MCQ 1011 Mark
Multiplication of $pq + qr + rp$ and ‘zero’ is:
- A
$pq + qr$
- B
$pq + rp$
- C
$pq + qr + nrp$
- ✓
$0$
View full question & answer→MCQ 1021 Mark
Tick $(\checkmark)$ the correct answer: $(x - 6)(x - 6) = ?$
- A
$(x^2 - 36)$
- B
$(x^2 + 36)$
- C
$(x^2 - 6x + 36)$
- ✓
$(x^2 - 12x + 36)$
AnswerCorrect option: D. $(x^2 - 12x + 36)$
D. $(x^2 - 12x + 36)$
Solution:
$(x - 6)(x - 6)$
$= x^2 + (-6 - 6)x + (-6)(-6)$
$= x^2 - 12x + 36$
View full question & answer→MCQ 1031 Mark
The value of $(a + b)^2 + (a - b)^2$ is:
- A
$2a + 2b$
- B
$2a - 2b$
- ✓
$2a^2 + 2b^2$
- D
$2a^2 - 2b^2$
AnswerCorrect option: C. $2a^2 + 2b^2$
C. $2 a^2+2 b^2$
Solution:
We have,
$(a+b)^2+(a-b)^2=\left(a^2+b^2+2 a b\right)+\left(a^2+b^2-2 a b\right) $
$=\left(a^2+a^2\right)+\left(b^2+b^2\right)+(2 a b-2 a b)$
$=2 a^2+2 b^2$
View full question & answer→MCQ 1041 Mark
The result of subtraction of $3x$ from $-4x$ is:
View full question & answer→MCQ 1051 Mark
The factorised form of $3x - 24$ is:
- A
$3x × 24$
- ✓
$3(x - 8)$
- C
$24(x - 3)$
- D
$3(x - 12)$
AnswerCorrect option: B. $3(x - 8)$
We have,
$3x - 24 = 3 × x - 3 × 8 = 3(x - 8)$
$[$taking $3$ as common$]$
View full question & answer→MCQ 1061 Mark
$(x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x)$ is equal to:
- ✓
$0$
- B
$x^2 + y^2 + z^2$
- C
$xy + yz + zx$
- D
$x + y + z$
AnswerA. $0$
Solution:
$(x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x) = x^2 - y^2 + y^2 - z^2 + z^2 - x^2 = 0$
View full question & answer→MCQ 1071 Mark
The like terms of the following are:
- ✓
$2x^2, 9x^2$
- B
$y^2, xy$
- C
$xy, 9a^2$
- D
$y^2, 9x^2$
AnswerCorrect option: A. $2x^2, 9x^2$
A. $2x^2, 9x^2$
View full question & answer→MCQ 1081 Mark
The value of $(x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x)$ is:
- ✓
$0$
- B
$x^2 + y^2 + z^2$
- C
$x + y + z$
- D
$xy + yz + zx$
AnswerA. $0$
Solution:
$(x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x)$
$= x^2 - y^2 + y^2 - z^2 + z^2 - x^2$
[By algebraic identity: $a^2 - b^2 = (a + b)(a - b)$]
$= 0$
View full question & answer→MCQ 1091 Mark
The common factor of $3ab$ and $2cd$ is:
AnswerWe have, monomials $3ab$ and $2cd$ Now, $3ab = 3 × a × b$ and $2cd = 2 × c × d$ Observing the monomials, we see that, there is no common factor (neither numerical nor literal) between them except $1.$
View full question & answer→MCQ 1101 Mark
Which of the following expression is trinomial:
- A
$xyz$
- B
$xy + z$
- ✓
$x + y + z$
- D
$x + yz$
AnswerCorrect option: C. $x + y + z$
$x + y + z$
View full question & answer→MCQ 1111 Mark
Simplify $7pq(q + r) - 8s(p + 2q) + 2r(pq + rs) + 4ps:$
- A
$7pq^2 + 9pqr + 4ps + 16qs + 2r^2s$
- B
$7pq^2 + 5pqr - 4ps + 16qs + 2r^2s$
- ✓
$7pq^2 + 9pqr - 4ps - 16qs + 2r^2s$
- D
$7pq^2 - 5pqr + 4ps - 16qs + 2r^2s$
AnswerCorrect option: C. $7pq^2 + 9pqr - 4ps - 16qs + 2r^2s$
C. $7pq^2 + 9pqr - 4ps - 16qs + 2r^2s$
Solution:
$7pq(q + r) - 8s(p + 2q) + 2r(pq + rs) + 4ps = 7pq (q) + 7pq(r) - 8s(p)-$
$8s(2q) + 2r(pq) + 2r(rs) + 4ps$
$7pq^2 + 7pq(r) - 8ps - 16qs + 2pqr + 2r^2s + 4ps 7pq^2 + 9pqr - 8ps - 4ps - 16qs + 2r^2$
View full question & answer→MCQ 1121 Mark
Product of the following monomials $4p, -7q^3, -7pq$ is:
- ✓
$196 p^2q^4$
- B
$196 pq^4$
- C
$-196 p^2q^4$
- D
$196 p^2q^3$
AnswerCorrect option: A. $196 p^2q^4$
A. $196 p^2q^4$
Solution:
Required Product $= 4p \times (-7q^3) \times (-7pq)$
$= 4 \times (-7) \times (-7)p × q^3 \times pq$
$= 196p^2q^4$
View full question & answer→MCQ 1131 Mark
What are added together to form an expression?
