Simplify : $z^2 + 11z^2 - 5z - 11z2 + 5z.$
- A$z^2$
- ✓$-z^2$
- C$5z$
- D$-5z$
Answer: B.
View full solution →Question types
Algebraic Expressions question types
376 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
376
Questions
7
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
224 Q→02Assertion (A) & Reason (B) MCQ
26 Q→03True False[1 Marks ]
20 Q→041 Marks Question
76 Q→052 Marks Questions
19 Q→065 Marks Questions
8 Q→07case /data -based (4 Marks)
3 Q→Sample Questions
Algebraic Expressions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What is the coefficient of $x^2$ in the expression $ax + b?$
- A$a$
- B$b$
- C$a + b$
- ✓$0$
Answer: D.
View full solution →Which of the following is a pair of like terms?
- A$-7xy^2z, - 7x^2yz$
- ✓$-10xyz^2, 3xyz^2$
- C$3xyz, 3x^2y^2z^2$
- D$4xyz^2, 4x^2yz$
Answer: B.
View full solution →The value of $x$ in the expression $[\text{x+x}^{\log_{\text{x}}(10)}]^{5}$ if the third term in the expansion is $10, 00, 000:$
- ✓$10$
- B$11$
- C$12$
- DNone of these
Answer: A.
View full solution →Add the terms $3xy$ and $2y^2:$
- ✓$3xy + 2y^2$
- B$5xy^3$
- C$4xy + y$
- DAll of the above
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The like terms are $xy, -6x$
Reasons: like terms are terms that have the different variables and powers
Assertion: The like terms are $xy, -6x$
Reasons: like terms are terms that have the different variables and powers
- ABoth assertion and reason are correct and reason is correct explanation for assertion.
- BBoth assertion and reason are correct but reason is correct explanation for assertion.
- CAssertion is correct but reason is false.
- ✓Both assertion and reason are false.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Like terms are terms that have the same variables and powers
Reason: The like terms are $5y, 6y.$
Assertion: Like terms are terms that have the same variables and powers
Reason: The like terms are $5y, 6y.$
- ✓Both assertion and reason are correct and reason is correct explanation for assertion.
- BBoth assertion and reason are correct but reason is correct explanation for assertion.
- CAssertion is correct but reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The area of a rectangle whose length and breadth are $3 y$ and $9 y^2$ respectively is $27 y^3$
Reason: Area of rectangle = length $\times $ breadth
Assertion: The area of a rectangle whose length and breadth are $3 y$ and $9 y^2$ respectively is $27 y^3$
Reason: Area of rectangle = length $\times $ breadth
- ✓Both assertion and reason are correct and reason is correct explanation for assertion.
- BBoth assertion and reason are correct but reason is correct explanation for assertion.
- CAssertion is correct but reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The product of $4x$ and $0$ is $0$
Reason: Any value multiplied by zero is zero
Assertion: The product of $4x$ and $0$ is $0$
Reason: Any value multiplied by zero is zero
- ✓Both assertion and reason are correct and reason is correct explanation for assertion.
- Bboth assertion and reason are correct but reason is correct explanation for assertion.
- CAssertion is correct but reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The coefficient of $x^{2 y}$ in $17 x^{2 y}+28 x y$ is $28$
Reason: A coefficient is a number multiplied by a variable
Assertion: The coefficient of $x^{2 y}$ in $17 x^{2 y}+28 x y$ is $28$
Reason: A coefficient is a number multiplied by a variable
- ABoth assertion and reason are correct and reason is correct explanation for assertion.
- BBoth assertion and reason are correct but reason is correct explanation for assertion.
- ✓Assertion is correct but reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →$p q^2$ and $-4 q^2 p$ are unlike terms.
View full solution →Factors of $5 x^2 y$ are $5, x$ and $y$.
View full solution →The numerical coefficient of $9 x^6 y^5 z^4$ is 9 .
View full solution →$x$ is a constant term in $7+5 x^2-3 x^3+x$.
