Sample QuestionsOperations on Algebraic Expressions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Tick $(\checkmark)$ the correct answer : $(x + 5)(x - 3) = ?$
- A
$ x^2+5 x-15 $
- B
$ x^2-3 x-15 $
- C
$ x^2+2 x+15 $
- ✓
$ x^2+2 x-15 $
Answer: D.
View full solution →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: C.
View full solution →Tick $(\checkmark)$ the correct answer : $\left(2 x^2+3 x+1\right) \div(x+1)=$ ?
- A
$(x + 1)$
- ✓
$(2x + 1)$
- C
$(x + 3)$
- D
$(2x + 3)$
Answer: B.
View full solution →Tick $(\checkmark)$ the correct answer: $\left(2 x^2+3 x+1\right) \div(x+1)=?$
- A
$(x + 1)$
- ✓
$(2x + 1)$
- C
$(x + 3)$
- D
$(2x + 3)$
Answer: B.
View full solution →Tick $(\checkmark)$ the correct answer: $8a^2b^3÷ (-2ab) = ?$
- A
$ 4 a b^2 $
- B
$ 4 a^2 b $
- ✓
$ -4 a b^2 $
- D
$ -4 a^2 b $
Answer: C.
View full solution →Assertion (A): $(p+1)(p-1)\left(p^2+1\right)\left(p^4+1\right)=\left(p^{16}-1\right)$
Reason (R): $(a+b)(a-b)=a^2-b^2$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): If we add $(-a+b-c)$ to $(a-b+c)$, we get $(2 a+2 b+2 c)$.
Reason (R): While adding algebraic expressions we add the like terms.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): $\frac{-30 x^3 y^2 z}{-6 x y^2 z^3}=\frac{-5 x^2}{z^2}$
Reason (R): Quotient of two monomials $=$ (quotient of their numerical coefficients) $\times$ (quotient of their variables).
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): If we add two monomials, we always get a binomial as the sum.
Reason (R): A monomial has only one term while a binomial has two terms.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): If we subtract $(-a-b)$ from $(2 a-b)$, we get $3 a$.
Reason (R): For subtraction, we change the sign of each term to be subtracted and then add.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Using the formula for squaring a binomial, evaluate the following:
$ (197)^2$
View full solution →Find the following products:$ (7x + 2y) × (x + 4y)$
View full solution →Find following products:
$(x + 6)(x + 6)$
View full solution →Expand:$ \left(x^2 y-y z^2\right)^2 $
View full solution →Using the formula for squaring a binomial, evaluate the following:
$(78)^2$
View full solution →If $\Big(\text{x}+\frac{1}{\text{x}}\Big)=4$ Find the values of: $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)$
View full solution →Write the quotient and remainder when we divide: $\left(2 x^3-5 x^2+8 x-5\right)$ by $\left(2 x^2-3 x+5\right)$
View full solution →Find the following product: $\left(x^2-5 x+8\right) \times\left(x^2+2 x-3\right)$
View full solution →Find the following products: $\Big(\text{x}^4+\frac{1}{\text{x}^4})×\Big(\text{x}+\frac{1}{\text{x}}\Big)$
View full solution →Write the quotient and remainder when we divide: $\left(x^3-6 x^2+11 x-6\right)$ by $\left(x^2-5 x+6\right)$
View full solution →Tanya had some sweets which she distributed among her five friends $A, B, C, D$ and $E$. She gave $x$ sweets to $A$. To $B$, she gave 10 sweets less than twice of those she gave to $A$. To $C$, she gave 4 sweets more than 4 times of those she gave to $A$. To $D$, she gave $(x+12)$ sweets more than those she gave to $B$. To $E$, she gave $(11-x)$ sweets less than those she gave to $C$. Tanya still had 16 sweets left.
(1) If $C$ got 28 sweets, how many sweets did Tanya have in all, in the beginning?
(a) 79$\quad$(b) 85$\quad$(c) 91$\quad$(d) 95
(2) How many more sweets does $E$ have than $D$ ?
(a) $(-2 x+9)$$\quad$(b) $(2 x-9)$$\quad$(c) $(2 x-5)$$\quad$(d) $(-2 x+5)$
(3) $B$ and $C$ mixed their sweets together and then distributed them equally between themselves. Which of the following algebraic expressions denotes the number of sweets that each of them got?
(a) $3(x-1)$$\quad$(b) $3(x-2)$$\quad$(c) $3(x+1)$$\quad$(d) $3(x+2)$
(4) Had Tanya distributed all the sweets equally amongst her five friends then how many toffees would each friends get?
(a) $\left(5 x-\frac{11}{3}\right)$$\quad$(b) $(3 x+1)$$\quad$(c) $\left(3 x-\frac{11}{3}\right)$$\quad$(d) $(3 x-1)$
View full solution →Find following products:
$(8 + x)(8 - x)$
View full solution →Find following products:
$(x + 3)(x - 3)$
View full solution →Subtract:
$3a^2b from -5a^2b$
View full solution →Tick $(\checkmark)$ the correct answer : $(x + 4)(x + 4) = ?$
Answer: C.
View full solution →Subtract: $-16p$ from $-11p$
View full solution →