AnswerThe correct option $(B)$ because expressions are formed by adding terms together.
View full question & answer→MCQ 1141 Mark
The number of like terms in $abc, - abc, - bca, acb, bac, \frac{1}{2}12cab$ is:
View full question & answer→MCQ 1151 Mark
The equality $b^2 + 5 > 9b + 12$ us satisfied if:
- A
$b > 8 (or) b < 0$
- B
$b = 10 (or) b = –1$
- ✓
$b > 9 (or) b < 0$
- D
$b > 9 (or) b < 1$
AnswerCorrect option: C. $b > 9 (or) b < 0$
C. $b > 9 (or) b < 0$
View full question & answer→MCQ 1161 Mark
The product of $7x$ and $-12x$ is:
- A
$84x^2$
- ✓
$-84x^2$
- C
$x^2$
- D
$-x^2$
AnswerCorrect option: B. $-84x^2$
B. $-84x^2$
Solution:
$(7x)(-12x) = -84x^2$
View full question & answer→MCQ 1171 Mark
What is the volume of a cube having side $(3ab)cm^2:$
- ✓
$(27a^3b^3)cm^3$
- B
$(9ab)cm^3$
- C
$(27ab)cm^3$
- D
$(9a^3b^3)cm^3$
AnswerCorrect option: A. $(27a^3b^3)cm^3$
A. $(27a^3b^3)cm^3$
Solution:
The volume of a cube having side $3ab = (3ab) \times (3ab) \times (3ab) = 3 \times 3 \times 3 (ab) (ab) (ab) = (27a^3b^3)cm^3$
View full question & answer→MCQ 1181 Mark
$(3x - 5y)^3 - (5x - 2y)^3 + (2x + 3y)^3$
- ✓
$-3(3x - 5y)(2x - 5y)(2x + 3y)$
- B
$3(3x - 5y)(5x - 2y)(2x + 3y)$
- C
$(3x - 5y)(2y - 5x)(2x + 3y)$
- D
$(3x - 5y)(5x - 2y)(2x + 3y)$
AnswerCorrect option: A. $-3(3x - 5y)(2x - 5y)(2x + 3y)$
A. $-3(3x - 5y)(2x - 5y)(2x + 3y)$
View full question & answer→MCQ 1191 Mark
If the product of two numbers is $10$ and the sum is $7,$ then the larger of the two numbers is:
View full question & answer→MCQ 1201 Mark
The product of $3xy^2z$ and $4x$ is:
- A
$12x^2yz$
- B
$12xy^2$
- C
$12xyz$
- ✓
$12x^2y^2z$
AnswerCorrect option: D. $12x^2y^2z$
D. $12x^2y^2z$
Solution:
The product of $3xy^2z$ and $4x$ is:
$\Rightarrow (3xy^2z) (4x)$
$\Rightarrow 3.x.y^2.z.4.x$
$\Rightarrow 12x^2y^2z$
View full question & answer→MCQ 1211 Mark
What do you get when you subtract $-3xy$ from $5xy?$
Answer$5xy - (-3xy) = 5xy + 3xy = 8xy$
View full question & answer→MCQ 1221 Mark
Which of the following is a monomial?
