MCQ 11 Mark
$(x+y)^3-(x-y)^3$ can be factorized as
- ✓
$2 y\left(3 x^2+y^2\right)$
- B
$2 x\left(3 x^2+y^2\right)$
- C
$2 y\left(3 y^2+x^2\right)$
- D
$2 x\left(x^2+3 y^2\right)$
AnswerCorrect option: A. $2 y\left(3 x^2+y^2\right)$
View full question & answer→MCQ 21 Mark
Which of the following is a factor of $(x+y)^3-\left(x^3+y^3\right) ?$
- A
$x^2+y^2+2 x y$
- B
$x^2+y^2-x y$
- C
$x y^2$
- ✓
$3 x y(x+y)$
AnswerCorrect option: D. $3 x y(x+y)$
View full question & answer→MCQ 31 Mark
The value of $\frac{(2.3)^3-0.027}{(2.3)^2+0.69+0.09}$, is
View full question & answer→MCQ 41 Mark
The value of $\frac{(0.013)^3+(0.007)^3}{(0.013)^2-0.013 \times 0.007+(0.007)^2}$, is
View full question & answer→MCQ 51 Mark
The factors of $x^4+x^2+25$, are
- ✓
$\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$
- B
$\left(x^2+3 x+5\right)\left(x^2+3 x-5\right)$
- C
$\left(x^2+x+5\right)\left(x^2-x+5\right)$
- D
AnswerCorrect option: A. $\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$
View full question & answer→MCQ 61 Mark
The factors of $x^3-x^2 y-x y^2+y^3$, are
AnswerCorrect option: D. $(x-y)^2(x+y)$
View full question & answer→MCQ 71 Mark
The factors of $x^3-7 x+6$, are
AnswerCorrect option: D. $(x-1)(x+3)(x-2)$
View full question & answer→MCQ 81 Mark
The factors of $x^3-1+y^3+3 x y$, are
- ✓
$(x-1+y)\left(x^2+1+y^2+x+y-x y\right)$
- B
$(x+y+1)\left(x^2+y^2+1-x y-x-y\right)$
- C
$(x-1+y)\left(x^2-1-y^2+x+y+x y\right)$
- D
$3(x+y-1)\left(x^2+y^2-1\right)$
AnswerCorrect option: A. $(x-1+y)\left(x^2+1+y^2+x+y-x y\right)$
View full question & answer→MCQ 91 Mark
The factors of $x^2+4 y^2+4 y-4 x y-2 x-8$, are
- ✓
$(x-2 y-4)(x-2 y+2)$
- B
$(x-y+2)(x-4 y-4)$
- C
$(x+2 y-4)(x+2 y+2)$
- D
AnswerCorrect option: A. $(x-2 y-4)(x-2 y+2)$
View full question & answer→MCQ 101 Mark
The factors of $a^2-1-2 x-x^2$, are
- A
$(a-x+1)(a-x-1)$
- B
$(a+x-1)(a-x+1)$
- ✓
$(a+x+1)(a-x-1)$
- D
AnswerCorrect option: C. $(a+x+1)(a-x-1)$
View full question & answer→MCQ 111 Mark
The factors of $8 a^3+b^3-6 a b+1$, are
- A
$(2 a+b-1)\left(4 a^2+b^2+1-3 a b-2 a\right)$
- B
$(2 a-b+1)\left(4 a^2+b^2-4 a b+1-2 a+b\right)$
- ✓
$(2 a+b+1)\left(4 a^2+b^2+1-2 a b-b-2 a\right)$
- D
$(2 a-1+b)\left(4 a^2+1-4 a-b-2 a b\right)$
AnswerCorrect option: C. $(2 a+b+1)\left(4 a^2+b^2+1-2 a b-b-2 a\right)$
View full question & answer→MCQ 121 Mark
The expression $x^4+4$ can be factorized as
- ✓
$\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
- B
$\left(x^2+2 x+2\right)\left(x^2+2 x-2\right)$
- C
$\left(x^2-2 x-2\right)\left(x^2-2 x+2\right)$
- D
$\left(x^2+2\right)\left(x^2-2\right)$
AnswerCorrect option: A. $\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
View full question & answer→MCQ 131 Mark
The expression $(a-b)^3+(b-c)^3+(c-a)^3$ can be factorized as
AnswerCorrect option: B. $3(a-b)(b-c)(c-a)$
