MCQ 511 Mark
Choose the terms which are like:
- A
$3x^2, 2xy, - x$
- B
$6x^2, 2y^2$
- C
$4xy, - y^2x, 2y$
- ✓
$7xy, - 2yx, xy$
AnswerCorrect option: D. $7xy, - 2yx, xy$
D. $7xy, - 2yx, xy$
Solution:
All the terms in $7xy, - 2y \times xy$ are like.
View full question & answer→MCQ 521 Mark
$N(4 + m) = 4n +$ _____.
View full question & answer→MCQ 531 Mark
If $\text{y}=\frac{\big(0.42\big)^3+\big(0.25\big)^3+\big(0.33\big)^3-3\times0.42\times0.25\times0.33}{\big(0.42\big)^2+\big(0.25\big)^2+\big(0.33\big)^2-0.42\times0.25-0.25\times0.33-0.33\times0.42}$ then the value of $y$ is:
View full question & answer→MCQ 541 Mark
The expression $x + 3$ is in:
AnswerThe only variable is $x.$
View full question & answer→MCQ 551 Mark
$a^2- b^2$ is a product of-
- ✓
$(a + b)(a - b)$
- B
$(a + b)(a + b)$
- C
$(a - b)(a - b)$
- D
AnswerCorrect option: A. $(a + b)(a - b)$
A. $(a + b)(a - b)$
Solution:
$a^2 - b^2$ is a product of $(a + b)(a - b).$
Because:
$a(a - b) + b(a - b)$
$a^2 - ab + ab - b^2$
$ab$ is catted by $ab$
$a^2 - b^2.$
View full question & answer→MCQ 561 Mark
Simplify $(2ab + 4c)^2 - (2ab - 4c)^2.$
- ✓
$32abc$
- B
$-32abc$
- C
$8a^2b^2 + 32c^2$
- D
$-8a^2b^2 + 32c^2$
AnswerCorrect option: A. $32abc$
.A. $32abc$
Solution:
Using identity $a^2 - b^2 = (a + b)(a - b)$
$(2ab + 4c)^2 - (2ab - 4c)^2 = [(2ab + 4c) + (2ab - 4c)] [(2ab + 4c) - (2ab - 4c)] = (4ab)(8c) = 32abc.$
View full question & answer→MCQ 571 Mark
Which of the following is a binomial$?$
- A
$7 – 3x + 4$
- ✓
$2x + 7$
- C
$4x + y + 2$
- D
$3x$
AnswerCorrect option: B. $2x + 7$
$2x + 7$
View full question & answer→MCQ 581 Mark
$a^2- b^2$ is equal to
- A
$2ab$
- B
$-2ab$
- ✓
$(a + b)(a - b)$
- D
$ab$
AnswerCorrect option: C. $(a + b)(a - b)$
C. $(a + b)(a - b)$
Solution:
$a^2 - b^2= (a + b)(a - b)$
View full question & answer→MCQ 591 Mark
$5x + 6y$ is a:
Answer The expression containing two terms is called binomial.
View full question & answer→MCQ 601 Mark
Multiplication of monomials $x^2, (-x)^3, (-x)^4$ is equal to:
AnswerC. $x^9$
Solution:
$(x^2)(-x^3)(-x)^4 = x^9$
View full question & answer→MCQ 611 Mark
How many terms are there in the expression $5xy^2?$
AnswerA. $1$
Solution:
Only one term $5xy^2$
View full question & answer→MCQ 621 Mark
Tick $(\checkmark)$ the correct answer: The sum of $(6a + 4b − c + 3), (2b − 3c + 4), (11b − 7a + 2c − 1)$ and $(2c − 5a − 6)$ is:
- A
$(4a - 6b + 2)$
- B
$(-3a + 14b - 3c + 2)$
- ✓
$(-6a + 17b)$
- D
$(-6a + 6b + c - 4)$
AnswerCorrect option: C. $(-6a + 17b)$
View full question & answer→MCQ 631 Mark
If we subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3,$ then the answer is:
- A
$8a + 2ab + 2b + 15$
- B
$8a + 2ab + 2b - 15$
- ✓
$8a - 2ab + 2b - 15$
- D
$8a - 2ab - 2b - 15$
AnswerCorrect option: C. $8a - 2ab + 2b - 15$
$ (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 641 Mark
The number of terms in the expression $2x^2 + 3x + 5$ is:
View full question & answer→MCQ 651 Mark
A polynomial contains $................$ number of terms:
AnswerA polynomial can contain any number of terms, i.e. one or more than one.
