1 Mark Question

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 _______.

Answer

A man spends Rs. x per week. The total money spent by him in $xy^2$ weeks is $x \times xy^2 = Rs. x^2y^2.$
Solution:
As, the money spent in one week =$ Rs. x.$
So, the total money spent in $xy^2$ weeks $= x \times xy^2 = Rs. x^2y^2.$

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Question 21 Mark

Write down the following in exponential form:
$a^3 \times 3ab^2 \times 2a^2b^2$

Answer

$3 \times 2 \times a^3 \times a \times a^2 \times b^2 \times b^2$
$= 6a^6b^4$

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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.

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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.

Answer

Let s, c and p be the selling price, cost price and profit, respectively.
Therefore, s = c + p

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Question 51 Mark

Write down the following in exponential form:
$4a^3 \times 6ab^2 \times c^2$

Answer

$4 \times 6 \times a^3 \times a \times b^2 \times c^2$
$= 24a^4b^2c^2$

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Question 61 Mark

Write the following products in exponential form:
$a \times a \times a \times a \times$ _____ $15 times.$

Answer

$a \times a \times a \times a \times a^{15} 15 times.$

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Question 71 Mark

Write down the following in the product form:
$6x^7y$

Answer

$6x^7y = 6 \times x \times x \times x \times x \times x \times x \times x \times y$

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Question 81 Mark

Write the following using numbers, literals and signs of basic operations:
One-third of a number x.

Answer

One-third of a number x is $\frac{\text{x}}{3}.$

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Question 91 Mark

Write the following using numbers, literals and signs of basic operations:
Number y less than a number 7.

Answer

Number y less than a number 7 means 7 - y.

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Question 101 Mark

Write the following in the product form:
$15a^9b^8c^6$

Answer

$15 \times a \times a \times a \times ... 9 times \times b \times b \times b \times ... 8 times.$

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Question 111 Mark

Write down the following in the product form:$10a^3b^3c^3$

Answer

$10a^3b^3c^3= 10 \times a \times a \times a \times b \times b \times b \times c \times c \times c$

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Question 121 Mark

Write the following using numbers, literals and signs of basic operations:
Quotient of x by 3 is multiplied by y.

Answer

Quotient of x by 3 is multiplied by y means:
$\frac{\text{x}}{3}\times\text{y}=\frac{\text{xy}}{3}$

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Question 131 Mark

Write the following in the product form:
$43 p^{10} q^5 r^{15}$

Answer

$43 \times p \times p \ldots . .10$ times $\times q \times q \ldots . .5$ times $\times r \times r \ldots . .15$ times.

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Question 141 Mark

Fill in the blank:
A chair costs Rs. $x$. The cost of $x^2 y$ chairs is_______.

Answer

A chair costs Rs. $x$. The cost of $x^2 y$ chairs is $x \times x^2 y=$ Rs. $x^3 y$.
Solution:

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Question 151 Mark

Write the following in the product form:
$7a^3b^4$

Answer

$7 \times a \times a \times a \times b \times b \times b \times b$

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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

$7 \times a \times a \times a 7 a ^8 8$ times $\times b \times b \times b \times b ^5 5$ times.

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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.

Answer

Let a be the side of the square.
Therefore, perimeter of the square = 4a

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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.

Answer

Let r and d be the radius and diameter of the circle, respectively.
Therefore, d = 2r

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Question 191 Mark

Write the following in the product form:
$30x^4y^4z^5$

Answer

$30 \times x \times x \times x \times x y \times y \times y \times y \times z \times z … 5 times.$

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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.

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Question 211 Mark

Write down the following in the product form:
$x^3y^4$

Answer

$x^3y^4 = x \times x \times x \times y \times y \times y \times y$

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Question 221 Mark

Write the following in the product form:
$8x^3$

Answer

$2 \times 2 \times 2 \times x \times x \times x$

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Question 231 Mark

Write down the following in the product form:
$9xy^2z^2$

Answer

$9xy^2z^2= 9 \times x \times y \times y \times x \times z$

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Question 241 Mark

Write the following using numbers, literals and signs of basic operations:
One-half of the sum of number x and y.

Answer

One-half of the sum of numbers x and y is $\frac{(\text{x}+\text{y})}{2}.$

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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:
$=\Big(4\times\frac{3}{2}\Big)\times\big(\text{x}^3\times\text{x}\times\text{x}\big)\times\big(\text{y}^2\times\text{y}^3\big)$
$=6\text{x}^5\text{y}^5$

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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

$8 \times b \times b \times b \times a \times a \times a \times a$
$8b^3a^4 = 8a^4b^3$

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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 $× b \times b \times b^{12}$ $12$ times $\times c \times c^{15}$ $15$ times.

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Question 281 Mark

Write the following in the product form:
$17p^{12}q^{20}$

Answer

$17 \times p \times p .... 12 times \times q \times q .... 20 times.$

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Question 291 Mark

Write the following in the product form:
$a^2b^5$

Answer

$a \times a \times b \times b \times b \times b \times b$

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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 $\frac{\text{x}}{\text{y}}-2$

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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

$5 \times a \times a \times a \times b \times b \times c \times c \times c$
$5a^3b^2c^3$

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Question 321 Mark

Write the following using numbers, literals and signs of basic operations:
The sum of 6 and x.

Answer

The sum of 6 and x is 6 + x.

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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.

Answer

The 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 $6a^2b^3c^4.$

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Question 341 Mark

Write down the following in exponential form:
$5xy \times 3x^2y \times 7y^2$

Answer

$5 \times 3 \times 7 \times x \times x^2 \times y \times y \times y^2$
$= 105x^3y^4$

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Question 351 Mark

Fill in the blank:
x + x + x + ... (y times) = ______.

Answer

x + x + x + ... (y times) = xy.
Solution:

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Question 361 Mark

If there are x rows of chairs and each row contains $x^2$ chairs. Determine the total number of chairs.

Answer

Total number of chairs = $Number of rows \times Number of chairs in each row:$
$= x \times x^2$
$= x^3$

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Question 371 Mark

Rohit covers x centimeters in one step. How much distance does he cover in y steps?

Answer

It is given that Rohit covers x cm in one step.
$\therefore$ Distance covered by him in y steps = x × y = xy cm.

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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. $

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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.

Answer

Let land b be the length and breadth of the rectangle, respectively.
Therefore, perimeter of rectangle = 2(l + b)

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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.

Answer

Let l and b be the length and breadth of the rectangle, respectively.
Therefore, area of rectangle = lb

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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 $\frac{\text{y}}{3}-4\text{x}.$

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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.

Answer

Let T, p and i be the total amount, principal and interest, respectively.
Therefore, T = p + i

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Maths 1 Mark Question

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