- ✓
$4x^2$
- B
$a + 6$
- C
$a + 6 + c$
- D
$a + b + c + d$
AnswerCorrect option: A. $4x^2$
A. $4x^2$
Solution:
$4x^2$ contains only one term.
View full question & answer→MCQ 1231 Mark
If $\text{a}+\text{b}+\text{c}=10$ and $\text{a}^2+\text{b}^2+\text{c}^2=36$ then $\text{ab}+\text{bc}+\text{ca}=\text{________}$
View full question & answer→MCQ 1241 Mark
The value of $x^2- 2x + 1$ when $x = 1$ is:
AnswerD. $0$
Solution:
Value $= (1)^2- 2(1) + 1 = 0$
View full question & answer→MCQ 1251 Mark
Factorised form of $p^2 - 17p - 38$ is:
- ✓
$(p - 19)(p + 2)$
- B
$(p - 19)(p - 2)$
- C
$(p + 19)(p + 2)$
- D
$(p + 19)(p - 2)$
AnswerCorrect option: A. $(p - 19)(p + 2)$
A. $(p - 19)(p + 2)$
Solution:
We have,
$p^2- 17p - 38$
$= p^2 - 19p + 2p - 38$
$= p(p - 19) + 2(p - 19)$
$= (p - 19)(p + 2)$
View full question & answer→MCQ 1261 Mark
$'2’$ is common factor of the expressions
- A
$12a^2b, 15ab^2$
- B
$5xy, 10x$
- ✓
$10x^2, -18x^3, 14x^4$
- D
$33y, -22z$
AnswerCorrect option: C. $10x^2, -18x^3, 14x^4$
C. $10x^2, -18x^3, 14x^4$
View full question & answer→MCQ 1271 Mark
The product of $4x$ and $0$ is:
AnswerAny value multiplied by zero is zero.
View full question & answer→MCQ 1281 Mark
What is the formulae for $(x - y)^2?$
- A
$x^2 + 2xy + y^2$
- ✓
$x^2 - 2xy + y^2$
- C
$x^2 - 2xy - y^ 2$
- D
$x^2 - y^2$
AnswerCorrect option: B. $x^2 - 2xy + y^2$
B. $x^2 - 2xy + y^2$
View full question & answer→MCQ 1291 Mark
Which of the following is a binomial?
- A
$7 \times a + a$
- B
$6a^2 + 7b + 2c$
- C
$4a \times 3b \times 2c$
- ✓
$6 (a^2 + b)$
AnswerCorrect option: D. $6 (a^2 + b)$
D. $6 (a^2 + b)$
Solution:
Binomials are algebraic consisting of two unlike terms.
$7 \times a + a = 7a + a = 8a$ (monomial)
$6a^2 + 7b + 2c$ (trinomial)
$4a \times 3b \times 2c$ (monomial)
$6(a^2 + b) = 6a^2 + 6b$ (binomial)
View full question & answer→MCQ 1301 Mark
Surbhi tries o make one of the first three identities from $(x+a)(x+b)=x^2+(a+b) x$ $+a b$ by replacing $a$ and $b$ both by - c which identity did she obtain by this?
AnswerCorrect option: B. $(a-b)^2=a^2-2 a b+b^2$
b. $(a-b)^2=a^2-2 a b+b^2$
Solution:
$(x+a)(x+b)=x^2+(a+b) x+a b$
Replacing $a$ and $b$ both by $-c$, we get
$(x-c)(x-c)=x^2+(-c-c) x+(-c)(-c)$
Or, $(x-c) 2=x^2-2 c x+c^2$
It is similar to
$(a-b)^2=a^2-2 a b+b^2$
View full question & answer→MCQ 1311 Mark
Which of the following is not binomial:
- A
$M + n$
- ✓
$Mn$
- C
$M - n$
- D
$M2 - n2$
View full question & answer→MCQ 1321 Mark
The result of subtraction of $7x$ from $0$ is:
View full question & answer→MCQ 1331 Mark
Evaluate $(199.5)^2$ using a suitable identity.