View full question & answer→MCQ 661 Mark
Which of the following is obtained by subtracting $x^2 - y^2$ from $y^2 - x^2?$
- ✓
$-2(x^2 - y^2)$
- B
$-2(x^2+ y^2)$
- C
$2(x^2 + y^2)$
- D
$2(x^2 - y^2)$
AnswerCorrect option: A. $-2(x^2 - y^2)$
A. $-2(x^2 - y^2)$
Solution:
Subtracting from $x^2 - y^2$ from $y^2- x^2$
$= (y^2 - x^2) - (x^2 - y^2)$
$= y^2- x^2- x^2+ y^2$
$= 2y^2 - 2x^2$
$= 2(y^2 - x^2)$
$= -2(x^2 - y^2)$
View full question & answer→MCQ 671 Mark
$(a - b)^2$ is equal to:
- ✓
$a^2 + b^2 - 2ab$
- B
$a^2 + b^2 + 2ab$
- C
$a^2 + b^2$
- D
$2ab$
AnswerCorrect option: A. $a^2 + b^2 - 2ab$
A. $a^2 + b^2 - 2ab$
Solution:
$(a - b)^2 = a^2 + b^2 - 2ab$
View full question & answer→MCQ 681 Mark
Evaluate $196 \times 204$ using a suitable identity.
- A
$40016$
- B
$39884$
- C
$39985$
- ✓
$39984$
AnswerCorrect option: D. $39984$
D. $39984$
Solution:
$196 \times 204 = (200 - 4) \times (200 + 4)$ and using $(a + b) (a - b)= a^2 - b^2 = (200)^2 - 4^2 = 40000 - 16 = 39984$
View full question & answer→MCQ 691 Mark
What is the volume of the cuboid of length 8xy breadth $3xy$ & height $xy?$
- A
$24xy^2$
- B
$24x^2y$
- C
$24x^3y^2$
- ✓
$24x^3y^3$
AnswerCorrect option: D. $24x^3y^3$
D. $24x^3y^3$
View full question & answer→MCQ 701 Mark
Which of the following is a like term as $8xy?$
View full question & answer→MCQ 711 Mark
Which of the following is a binomial$?$
- A
$4x + y + 2$
- ✓
$2x + 7$
- C
$3x + 4y - 6$
- D
$3x$
AnswerCorrect option: B. $2x + 7$
$2x + 7$
View full question & answer→MCQ 721 Mark
How many terms are there in the expression $7x^2 + 5x - 5?$
AnswerC. $3$
Solution:
$7x^2, 5x, - 5$
View full question & answer→MCQ 731 Mark
The algebraic expression $3x + 2y + 6$ is:
Answer The algebraic expression containing three terms is called a trinomial.
Here, $3x, 2y$ and $6$ are three terms.
View full question & answer→MCQ 741 Mark
If $<\text{a}<1$ then the value of $\text{a}+\frac{1}{\text{a}}$ is:
- ✓
Greater than $2$
- B
Grater than $4$
- C
Less than $4$
- D
Less than $2$
AnswerCorrect option: A. Greater than $2$
Greater than $2$
View full question & answer→MCQ 751 Mark
Simplify $4x(5x^2 + 3x) + 2x$ and find its value for $x = 2$
AnswerCorrect option: D. $20x^3 + 12x^2 + 2x ; 212$
D. $20x^3 + 12x^2 + 2x ; 212$
Solution:
Simplifying the given expression, $4x(5x^2) + 4x(3x) + 2x = 20x^3 + 12x^2 + 2x$
For $x = 2,$ the value of expression $= 20(2)^3 + 12(2)^2 + 2(2) = 20 \times 8 + 12 \times 4 + 4 = 160 + 48 + 4 = 212$
View full question & answer→MCQ 761 Mark
Tick $(\checkmark)$ the correct answer: If $(a - b) = 7$ and $ab = 9,$ then $(a^2 + b^2) = ?$
AnswerA. $67$
Solution:
$a - b = 7$
$ab = 9$
$a^2+ b^2 = (a - b)^2+ 2ab$
$= (7)^2 + 2 \times 9$
$= 49 + 18$
$= 67$
View full question & answer→MCQ 771 Mark
The sum of $5x^2, - 7x^2, 8x^2, 11x^2$ and $-9x^2$ is:
- A
$2x^2$
- B
$4x^2$
- C
$6x^2$
- ✓
$8x^2$
AnswerCorrect option: D. $8x^2$
D. $8x^2$
Solution:
Sum $= {5 + (-7) + 8 + 11 + (-9)} x^2 = 8x^2$
View full question & answer→MCQ 781 Mark
The volume of a cube of side $2a$ is:
AnswerCorrect option: C. $8a^3$
C. $8a^3$
Solution:
Volume $= 2a \times 2a \times 2a = 8a^3 $
View full question & answer→MCQ 791 Mark
The algebraic expression $3x + 2y + 6$ is $a:$
Answer The algebraic expression containing three terms is called a trinomial.
