\frac{7}{\text{z}}^2\Bigg)$using a suitable identity.
- A
$16\frac{\text{x}}{\text{y}}+56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
- B
$16\frac{\text{x}^2}{\text{y}^2}+56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
- ✓
$16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
- D
$16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}-\frac{49}{\text{z}^2}$
AnswerCorrect option: C. $16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
C. $16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
Solution:
Using $(a - b)^2 = a^2 - 2ab + b^2$
$\Bigg(\frac{4\text{x}}{\text{y}}-\frac{7}{\text{z}}\Bigg)^2=\Bigg(\frac{4\text{x}}{\text{y}}\Bigg)^2-2\times\frac{4\text{x}}{\text{y}}\times\frac{7}{\text{z}}+\Big(\frac{7}{\text{z}}\Big)^2$
$=16\frac{\text{x}^2}{\text{y}^2}-56\frac{\text{x}}{\text{yz}}+\frac{49}{\text{z}^2}$
View full question & answer→MCQ 241 Mark
Which of the following statements incorrect$?$
- A
If we multiply two monomials together, the product is also a monomial.
- B
Like terms are formed from the same variables and their powers are also same.
- ✓
Coefficients of like terms need to be the same.
- D
An equation is true only for certain values of its variables.
AnswerCorrect option: C. Coefficients of like terms need to be the same.
The option $(C)$ is the correct option because coefficients of like terms need not to be the same
View full question & answer→MCQ 251 Mark
Tick $(\checkmark)$ the correct answer: $(2x^2 + 3x + 1) \div (x + 1) = ?$
- A
$(x + 1)$
- ✓
$(2x + 1)$
- C
$(x + 3)$
- D
$(2x + 3)$
AnswerCorrect option: B. $(2x + 1)$
B. $(2x + 1)$
Solution:
View full question & answer→MCQ 261 Mark
If $a + b + c = 9$ and $ab + bc + ca = 26,$ then the value of $a^3 + b^3 + c^3 – 3abc$ is:
View full question & answer→MCQ 271 Mark
The coefficient of xy in $6x^2y^2$ is:
AnswerD. $6xy$
Solution:
$6x^2y^2 = (6xy)(xy)$
View full question & answer→MCQ 281 Mark
Coefficient of ? in the term $-\frac{\text{y}}{3}$ is:
- A
$-1$
- B
$-3$
- ✓
$-\frac{1}{3}$
- D
$\frac{1}{3}$
AnswerCorrect option: C. $-\frac{1}{3}$
We can write $-\frac{\text{y}}{3}$ as $-\frac{1}{3}xy$
so, the cofficient of $y$ is $-\frac{1}{3}$
View full question & answer→MCQ 291 Mark
The product of $4mn$ and $0$ is:
View full question & answer→MCQ 301 Mark
The expression $7xy$ has the factors:
- ✓
$7, x, y$
- B
$x, y$
- C
$7, x$
- D
$7, y$
AnswerCorrect option: A. $7, x, y$
$7, x, y$
View full question & answer→MCQ 311 Mark
The coefficient in the term $20$ is:
View full question & answer→MCQ 321 Mark
Tick $(\checkmark)$ the correct answer: $(2x^2 + 3x + 1) \div (x + 1) = ?$
- A
$(x + 2)$
- ✓
$(2x + 1)$
- C
$(x + 3)$
- D
$(2x + 3)$
AnswerCorrect option: B. $(2x + 1)$
(B). $(2x + 1)$
Solution:
$= x - 2$ View full question & answer→MCQ 331 Mark
The volume of a cuboid with length, breadth and height as $5x, 3x^2$ and $7x^4$ respectively is:
- A
$105x^2$
- B
$105x$
- ✓
$105x^7$
- D
$105x^4$
AnswerCorrect option: C. $105x^7$
C. $105x^7$
Solution:
Volume of cuboid $= Length \times breadth \times height$
$V = 5x \times 3x^2 \times 7x^4$
$V = 105x^{1 + 2 + 4}$
$V = 105x^7$ cubic units
View full question & answer→MCQ 341 Mark
The expression $x + y + z$ is in:
Answer There are three variables $x, y$ and $z.$
View full question & answer→MCQ 351 Mark
Number of factors of $(a + b) 2$ is:
AnswerC. $2$
Solution:
We can write $(a + b)^2$ as, $(a + b)(a + b)$ and this cannot be factorised further.
