What is the value of $5 x^{25}-3 x^{32}+2 x^{-12}$ as $x=1$ ?
- A$0$
- B$2$
- ✓$4$
- DNone of these
Answer: C.
View full solution →Question types
Algebraic Expressions and Identities question types
121 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
121
Questions
9
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
15 Q→02TRUE-FLASE [1 Marks Each]
5 Q→03Assertion (A) & Reason (B) MCQ
3 Q→042 Marks Questions
19 Q→053 Marks Question
21 Q→065 Marks Questions
16 Q→07MATCH THE FOLLOWING.
1 Q→081 Marks Question
36 Q→09BLANKS [1 Marks Each]
5 Q→Sample Questions
Algebraic Expressions and Identities questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If we subtract $4 a-7 a b+3 b+12$ from $12 a-9 a b+5 b-3$, then the answer, is
- A$8 a+2 a b+2 b+15$
- B$8 a+2 a b+2 b-15$
- ✓$8 a-2 a b+2 b-15$
- D$8 a-2 a b-2 b-15$
Answer: C.
View full solution →A polynomlal contalns _____________ number of terms
- AOne
- BTwo
- CThree
- ✓Any
Answer: D.
View full solution →$(x-y)(x+y)+(y-z)(y+z)+(z-x)(z+x)$ is equal to
- ✓$0$
- B$x y+y z+z x$
- C$x+y+z$
- D$x^2+y^2+z^2$
Answer: A.
View full solution →The number of like terms in $8 x^3, 16 x^2 y,-8 x^3, 12 x y^2, 6 x^3$, is
- A2
- B1
- ✓3
- D4
Answer: C.
View full solution →$3 x \times\left(9 x^2+6 y\right)$ is an algebraic expression which is a product of monomial and binomial.
View full solution →The product of $(3+a)(3+b)$ is $9+(a+b) 3+3 a b.$
View full solution →Multiplication of $\left(x^2+5 x+3\right) \times(3 x)$ gives $3 x^3+15 x^2+9 x.$
View full solution →An algebraic expression, which contains 2 terms is called trinomial.
Using distributive law, we can multiply a monomial with a binomial.
Assertion (A) 5 terms are there in the expression $5 x y+9 y z+3 z x+5 x-4 y$.
Reason (R) An algebraic expression consists of a group of terms separated by operators, which are either plus signs or minus signs?
Reason (R) An algebraic expression consists of a group of terms separated by operators, which are either plus signs or minus signs?
- ABoth A and R are correct and R is the correct explanation of A.
- BBoth A and R are correct but R is not the correct explanation of A.
- CA is false but R is true.
- ✓A is true but R is false.
Answer: D.
View full solution →Assertion (A) The algebraic expression $2 x^2+5 x-3$ is a binomial.
Reason (R) An algebraic expression, which contains three terms separated by addition (+) or subtraction (-) operators, is called a trinomial.
Reason (R) An algebraic expression, which contains three terms separated by addition (+) or subtraction (-) operators, is called a trinomial.
- ABoth A and R are correct and R is the correct explanation of A.
- BBoth A and R are correct but R is not the correct explanation of A.
- ✓A is false but R is true.
- DA is true but R is false.
Answer: C.
View full solution →Assertion (A) The algebraic expression $(x+3)(x-3)$ can be simplified as $x^2-9$.
Reason (R) The expression $(a+b)(a-b)$ can always be simplified as $a^2-b^2$.
Reason (R) The expression $(a+b)(a-b)$ can always be simplified as $a^2-b^2$.
- ✓Both A and R are correct and R is the correct explanation of A.
- BBoth A and R are correct but R is not the correct explanation of A.
- CA is false but R is true.
- DA is true but R is false.
Answer: A.
View full solution →Find the product.
$2 x(3 x+5 x y)$
View full solution →$2 x(3 x+5 x y)$
Simplify
$(a^2+5)(b^3+3)+5$
View full solution →$(a^2+5)(b^3+3)+5$
Simplify
$(x^2-5)(x+5)+25$
View full solution →$(x^2-5)(x+5)+25$
Find the product.
$(x+7y)(7x-y)$
View full solution →$(x+7y)(7x-y)$
Find the product.
$(5-2x)(3+x)$
View full solution →$(5-2x)(3+x)$
Find $4 x \times 5 y \times 7 z.$ First, find $4 x \times 5 y$ and multiply it by $7 z$; or first find $5 y \times 7 z$ and multiply it by $4 x$. Is the result same? What do you observe? Does the order in which you carry out the multiplication matter?