Here, $3x, 2y$ and $6$ are three terms.
View full question & answer→MCQ 801 Mark
The volume of a rectangle with length, breadth and height as $5x, 3x^2$ and $7x^4$ respectively is:
- ✓
$105x^7$
- B
$105x^2$
- C
$105x^4$
- D
$105x$
AnswerCorrect option: A. $105x^7$
A. $105x^7$
Solution:
Volume of rectangle = Length $\times$ breadth $\times$ height
$V = 5x \times 3x^2 \times 7x^4$
$V = 105x^{1+2+4}$
$V = 105x^7$cubic unit.
View full question & answer→MCQ 811 Mark
The value of $(2x^2+ 4) \div 2$ is:
- A
$2x^2+ 2$
- ✓
$x^2+ 2$
- C
$x^2 + 4$
- D
$2x^2 + 4$
AnswerCorrect option: B. $x^2+ 2$
B. $x^2 + 2$
Solution:
We have,
$(2x^2 + 4) \div 2$
$=\frac{2\text{x}^2+4}{2}$
$=\frac{2(\text{x}^2+4)}{2}$
$=\text{x}^2+2$
View full question & answer→MCQ 821 Mark
The Value of $\frac{7.83\times7.83-1.17\times1.17}{6.66}$ is:
View full question & answer→MCQ 831 Mark
Square of $3x - 4y$ is:
- A
$9x^2 - 16y^2$
- B
$6x^2 - 8y^2$
- C
$9x^2 + 16y^2+ 24xy$
- ✓
$9x^2 + 16y^2 - 24xy$
AnswerCorrect option: D. $9x^2 + 16y^2 - 24xy$
D. $9x^2 + 16y^2 - 24xy$
Solution:
Square of $(3x - 4y)$ will be $(3x - 4y)^2$
comparing $(3x - 4y)^2$ with $(a - b)^2$
We get $a = 3x$ and $b = 4y$
now, using identity, $(a - b)^2 = a^2 - 2ab + b^2$
$(3x - 4y)^2 = (3x)^2 - 2.3x.4y + (4y)^2$
$= 9x^2 + 16y^2 - 24xy$
View full question & answer→MCQ 841 Mark
The value of $25x^2 + 16y^2 + 40xy$ at $x = 1$ and $y = -1$ is:
View full question & answer→MCQ 851 Mark
The coefficient of $x^2y$ in $-15 x^2y$ is:
View full question & answer→MCQ 861 Mark
On dividing $p(4p^2- 16)$ by $4p(p - 2),$ we get
- A
$2p + 4$
- B
$2p - 4$
- ✓
$p + 2$
- D
$p - 2$
AnswerCorrect option: C. $p + 2$
C. $p + 2$
Solution:
We have,
$\frac{\text{p}(4\text{p}^2-16)}{4\text{p}(\text{p}-2)}=\frac{\text{p}\big[(2\text{p})^2-4^2\big]}{4\text{p}(\text{p}-2)}$
$=\frac{(2\text{p}-4)(2\text{p}+4)}{4(\text{p}-2)}$
$=\frac{2(\text{p}-2).2(\text{p}+2)}{4(\text{p}-2)}$
$=\frac{4(\text{p}-2)(\text{p}+2)}{4(\text{p}-2)}$
$=\text{p}+2$
View full question & answer→MCQ 871 Mark
The value of the product $\Big(3+\frac{5}{\text{x}}\Big)\Big(9-\frac{15}{\text{x}}+\frac{25}{\text{x}^2}\Big)\text{at}\text{ x}=1$ is:
View full question & answer→MCQ 881 Mark
The number of like terms in $9x^3, 16x^2 y, - 8x^3, 12xy^2, 6x^3$ is:
AnswerA. $3$
Solution:
$9x^3, - 8x^3, 6x^3$
View full question & answer→MCQ 891 Mark
Tick $(\checkmark)$ the correct answer: $(82)^2 - (18)^2 = ?$
- A
$8218$
- B
$6418$
- ✓
$6400$
- D
$7204$
AnswerCorrect option: C. $6400$
C. $6400$
Solution:
$(82)^2- (18)^2$
$= (82 + 18)(82 - 18)$
$= 100 \times 64$
$= 6400$
View full question & answer→MCQ 901 Mark
The area of a rectangle whose length and breadth are $3y$ and $9y^2$ respectively is:
- A
$21y^3$
- ✓
$27y^3$
- C
$12y^3$
- D
$y^3$
AnswerCorrect option: B. $27y^3$
B. $27y^3$
Solution:
Area of rectangle = length $\times$ breadth $= 3y \times 9y^2 = 27y^3$
View full question & answer→MCQ 911 Mark