View full solution →Subtracting $1$ from one-half of sum of $x$ and $y$. we get $\frac{x+y}{2}-1$.
View full solution →When $a = 0, b = –1$, find the value of the given expression: $a^2+a b+2$
View full solution →When $a = 0, b = – 1$, find the value of: $2 a^2 b+2 a b^2+a b$
View full solution →When $a = 0, b = – 1$, find the value of: $2 a^2+b^2+1$
View full solution →When $a = 0, b = – 1$, find the value of: $2a + 2b$
View full solution →If $a = 2, b = –2$ find the value of $a^2-b^2$
View full solution →What should be the value of a if the value of $2 x^2+x-a$ equals $5,$ when $x = 0?$
View full solution →If $p=-10$, find the value of $p^2-2 p-100$
View full solution →If $z = 10$, find the value of $=z^3-3(z-10)$
View full solution →Simplify the expression $2a – 2b – 4 – 5 + a$ and find their value if $a = –1, b = –2.$
View full solution →Simplify the expression $10 – 3b – 4 – 5b$ and find their value if $b = –2.$
View full solution →Identify like terms in the following: $10 pq, 7 p, 8 q,-p^2q^2,-7 qp,-100 q,-23,12 q^2p^2,-5 p^2, 41,2405 p, 78 qp, 13 p^2qp^2, 701 p^2$
View full solution →Identify like terms among the following: $-x y^2,-4 y x^2, 8 x^2, 2 x y^2, 7 y,-11 x^2,-100 x,-11 y x, 20 x^2 y,-6 x^2, y, 2 x y, 3 x$
View full solution →Identify terms and factors in the expressions given below:
$a. – 4x + 5$
$b. – 4x + 5y$
$c. 5y + 3y^2$
$d. xy + 2x^2 y^2$
$e. pq + q$
$f. 1.2 ab – 2.4 b + 3.6 a$
$g. \frac{3}{4} x+\frac{1}{4}$
$h. 0.1 p^2 + 0.2 q^2$
View full solution →$a. – 4x + 5$
$b. – 4x + 5y$
$c. 5y + 3y^2$
$d. xy + 2x^2 y^2$
$e. pq + q$
$f. 1.2 ab – 2.4 b + 3.6 a$
$g. \frac{3}{4} x+\frac{1}{4}$
$h. 0.1 p^2 + 0.2 q^2$
From the sum of $2 y^2+3 y z,-y^2-y z-z^2$ and $y z+2 z^2$, subtract the sum of $3 y^2-z^2$ and $-y^2+y z+z^2$.
View full solution →State with reasons, which of the following pairs of terms are like terms and which are unlike terms:
$i. 7x, 12y$
$ii. 15x, –21x$
$iii. – 4\ ab, 7\ ba$
$iv. 3\ xy, 3x$
$v. 6\ xy^2 , 9\ x^2 y$
$vi. pq^2 , – 4\ pq^2$
$vii. mn^2 , 10\ mn$
View full solution →$i. 7x, 12y$
$ii. 15x, –21x$
$iii. – 4\ ab, 7\ ba$
$iv. 3\ xy, 3x$
$v. 6\ xy^2 , 9\ x^2 y$
$vi. pq^2 , – 4\ pq^2$
$vii. mn^2 , 10\ mn$
Riya wrote an algebraic expression.
$56t^3 + 12t^2 + 6t + 16s^2 + 2s + 106$
$1.$ Which of the following terms has 6 as the coeficient$?$
$A. s$
$B. s^2$
$C. t$
$D. t^3$
$2.$ Write the factors of $56t^3.$
$3.$ What is the type of the algebraic expression written by Riya$?$
$A.$ Monomial
$B.$ Binomial
$C.$ Trinomial
$D.$ Polynomial
$4.$ Riya said, “There are two like terms in the algebraic expression.” Is Riya correct? Give reason.
$5.$ Riya added an algebraic expression to $56t^3 + 12t^2 + 6t + 16s^2 + 2s + 106.$ The resultant expression is $14t^2+ 7t + 9s.$ Which of the following algebraic expressions did she add?