View full question & answer→MCQ 141 Mark
$\left.(a+b+c)\left\{(c-b)^2+(b-c)^2+(c-a)^2\right)\right\}=$
AnswerC. $2\left(a^3+b^3+c^3-3 a b c\right)$
$(a-b+c)\left\{(a-b)^2+(b-c)^2+(c-a)^2\right\}$
$=2(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)=2\left(a^3+b^3+c^3-3 a b c\right)$
View full question & answer→MCQ 151 Mark
If $x+y=-4$, then $x^3+y^3-12 x y+64=$
AnswerC. 0
$\begin{array}{l}\text { We have, } x+y=-4 \text { or, } x+y+4=0 . \\ \therefore \quad x^2+y^3+4^3=3 x y \times 4 \text { or, } x^3+y^3+64=12 x y \text { or, } x^3+y^3-12 x y+64=0\end{array}$
View full question & answer→MCQ 161 Mark
If $(x+y)^3-(x-y)^3-6 y\left(x^2-y^2\right)=k y^3$, then $k=$
View full question & answer→MCQ 171 Mark
If $x+y=12$ and $x y=27$, then $x^3+y^3=$
AnswerB. 756
We know that
$\begin{array}{ll}\therefore & x^3+y^3=(x+y)\left(x^2-x y+y^2\right) \\ \Rightarrow & x^3+y^3=(x+y)\left\{\left((x+y)^2-3 x y\right)\right\}=12\left(12^2-3 \times 27\right)=12(144-81)=756\end{array}$
View full question & answer→MCQ 181 Mark
If $x^3-3 x^2+3 x+7=(x+1)\left(a x^2+b x+c\right)$, then $a+b+c=$
View full question & answer→MCQ 191 Mark
If $x=2 y+6$, then $x^3-8 y^3-36 x y=$
AnswerA. 216
We have, $x=2 y+6$ or, $x-2 y-6=0$.
$\therefore$ $x^3-(-2 y)^3+(-6)^3=3 x(-2 y)(-6)$
$\Rightarrow$ $x^3-8 y^3-216=36 x y$ $\Rightarrow$ $x^3-8 y^3-36 x y=216$
View full question & answer→MCQ 201 Mark
If $\frac{x}{y}+\frac{y}{x}=-1(x, y \neq 0)$, then the value of $x^3-y^3$ is
View full question & answer→MCQ 211 Mark
If $a+b+c=0$, then $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}=$
AnswerD. 3
We have, $a+b-c=0$
$\Rightarrow$ $a^3+b^3-c^2$ = 3 abc $\Rightarrow$ $\frac{a^3+b^3+c^3}{a b c}$ = 3 $\Rightarrow$ $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}$ =3
View full question & answer→MCQ 221 Mark
If $a^3-(b-a)^3-b^3=k(a-b)$, then $k=$
AnswerB. 3 ab
We observe that $a+(b-a)+(-b)=0$.\[\begin{array}{ll}\therefore & a^3+(b-a)^3+(-b)^3=3 a(b-a)(-b) \\\Rightarrow & a^3-(b-a)^3-b^3=3 a b(a-b) \Rightarrow k(a-b)=3 a b(a-b) \Rightarrow k=3 a b\end{array}\]
View full question & answer→MCQ 231 Mark
If $a^3+b^3=5$ and $a \div b=1$, then $a b=$
- A
$-\frac{4}{3}$
- B
$\frac{4}{3}$
- C
$\frac{-3}{4}$
- D
$\frac{3}{4}$
AnswerC. $\frac{-3}{4}$
$\left(a^3-b^2\right)=(a+b)\left(a^2-a b+b^2\right)$
$\Rightarrow$ $a^3-b^3=(a+b)\left\{(a+b)^2-3 a b\right\} \Rightarrow 5=(1-3 a b) \Rightarrow a b=-\frac{4}{3}$
View full question & answer→MCQ 241 Mark
If $3 x=a+b+c$, then the value of $(x-a)^3+(x-b)^3+(x-c)^3-3(x-a)(x-b)(x-c)$, is
View full question & answer→MCQ 251 Mark
$(a-b)^3+(b-c)^3+(c-a)^3$ is equal to
AnswerD. 3(a-b)(b-c)(c-a)
We observe that $(a-b)+(b-c)+(c-a)=0$.
\[\therefore \quad(a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)\]
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