Hence, number of factors of $(a + b)^2$ is $2.$
View full question & answer→MCQ 361 Mark
Area of a rectangle with length $4ab$ and breadth $6b^2$ is:
- A
$24a^2b^2$
- ✓
$24ab^3$
- C
$24ab^2$
- D
$24ab$
AnswerCorrect option: B. $24ab^3$
B. $24ab^3$
Solution:
We know that, area of a rectangle = Lenght $\times$ Breadth
$= 4ab \times 6b^2$
This is the product of two monomials
Area of a rectangle $= (4 \times 6)ab \times b^2 = 24ab^3$
View full question & answer→MCQ 371 Mark
Subtract $4ab(a + b)$ from $7b(a - b).$
AnswerCorrect option: B. $7ab - 4a^2b - 4ab^2 - 7b^2$
B. $7ab - 4a^2b - 4ab^2 - 7b^2$
Solution:
$4ab(a + b) = 4a^2b + 4ab^2$ and $7b(a - b) = 7ab - 7b^2$
View full question & answer→MCQ 381 Mark
The sum of $7x, 10x$ and $12x$ is:
AnswerSum $= (7 + 10 + 12) x = 29x$
View full question & answer→MCQ 391 Mark
How many terms are there in the expression $5 - 3xy?$
View full question & answer→MCQ 401 Mark
The sum of $x^2 - y^2, y^2 - z^2$ and $z^2 - x^2$ is:
- ✓
$0$
- B
$3x^2$
- C
$3y^2$
- D
$3z^2$
AnswerA. $0$
Solution:
Sum $= (x^2 - y^2) + (y^2- z^2) + (z^2 - x^2) = 0$
View full question & answer→MCQ 411 Mark
Tick $(\checkmark)$ the correct answer: $(x + 4)(x + 4) = ?$
- A
$(x^2 + 16)$
- B
$(x^2 + 4x + 16)$
- ✓
$(x^2 + 8x + 16)$
- D
$(x^2 + 16x)$
AnswerCorrect option: C. $(x^2 + 8x + 16)$
C. $(x^2 + 8x + 16)$
Solution:
$(x + 4)(x + 4)$
$= x^2 + (4 + 4)x + 4 × 4$
$= x^2 + 8x + 16$
View full question & answer→MCQ 421 Mark
The value of $\frac{\big(67.542\big)^2-\big(32.458\big)^2}{72.458-40.374}$ is:
View full question & answer→MCQ 431 Mark
Square of $9x - 7xy$ is:
AnswerCorrect option: C. $81x^2 + 49x^2y^2 - 126x^2y$
C. $81x^2 + 49x^2y^2 - 126x^2y$
Solution:
Square of $(9x - 7xy) = (9x- 7x)^2$
Comparing with $(a - b)^2$
we get $a = 9x$ and $b = 7xy$
$(9x - 7xy)^2 = (9x)^2 - 2.9x. 7xy + (7xy)^2$
$= 81x^2 - 126x^2y + 49x^2y^2$
$= 81x^2+ 49x^2y^2 - 126x^2y$
View full question & answer→MCQ 441 Mark
The value of $5x$ when $x = 5$ is:
AnswerValue$ = 5 \times 5 = 25$
View full question & answer→MCQ 451 Mark
Using suitable identity, evaluate $(7.5)^2$
- ✓
$56.25$
- B
$56.5$
- C
$56.025$
- D
$81$
AnswerCorrect option: A. $56.25$
A. $56.25$
Solution:
Writing $7.5 = 7 + 0.5$
$(7.5)^2 = (7 + 0.5)^2$
Using $(a + b)^2 = a^2 + b^2 + 2ab,$ we have $(7.5)^2 = (7 + 0.5)^2 = 7^2 + 2 × 7 \times 0.5 + (0.5)^2= 49 + 7 + 0.25 = 56.25$
View full question & answer→MCQ 461 Mark
Which of the following is a trinomial$?$
- ✓
$3a + 4b + 5$
- B
$2x + 7$
- C
$3x$
- D
$4x + y$
AnswerCorrect option: A. $3a + 4b + 5$
$3a + 4b + 5$
View full question & answer→MCQ 471 Mark
Tick $(\checkmark)$ the correct answer: $8a^2b^3 \div (-2ab) = ?$
- A
$4ab^2$
- B
$4a^2b$
- ✓
$-4ab^2$
- D
$-4a^2b$
AnswerCorrect option: C. $-4ab^2$
C. $-4ab^2$
Solution:
$8\text{a}^2\text{b}^3\div(-2\text{ab})$
$\Rightarrow\frac{8\text{a}^2\text{b}^3}{-2\text{ab}}$
$\Rightarrow-4\text{a}^{2-1}\text{b}^{3-1}$
View full question & answer→MCQ 481 Mark
Add: $7xy + 5yz - 3zx, 4yz + 9zx - 4y, –3xz + 5x - 2xy.$
AnswerCorrect option: C. $5xy + 9yz + 3zx + 5x - 4y$
$5xy + 9yz + 3zx + 5x - 4y$
View full question & answer→MCQ 491 Mark
What should be subtracted from $2x^2 - 5y^2 + 7z^2$ to get $x^2 - y^2 + z^2$
- ✓
$x^2 - 4y^2 + 6z^2$
- B
$x^2 - 3y^2 + 6z^2$
- C
$3x^2 - 2y^2 + 2z^2$
- D
$x^2 - y^2 + z^2$
AnswerCorrect option: A. $x^2 - 4y^2 + 6z^2$
A. $x^2 - 4y^2 + 6z^2$
View full question & answer→MCQ 501 Mark
If $\text{x}-\text{y}=4$ and $\text{xy}=21$ then $\text{x}^3-\text{y}^3$
View full question & answer→