$A. 56t^3+ 2t^2+ t - 16s^2+ 7s + 106$
$B. -56t^3+ 2t^2+ t - 16s^2+ 7s – 106$
$C. -56t^3 - 2t^2 - t - 16s^2 - 7s – 106$
$D. 56t^3+ 26t^2+ 11t + 16s^2+ 11s + 106$
View full solution →$56t^3 + 12t^2 + 6t + 16s^2 + 2s + 106$
$1.$ Which of the following terms has 6 as the coeficient$?$
$A. s$
$B. s^2$
$C. t$
$D. t^3$
$2.$ Write the factors of $56t^3.$
$3.$ What is the type of the algebraic expression written by Riya$?$
$A.$ Monomial
$B.$ Binomial
$C.$ Trinomial
$D.$ Polynomial
$4.$ Riya said, “There are two like terms in the algebraic expression.” Is Riya correct? Give reason.
$5.$ Riya added an algebraic expression to $56t^3 + 12t^2 + 6t + 16s^2 + 2s + 106.$ The resultant expression is $14t^2+ 7t + 9s.$ Which of the following algebraic expressions did she add?
$A. 56t^3+ 2t^2+ t - 16s^2+ 7s + 106$
$B. -56t^3+ 2t^2+ t - 16s^2+ 7s – 106$
$C. -56t^3 - 2t^2 - t - 16s^2 - 7s – 106$
$D. 56t^3+ 26t^2+ 11t + 16s^2+ 11s + 106$
The amusement park is divided into three regular-shaped sections for rides, ticket room and
car parking respectively.
$1.$ What is the perimeter of the amusement park$?$
$A. 6P$
$B. 8P$
$C. 9P$
$D. 11P$
$2.$ What area of the amusement park is occupied by the parking space$?$
View full solution →car parking respectively.
$1.$ What is the perimeter of the amusement park$?$
$A. 6P$
$B. 8P$
$C. 9P$
$D. 11P$
$2.$ What area of the amusement park is occupied by the parking space$?$
The costs of entry tickets to an amusement park are different for adults and children. An adult
ticket costs $Rs.800$ and a child ticket costs $Rs.500.$
$1.$ On Sunday, $x$ adult tickets and $y$ child tickets were sold. Which of the following expressions show the money collected through the ticket sale?
$A. 1300x$
$B. 800x+ 500x$
$C. 800x+ 500 y$
$D. (800 + 500) ( x + y)$
$2.$ A car parking ticket at the amusement park costs $Rs.150$ on Saturdays and Sundays and $Rs.100$ on weekdays. In a month with $5$ Saturdays and $4$ Sundays, the total parking ticket sale was worth $Rs.250,000.$ Write an equation to represent the situation algebraically.
$3.$ On Monday, the number of adults who visited the amusement park was the square of the number of children who visited. How much money was collected by selling entry tickets on Monday$?$
$A. x^2$
$B. 800x^2+ 500x$
$C. 800x + 500x^2$
$D.1300 (x+ x^2)$
View full solution →ticket costs $Rs.800$ and a child ticket costs $Rs.500.$
$1.$ On Sunday, $x$ adult tickets and $y$ child tickets were sold. Which of the following expressions show the money collected through the ticket sale?
$A. 1300x$
$B. 800x+ 500x$
$C. 800x+ 500 y$
$D. (800 + 500) ( x + y)$
$2.$ A car parking ticket at the amusement park costs $Rs.150$ on Saturdays and Sundays and $Rs.100$ on weekdays. In a month with $5$ Saturdays and $4$ Sundays, the total parking ticket sale was worth $Rs.250,000.$ Write an equation to represent the situation algebraically.
$3.$ On Monday, the number of adults who visited the amusement park was the square of the number of children who visited. How much money was collected by selling entry tickets on Monday$?$
$A. x^2$
$B. 800x^2+ 500x$
$C. 800x + 500x^2$
$D.1300 (x+ x^2)$
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