Sample QuestionsAlgebraic Identities [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$(x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right)$ is equal to
- A
$x^{16}-y^{16}$
- ✓
$x^8-y^8$
- C
$x^8+y^8$
- D
$x^16+y^16$
Answer: B.
View full solution →Which of the following is a factor of $(x+y)^3-\left(x^3+y^3\right)$ ?
- A
$x^2+2 x y+y^2$
- B
$x^2-x y+y^2$
- C
$x y^2$
- ✓
$3 x y(x+y)$
Answer: D.
View full solution →The value of $\frac{(a+b)^2}{(b-c)(c-a)}+\frac{(b+c)^2}{(a-b)(c-a)}+\frac{(c+a)^2}{(a-b)(b-c)}$ is
Answer: A.
View full solution →The value of $249^2-248^2$ is
Answer: D.
View full solution →The square root of the expression $(x y+x z-y z)^2-4 x y z(x-y)$ is
- A
$x y+y z-2 x y z$
- B
$x+y-2 x y z$
- C
$x y+z-y$
- ✓
$x y+y z-z x$
Answer: D.
View full solution →Statement-1 (A): The square root of $\frac{1}{a b c}\left(a^2+b^2+c^2\right)+2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$ is $\sqrt{\frac{a}{b c}}+\sqrt{\frac{b}{c a}}+\sqrt{\frac{c}{a b}}$.
Statement-2 (R): $a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
- A
Statement- 1 is true, Statement-2 is true; Statement- 2 is a correct explanation for Statement- 1.
- ✓
Statement- 1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement- 1 is false, Statement- 2 is true.
Answer: B.
View full solution →Statement-1 (A): $\sqrt{(a+b+c)^2+(a-b+c)^2+2\left(b^2-a^2-c^2-2 a c\right)}=2 b$
Statement-2 (R): $(x+y+z)^2=x^2+y^2+z^2+2(x y+y z+z x)$
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If $a+b+c=6, a b+b c+c a=11$, then $a^2+b^2+c^2=14$
Statement-2 (R): $(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
- ✓
Statement- 1 is true, Statement-2 is true; Statement- 2 is a correct explanation for Statement- 1.
- B
Statement- 1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement- 1 is false, Statement- 2 is true.
Answer: A.
View full solution →Statement-1 (A): If $a+b+c=0$, then $a^3+b^3+c^3=3 a b c$
Statement-2 (R): $a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
- ✓
Statement- 1 is true, Statement-2 is true; Statement- 2 is a correct explanation for Statement- 1.
- B
Statement- 1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement- 1 is false, Statement- 2 is true.
Answer: A.
View full solution →Statement-1 (A): $\frac{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}{(x-y)^3+(y-z)^3+(z-x)^3}=(x+y)(y+z)(z+x)$
Statement-2 (R): If $a+b+c=0$, then $a^3+b^3+c^3=3 a b c$.
- ✓
Statement- 1 is true, Statement-2 is true; Statement- 2 is a correct explanation for Statement- 1.
- B
Statement- 1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement- 1 is false, Statement- 2 is true.
Answer: A.
View full solution →lf $\frac{37^3-28^5}{37^2+37.28+28^2}=$ _______________ .
View full solution →If $x+y+z=5$ and $x y+y z+z x=7$, then $x^3+y^3+z^3-3 x y z=$ _______________ .
View full solution →if $x+y+z=0$, then $(x+y)^3+(y+z)^3+(z+x)^3=$ _______________ .
View full solution →If $x^2+y^2-x y=3$ and $y-x=1$, then $\frac{x y}{x^2+y^2}=$ _______________ .
View full solution →If $\frac{a}{b}+\frac{b}{a}=2$, then $\left(\frac{a}{b}\right)^{100}-\left(\frac{b}{a}\right)^{100}=$ _______________ .
View full solution →If $x-\frac{1}{x}=\frac{1}{2}$, then write the value of $4 x^2+\frac{4}{x^2}$.
View full solution →If $x+\frac{1}{x}=3$, then find the value of $x^6+\frac{1}{x^6}$.
View full solution →If $x+\frac{1}{x}=3$, then find the value of $x^2+\frac{1}{x^2}$.
View full solution →If $a+b+c=0$, then write the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}$.
View full solution →If $a+b=7$ and $a b=12$, find the value of $a^2+b^2$.
View full solution →Write the following in the expanded form:
(a2 + b2 + c2)2
Write the following in the expanded form:
(2 + x - 2y)2
Write the following in the expanded form:
(x + 2y + 4z)2
Write the following in the expanded form:
$\Big(\frac{\text{x}}{\text{y}}+\frac{\text{y}}{\text{z}}+\frac{\text{z}}{\text{x}}\Big)^2$
View full solution →Write the following in the expanded form:
$\Big(\frac{\text{a}}{\text{bc}}+\frac{\text{b}}{\text{ca}}+\frac{\text{c}}{\text{ab}}\Big)^2$
View full solution →Simplify the following products:
$(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)$
View full solution →Simplify the following products:
$(\text{x}^2 +\text{x}- 2)(\text{x}^2-\text{x} + 2)$
View full solution →Simplify the following products:
$(2\text{x}^4 -4\text{x}^2+1)(2\text{x}^4-4\text{x}^2-1)$
View full solution →If x = 3, find the values of the following using in identity:
$\Big(\frac{3}{\text{x}}-\frac{\text{x}}{3}\Big)\Big(\frac{\text{x}^2}{9}+\frac{9}{\text{x}^2}+1\Big)$
View full solution →If x = 3 and y = -1, find the values of the following using in identity:
$\Big(\frac{\text{x}}{7}+\frac{\text{y}}{3}\Big)\Big(\frac{\text{x}^2}{49}+\frac{\text{y}^2}{9}-\frac{\text{xy}}{21}\Big)$
View full solution →Simplify the following:
(x + 3)3 + (x - 3)3
Simplify the following:
$\Big(\frac{\text{x}}{2}+\frac{\text{y}}{3}\Big)^3-\Big(\frac{\text{x}}{2}-\frac{\text{y}}{3}\Big)^3$
View full solution →Simplify the following products:
$\Big(\text{m}+\frac{\text{n}}{7}\Big)^3\Big(\text{m}-\frac{\text{n}}{7}\Big)$
View full solution →Simplify the following products:
$\Big(\frac{1}{2}\text{a}-3\text{b}\Big)\Big(3\text{b}+\frac{1}{2}\text{a}\Big)\Big(\frac{1}{4}\text{a}^2+9\text{b}^2\Big)$
View full solution →Simplify the following:
(2x - 5y)3 - (2x + 5y)3
Simplify the following:
$\Big(\text{x}+\frac{2}{\text{x}}\Big)^3+\Big(\text{x}-\frac{2}{\text{x}}\Big)^3$
View full solution →Simplify the following products:
$\Big(\frac{\text{x}}{2}-\frac{2}{5}\Big)\Big(\frac{2}{5}-\frac{\text{x}}{2}\Big)-\text{x}^2+2\text{x}$
View full solution →Simplify the following expressions:
$\big(\text{x}+\text{y}+\text{z}\big)^2+\Big(\text{x}+\frac{\text{y}}{2}+\frac{\text{z}}{3}\Big)^2-\Big(\frac{\text{x}}{2}+\frac{\text{y}}{3}+\frac{\text{z}}{4}\Big)^2$
View full solution →Simplify:
(a + b + c)2 + (a - b + c)2 + (a + b - c)2
If $\text{x}+\frac{1}{\text{x}}=3, $ then find the value of $\text{x}^6+\frac{1}{\text{x}^6}.$
View full solution →