View full solution →Can you think of two more such situations, where we may need to multiply algebraic expressions?
Hint Think of speed and tirne.
Think of interest to be paid, the principal and the rate of simple interest etc.
Hint Think of speed and tirne.
Think of interest to be paid, the principal and the rate of simple interest etc.
Simplify $a\left(a^2+a+1\right)+5$ and find its value for
(a) $a=0$ $\quad$ (b) $a=1$ $\quad$ (c) $a=-1$
View full solution →(a) $a=0$ $\quad$ (b) $a=1$ $\quad$ (c) $a=-1$
Simplify $3 x(4 x-5)+3$ and find its values for
(a) $x=3$ $\quad$ (b) $x=\frac{1}{2}$
View full solution →(a) $x=3$ $\quad$ (b) $x=\frac{1}{2}$
Find the product.
$\left(\frac{2}{3} x y\right) \times\left(\frac{-9}{10} x^2 y^2\right)$
View full solution →$\left(\frac{2}{3} x y\right) \times\left(\frac{-9}{10} x^2 y^2\right)$
(i) Add $p(p-q), q(q-r)$ and $r(r-p).$
(ii) Add $2 x(z-x-y)$ and $2 y(z-y-x).$
(iii) Subtract $3 I(I-4 m+5 n)$ from $4 I(10 n-3 m+2I).$
(iv) Subtract $3 a(a+b+c)-2 b(a-b+c)$ from $4 c(-a+b+c).$
View full solution →(ii) Add $2 x(z-x-y)$ and $2 y(z-y-x).$
(iii) Subtract $3 I(I-4 m+5 n)$ from $4 I(10 n-3 m+2I).$
(iv) Subtract $3 a(a+b+c)-2 b(a-b+c)$ from $4 c(-a+b+c).$
Complete the table.
View full solution →| First expression | Second expression | Product | |
| (i) | $a$ | $b+c+d$ | |
| (ii) | $x+y-5$ | $5xy$ | |
| (iii) | $p$ | $6 p^2-7 p+5$ | |
| (iv) | $4 p^2 q^{2}$ | $p^2-q^2$ | |
| (v) | $a+b+c$ | $abc$ |
The given figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.
Find the product of $(\text x-2\text y)(\text x+2\text y)\left(\text x^2+4\text y^2\right)$ at $\text x=1$ and $\text y=1.$
View full solution →Multiply $\left(3\text y^5-7\text y^3+2\text y^2-\text y+4\right)$ by $\left(\text y^3-2\text y^2+3\text y-1\right).$
View full solution →Match the Column A with Column B
View full solution →| Column A (length, breadth) = (x, y) of rectangle | Column B A = Area of rectangle |
| (i) $(l b)=(9 \times 4)$ | (a) $A=36xy^{3} $ |
| (ii) $(l b)=(3 \times 4 y)$ | (b) $ A=36$ |
| (iii) $(lb)=(9xy \times 4 y^{2})$ | (c) $ A=20xy $ |
| (iv) $(lb)=(4 x\times 5 y)$ | (d) $ A=12 xy$ |
Find the product of $\left(4 p^2+5 p+7\right) \times 3 p$.
View full solution →Find the product.
$a^2(2 a b-5 c)$
View full solution →$a^2(2 a b-5 c)$
Simplify
$(a+b+c)(a+b-c)$
View full solution →$(a+b+c)(a+b-c)$
Simplify
$(1.5 x-4 y)(1.5 x+4 y+3)-(4.5 x+12 y)$
View full solution →$(1.5 x-4 y)(1.5 x+4 y+3)-(4.5 x+12 y)$
Simplify
$(x+y)(x^2-x y+y^2)$
View full solution →$(x+y)(x^2-x y+y^2)$
The area of rectangular plot with sides $4 x$ and $3 x$ is _____________.
View full solution →On subtracting $-3 a^2 b^2$ from $a^2 b^2$, we get _____________.
View full solution →The product of two polynomials is a _____________.
The coefficient of $x^2 y^2 \operatorname{in}\left(x^2+5 x y+3\right)(5 x y)$ is _____________.
View full solution →The given algebraic expression $3 a^2+5 a b \times c \text { is a}$ _____________.
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