- A
$400200.25$
- B
$39800.025$
- ✓
$39800.25$
- D
$39800$
AnswerCorrect option: C. $39800.25$
C. $39800.25$
Solution:
$(199.5)^2 = (200 - 0.5)^2$ and using $(a - b)^2 = a^1 - 2ab + b^2= (200)^2 - 2 \times 200 \times 0.5 + (0.5)^2= 40000 - 200 + 0.25 = 39800.25$
View full question & answer→MCQ 1341 Mark
Which of the following is a binomial$?$
- A
$3xy$
- ✓
$4l + 5m$
- C
$2x + 3y - 5$
- D
$4a - 7ab + 3b + 12$
AnswerCorrect option: B. $4l + 5m$
$4l + 5m$ contains two terms.
View full question & answer→MCQ 1351 Mark
Tick $(\checkmark)$ the correct answer:
$\left(3 q+7 p^2-2 r^3+4\right)-\left(4 p^2-2 q+7 r^3-3\right)=?$
- A
$\left(p^2+2 q+5 r^3+1\right)$
- B
$\left(11 p^2+q+5 r^3+1\right)$
- C
$\left(-3 p^2-5 q+9 r^3-7\right)$
- ✓
$\left(3 p^2+5 q-9 r^3+7\right)$
AnswerCorrect option: D. $\left(3 p^2+5 q-9 r^3+7\right)$
D. $\left(3 p^2+5 q-9 r^3+7\right)$
Solution:
$\left(3 q+7 p^2-2 r^3+4\right)-\left(4 p^2-2 q+7 r^3-3\right) $
$=3 q+7 p^2-2 r^3+4-4 p^2+2 q-7 r^3+3 $
$=5 q+3 p^2-9 r^3+7 $
$=3 p^2+5 q-9 r^3+7$
View full question & answer→MCQ 1361 Mark
The value of $\left(3 x^3+9 x^2+27 x\right) \div 3 x$ is:
- A
$x^2+9+27 x$
- B
$3 x^3+3 x^2+27 x$
- C
$3 x^3+9 x^2+9$
- ✓
$x^2+3 x+9$
AnswerCorrect option: D. $x^2+3 x+9$
D. $x^2+3 x+9$
Solution:
$(3\text{x}^2+9\text{x}^2+27\text{x})$
$=\frac{3\text{x}^3+9\text{x}^2+27\text{x}}{3\text{x}}$
$=\frac{3\text{x}^3}{3\text{x}}+\frac{9\text{x}^2}{3\text{x}}+\frac{27\text{x}}{3\text{x}}$
$=\text{x}^2+3\text{x}+9$
View full question & answer→MCQ 1371 Mark
$(a - b)^2$ is equal to:
- A
$a^2 + b^2 + 2ab$
- B
$2ab$
- ✓
$a^2 + b^2 - 2ab$
- D
$a^2 + ba^2$
AnswerCorrect option: C. $a^2 + b^2 - 2ab$
C. $a^2 + b^2 - 2ab$
Solution:
By algebraic identity,
$(a + b)^2 = a^2 + b^2 - 2ab$
View full question & answer→MCQ 1381 Mark
Use suitable identity to evaluate $992.$
- ✓
$9801$
- B
$10199$
- C
$10201$
- D
$10001$
AnswerCorrect option: A. $9801$
$9801$
View full question & answer→MCQ 1391 Mark
The value of $x^2 - 2yx + y^2$ when $x = 1, y = 2$ is:
AnswerA. $1$
Solution:
Value $= (1)^2 - 2(2)(1) + (2)^2 = 1$
View full question & answer→MCQ 1401 Mark
What should be added to $9y^2 -7xyz + 8z - xy$ to get $3xy + 8zy - 2xyz + z^2$ we get:
- ✓
$-9y^2 + 4xy + 8zy + 5xyz + z^2- 8z$
- B
$9y^2 + 4xy + 8yz + 5xyz + z^2 + 8z$
- C
$9y^2 + 4xy + 8zy + 5xyz + z^2 - 8z$
- D
AnswerCorrect option: A. $-9y^2 + 4xy + 8zy + 5xyz + z^2- 8z$
A. $-9y^2 + 4xy + 8zy + 5xyz + z^2- 8z$
Solution:
Subtracting $9y^2- 7xyz + 8z - xy$ from $3xy + 8zy - 2xyz + z^2,$ we ge
$3 x y+8 z y-2 x y z+z^2 $
$-\left(-x y-7 x y z+8 z+9 y^2\right) $
$(+) \quad(+) \quad(-) \quad(-) $
$--------------$
$ 4 x y+8 z y+5 x y z+z^2-8 z-9 y^2$
View full question & answer→MCQ 1411 Mark
The side of a cube is $2a.$ Find the volume of the cube.
