Question 11 Mark
Fill in the blank: A man spends $Rs. x$ per week. The total money spent by him in $xy^2$ weeks is _______.
AnswerAs, the money spent in one week $= Rs. x$. So, the total money spent in $xy^2$ weeks $= x × xy^2 = Rs. x^2y^2$.
View full question & answer→Question 21 Mark
Write down the following in exponential form: $a^3 \times 3 a b^2 \times 2 a^2 b^2$
Answer$3 \times 2 \times a^3 \times a \times a^2 \times b^2 \times b^2$
$=6 a^6 b^4$
View full question & answer→Question 31 Mark
Write the following using numbers, literals and signs of basic operations: $7$ taken away from $x.$
Answer$7$ taken away from $x$ means $x - 7.$
View full question & answer→Question 41 Mark
Write the following using number, literals and sings of basic operations. State what each letter represents: The selling price equals the sum of the cost price and profit.
AnswerLet $s, c$ and $p$ be the selling price, cost price and profit, respectively. Therefore, $s = c + p$
View full question & answer→Question 51 Mark
Write down the following in exponential form: $4a^3× 6ab^2× c^2$
Answer$4 × 6 × a^3× a × b^2× c^2$
$= 24a^4b^2c^2$
View full question & answer→Question 61 Mark
Write the following products in exponential form: $a \times a \times a \times a \times $ _____ $15$ times.
Answer$a \times a \times a \times a \times a^{15} 15$ times.
View full question & answer→Question 71 Mark
Write down the following in the product form: $6x^7y$
Answer$6x^7y = 6 × x × x × x × x × x × x × x × y$
View full question & answer→Question 81 Mark
Write the following using numbers, literals and signs of basic operations: One-third of a number x.
AnswerOne-third of a number x is $\frac{\text{x}}{3}.$
View full question & answer→Question 91 Mark
Write the following using numbers, literals and signs of basic operations: Number $y$ less than a number $7.$
AnswerNumber y less than a number $7$ means $7 - y.$
View full question & answer→Question 101 Mark
Write the following in the product form: $15a^9b^8c^6$
Answer$15 \times a \times a \times a \times ... 9 $times $\times b \times b \times b \times ... 8$ times.
View full question & answer→Question 111 Mark
Write down the following in the product form:$10a^3b^3c^3$
Answer$10a^3b^3c^3= 10 \times a \times a \times a \times b \times b \times b \times c \times c \times c $
View full question & answer→Question 121 Mark
Write the following using numbers, literals and signs of basic operations:
Quotient of $x$ by $3$ is multiplied by $y.$
AnswerQuotient of $x$ by $3$ is multiplied by $y$ means:
$\frac{\text{x}}{3}\times\text{y}=\frac{\text{xy}}{3}$
View full question & answer→Question 131 Mark
Write the following in the product form: $43p^{10}q^5r^{15}$
Answer$43 \times p \times p .... 10$ times $\times q \times q .... 5$ times $\times r \times r .... 15$ times.
View full question & answer→Question 141 Mark
Fill in the blank: A chair costs $Rs. x$. The cost of $x^2y$ chairs is _______.
AnswerA chair costs $Rs. x$. The cost of $x^2y$ chairs is $x × x^2y = Rs. x^3y$.Solution:
View full question & answer→Question 151 Mark
Write the following in the product form: $7a^3b^4$
Answer$7 \times a \times a \times a \times b \times b \times b \times b$
View full question & answer→Question 161 Mark
Write the following products in exponential form: $7 \times a \times a \times a$ ____ $8$ times $\times b \times b \times b \times $ ____ $5$ times.
Answer$7 \times a \times a \times a 7a^88$ times $\times b \times b \times b \times b^5 5$ times.
View full question & answer→Question 171 Mark
Write the following using number, literals and sings of basic operations. State what each letter represents: The perimeter of a square is four times its side.
AnswerLet a be the side of the square. Therefore, perimeter of the square $= 4a$
View full question & answer→Question 181 Mark
Write the following using number, literals and sings of basic operations. State what each letter represents: The diameter of a circle is twice its radius.
AnswerLet r and d be the radius and diameter of the circle, respectively. Therefore, $d = 2r$
View full question & answer→Question 191 Mark
Write the following in the product form: $30x^4y^4z^5$
Answer$30 \times x \times x \times x \times x y \times y \times y \times y \times z \times z … 5$ times.