The area of a rectangle whose length and breadth are $9y$ and $4y^2$ respectively is:
- A
$4y^3$
- B
$9y^3$
- ✓
$36y^3$
- D
$13y^3$
AnswerCorrect option: C. $36y^3$
C. $36y^3$
Solution:
Area $= (9y)(4y^2) = 36y^3$
View full question & answer→MCQ 921 Mark
Add $9x^2 + 2xy - 3x$ and $3yx + 2xy - y.$
- A
$5xy.+x$
- B
$5yx - x$
- ✓
$9x^2 + 5xy - x - y$
- D
$9x^2+ 5xy + x - y$
AnswerCorrect option: C. $9x^2 + 5xy - x - y$
C. $9x^2 + 5xy - x - y$
Solution:
$\ \ \ \ 9\text{x}^{2} + 2\text{xy} - 3\text{x}\\ + \text{3xy} + 2\text{x} - \text{y}\\ \overline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\\9\text{x}^{2} + 5\text{xy} - \text{x}- \text{y}$
View full question & answer→MCQ 931 Mark
The value of $(a+b)^2-(a-b)^2$ is:
- ✓
$4ab$
- B
$-4ab$
- C
$2a^2 + 2b^2$
- D
$2a^2 - 2b^2$
AnswerA. $4ab$
Solution:
We have,
$(a+b)^2-(a-b)^2=a^2+b^2+2 a b-\left(a^2+b^2-2 a b\right) $
$=a^2+b^2+2 a b-a^2-b^2+2 a b=a^2-a^2+b^2-b^2+2 a b+2 a b $
$=2 a b+2 a b $
$=4 a b$
View full question & answer→MCQ 941 Mark
The value of $(x + 3)^3 - (x - 3)^3$ is:
- A
$1 - x^3$
- ✓
$18x^2 + 54$
- C
$3x^2 - 5$
- D
$0$
AnswerCorrect option: B. $18x^2 + 54$
B. $18x^2 + 54$
View full question & answer→MCQ 951 Mark
The coefficient of $xy$ $2z$ in $-7x 2y 3z$ is:
AnswerA. $7xy$
Solution:
$-7x^2y^3z = (-7xy)(xy^2z)$
View full question & answer→MCQ 961 Mark
The number of like terms in $\frac{1}{4}\text{a}^2\text{bc},-\frac{2}{3}\text{bca}^2,\frac{2}{5}\text{ba}^2\text{c}-\frac{1}{2}\text{cba}^2$ is:
View full question & answer→MCQ 971 Mark
Like term as $4m^3n^2$ is:
- A
$4m^2n^2$
- ✓
$-6m^3n^2$
- C
$6pm^3n^2$
- D
$4m^3n$
AnswerCorrect option: B. $-6m^3n^2$
B. $-6m^3n^2$
Solution:
We knoe that, the like terms contain the same literal factor. so, the like as $4m^3n^2, -6m^3n^2,$ as it contains the same literal factor $m^3n^2.$
View full question & answer→MCQ 981 Mark
Which of the following is the numerical coefficient of $x^2y^2?$
AnswerB. $1$
Solution:
So, if is asked that the numerical coefficient of $5x^2$ then the answer will be $5.$
the numerical coefficient is the number, which is before any constant like $x, y, z.$ etc. and we know if we multiply any number or variable with $1$ it remains same.
Here there is no number before $(x^2y^2)$ so we assume it as $1.$
Hence the answer is $1.$
View full question & answer→MCQ 991 Mark
The coefficient of $x^2y$ in $7pqrx^2$ is:
- ✓
$7pqr$
- B
$pqr$
- C
$-7pqr$
- D
$7$
AnswerCorrect option: A. $7pqr$
A. $7pqr$
View full question & answer→MCQ 1001 Mark
Tick $(\checkmark)$ the correct answer: If $\Big(\text{x}-\frac{1}{\text{x}}\Big)=6,$ then $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)=?$
- ✓
$36$
- B
$38$
- C
$32$
- D
$36\frac{1}{36}$
Answer$\Big(\text{x}-\frac{1}{\text{x}}\Big)=6,$
Squaring on both sides
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=(6)^2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}-2=36$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=36+2=38$
View full question & answer→