AnswerCorrect option: B. $8a^3$
B. $8a^3$
Solution:
Volume of the cube $= 2a \times 2a \times 2a = 8a^3$
View full question & answer→MCQ 1421 Mark
The volume of a cuboid of dimensions $a, b, c$ is:
- ✓
$abc$
- B
$a^2b^2c^2$
- C
$a^3b^3c^3$
- D
AnswerA. $abc$
Solution:
Volume $= a \times b \times c = abc$
View full question & answer→MCQ 1431 Mark
On dividing $57p^2qr$ by $114pq,$ we get
- A
$\frac{1}{4}\text{pr}$
- B
$\frac{3}{4}\text{pr}$
- ✓
$\frac{1}{2}\text{pr}$
- D
$2\text{pr}$
AnswerCorrect option: C. $\frac{1}{2}\text{pr}$
C. $\frac{1}{2}\text{pr}$
Solution:
Required value = $\frac{57\text{p}^2\text{qr}}{114\text{pq}}$
$=\frac{57\times\text{p}\times\text{p}\times\text{q}\times\text{r}}{114\times\text{p}\times\text{q}}$
$=\frac{57}{114}\text{pr}$
$=\frac{1}{2}\text{pr}$
View full question & answer→MCQ 1441 Mark
If we multiply $5x$ and $(-4xyz),$ then we get:
- ✓
$-20x^2yz$
- B
$-2xyz$
- C
$20x^2yz$
- D
$x^2yz$
AnswerCorrect option: A. $-20x^2yz$
A. $-20x^2yz$
Solution:
$(5x) \times (-4xyz)$
$= 5 \times x \times (-4) \times x \times y \times z$
$= -20x^{1+1}yz$
$= -20x^2yz$
View full question & answer→MCQ 1451 Mark
What is the product of $(x + a)$ and $(x + b)?$
- A
$x^2+ (a - b)x + ab$
- B
$x^2 + (a + b)x - ab$
- C
$x^2 + (a + b)x - ab$
- ✓
$x^2 + (a + b)x + ab$
AnswerCorrect option: D. $x^2 + (a + b)x + ab$
D. $x^2 + (a + b)x + ab$
Solution:
$(x + a)(x + b) = x(x + b) + a(x + b)$
$= x^2 + xb + ax + ab$
$= x^2 + (a + b)x + ab$
View full question & answer→MCQ 1461 Mark
$5x + 6y$ is $a:$
AnswerThe expression containing two terms is called binomial.
View full question & answer→MCQ 1471 Mark
The product of $x^2,- x^3, - x^4$ is:
AnswerA. $x^9$
Solution:
Product $= (x^2)(-x^3)(-x^4) = x^9$
View full question & answer→MCQ 1481 Mark
Factorised form of $23xy - 46x + 54y - 108$ is:
AnswerCorrect option: A. $(23x + 54)(y - 2)$
We have, $23xy- 46x + 54y - 108 $
$= 23xy - 2 × 23x + 54y - 2 × 54$
$= 23x(y - 2) + 54(y - 2)$
$= (y - 2)(23x + 54)$
$= (23x + 54)(y - 2)$
View full question & answer→MCQ 1491 Mark
Common factor of $17abc, 34ab^2, 51a^2b$ is:
- A
$17abc$
- ✓
$17ab$
- C
$17ac$
- D
$17a^2b^2c$
AnswerCorrect option: B. $17ab$
B. $17ab$
Solution:
Given, $17 a b c=17 \times a \times b \times c$
$34 a b^2=2 \times 17 \times a \times b \times b $
$34 a^2 b=3 \times 17 \times a \times a \times b$
Now, collecting the common factors, we get $17 \times a \times b=17 a b$
View full question & answer→MCQ 1501 Mark
One of the example of binomial is:
- A
$3xyz$
- ✓
$3xy + z$
- C
$3x + y + z$
- D
$3 + x + y + z$
AnswerCorrect option: B. $3xy + z$
$3xy + z$
View full question & answer→