View full question & answer→Question 201 Mark
Write the following using numbers, literals and signs of basic operations: $3$ more than a number $y.$
Answer$3$ more than a number $y$ means $y + 3.$
View full question & answer→Question 211 Mark
Write down the following in the product form: $x^3y^4$
Answer$x^3y^4 = x × x × x × y × y × y × y$
View full question & answer→Question 221 Mark
Write the following in the product form: $8x^3$
Answer$2 \times 2 \times 2 \times x \times x \times x$
View full question & answer→Question 231 Mark
Write down the following in the product form:$9xy^2z^2$
Answer$9xy^2z^2= 9 \times x \times y \times y \times x \times z$
View full question & answer→Question 241 Mark
Write the following using numbers, literals and signs of basic operations: One-half of the sum of number $x$ and $y.$
AnswerOne-half of the sum of numbers $x$ and $y$ is $\frac{(\text{x}+\text{y})}{2}.$
View full question & answer→Question 251 Mark
Fill in the blank:
$\text{x}^3\times4\text{xy}^2\times\frac{3}{2}\text{xy}^3=\underline{\ \ \ \ \ \ \ \ \ \ }.$
Answer $\text{x}^3\times4\text{xy}^2\times\frac{3}{2}\text{xy}^3=\underline{6\text{x}^2\text{y}^5}.$
Solution:
$=\Big(4\times\frac{3}{2}\Big)\times\big(\text{x}^3\times\text{x}\times\text{x}\big)\times\big(\text{y}^2\times\text{y}^3\big)$
$=6\text{x}^5\text{y}^5$
View full question & answer→Question 261 Mark
Write the following products in exponential form: $8 \times b \times b \times b \times a \times a \times a \times a$
Answer$8 \times b \times b \times b \times a \times a \times a \times a$
$ 8b^3a^4 = 8a^4b^3$
View full question & answer→Question 271 Mark
Write the following products in exponential form: $4 \times a \times a \times $ ____ $5$ times $\times b \times b \times $ ____ $12$ times $\times c \times c$ ____ $15$ times.
Answer$4 \times a \times a \times 4a^5 5$ times $\times b \times b \times b^{12}12$ times $\times c \times c^{15}15$ times.
View full question & answer→Question 281 Mark
Write the following in the product form: $17p^{12}q^{20}$
Answer$17 \times p \times p .... 12$ times $\times q \times q .... 20$ times.
View full question & answer→Question 291 Mark
Write the following in the product form: $a^2b^5$
Answer$a \times a \times b \times b \times b \times b \times b$
View full question & answer→Question 301 Mark
Write the following using numbers, literals and signs of basic operations: $2$ less than the quotient of $x$ by $y.$
Answer$2$ less than the quotient of $x$ by $y$ is $\frac{\text{x}}{\text{y}}-2$
View full question & answer→Question 311 Mark
Write the following products in exponential form:$ 5 \times a \times a \times a \times b \times b \times c \times c \times c$
Answer$5 \times a \times a \times a \times b \times b \times c \times c \times c$
$5a^3b^2c^3$
View full question & answer→Question 321 Mark
Write the following using numbers, literals and signs of basic operations: The sum of $6$ and $x.$
AnswerThe sum of $6$ and $x$ is $6 + x.$
View full question & answer→Question 331 Mark
Write $3 \times a \times a \times 2 \times b \times b \times b \times c \times c \times c \times c$ in the exponential form.
AnswerThe exponential form of $(3 \times a \times a \times 2 \times b \times b \times b \times c \times c \times c \times c)$ is $6a^2b^3c^4$.
View full question & answer→Question 341 Mark
Write down the following in exponential form: $5 x y \times 3 x^2 y \times 7 y^2$
Answer$5 \times 3 \times 7 \times x \times x^2 \times y \times y \times y^2$
$=105 x^3 y^4$
View full question & answer→Question 351 Mark
Fill in the blank: $x + x + x + ... (y$ times$) =$ ______.
Answer$x + x + x + ... (y$ times$)$ = xy. Solution:
View full question & answer→Question 361 Mark
If there are x rows of chairs and each row contains $x^2$ chairs. Determine the total number of chairs.
AnswerTotal number of chairs = Number of rows $\times $ Number of chairs in each row:
$= x × x^2$
$= x^3$
View full question & answer→Question 371 Mark
Rohit covers $x$ centimeters in one step. How much distance does he cover in $y$ steps?
AnswerIt is given that Rohit covers $x \ cm$ in one step. $\therefore$ Distance covered by him in y steps $= x \times y = xy \ cm.$
View full question & answer→Question 381 Mark
Fill in the blank: $a \times a \times 3 \times b \times b \times b \times 2 \times c \times c =$_______.
Answer$a \times a \times 3 \times b \times b \times b \times 2 \times c \times c$
$= 6a^2b^3c^2$.
View full question & answer→Question 391 Mark
Write the following using number, literals and sings of basic operations. State what each letter represents:
The perimeter of a rectangle is two times the sum of its length and breadth.
AnswerLet land b be the length and breadth of the rectangle, respectively.
Therefore, perimeter of rectangle $= 2(l + b)$
View full question & answer→Question 401 Mark
Write the following using number, literals and sings of basic operations. State what each letter represents: The area of a rectangle is the product of its length and breadth.
AnswerLet l and b be the length and breadth of the rectangle, respectively. Therefore, area of rectangle $= lb$
View full question & answer→Question 411 Mark
Write the following using numbers, literals and signs of basic operations:
$4$ time $x$ taken away from one-third of $y.$
Answer$4$ times $x$ taken away from one-third of $y$ is $\frac{\text{y}}{3}-4\text{x}.$
View full question & answer→Question 421 Mark
Write the following using number, literals and sings of basic operations. State what each letter represents:
The total amount equals the sum of the principal and the interest.
AnswerLet T, p and i be the total amount, principal and interest, respectively.
Therefore, $T = p + i$
View full question & answer→