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Question 1:

Write each of the following products in exponential form:

(i) a × a × a × a × ..... 15 times
(ii) 8 × b × b × b × a × a × a × a
(iii) 5 × a × a × a × b × b × c × c × c
(iv) 7 × a × a × a.... 8 times × b × b × b ×.... 5 times
(v) 4 × a × a ×..... 5 times × b × b ×....12 times × c × c.... 15 times

Question 2:

Write each of the following in the product form:

(i) a2b5
(ii) 8x3
(iii) 7a3b4
(iv) 15a9b8c6
(v) 30x4y4z5
(vi) 43p10q5r15
(vii) 17p12q20

Question 3:

Write down each of the following in exponential form:

(i) 4a3 × 6ab2 × c2
(ii) 5xy × 3x2y × 7y2
(iii) a3 × 3ab2 × 2a2b2

Question 4:

The number of bacteria in a culture is x now. If becomes square of itself after one week. What will be its number after two weeks?

Present number of bacteria in a culture = x

Number of bacteria in the culture after one week = ${x}^{2}$

Number of bacteria in the culture after two weeks =

Question 5:

The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two-third of its breadth. Find its area if its breadth is x cm.

Breadth of the given rectangle = cm

Length of the rectangle = $\frac{2}{3}x$ cm
$\therefore$ Area of the rectangle = ​ cm2

Question 6:

If there are x rows of chairs and each row contains x2 chairs. Determine the total number of chairs.

Total number of chairs = Number of rows $×$ Number of chairs in each row

Question 1:

5 more than twice a number x is written as

(a) 5 + x + 2
(b) 2x + 5
(c) 2x − 5
(d) 5x + 2

(b) 2x + 5

Question 2:

The quotient of x by 2 is added to 5 is writen as

(a) $\frac{x}{2}+5$
(b) $\frac{2}{x}+5$
(c) $\frac{x+2}{5}$
(d) $\frac{x}{2+5}$

(a)

Question 3:

The quotient of x by 3 is multiplied by y is written as

(a) $\frac{x}{3y}$
(b) $\frac{3x}{y}$
(c) $\frac{3y}{x}$
(d) $\frac{xy}{3}$

(d) $\frac{xy}{3}$

Question 4:

9 taken away from the sum of x and y is

(a) x + y − 9

(b) 9 − (x+y)

(c) $\frac{x+y}{9}$
(d) $\frac{9}{x+y}$

(a) x + y − 9

Question 5:

The quotient of x by y added ot the product of x and y is written as

(a) $\frac{x}{y}+xy$
(b) $\frac{y}{x}+xy$
(c) $\frac{xy+x}{y}$
(d) $\frac{xy+y}{x}$

(a)

Question 6:

a2b3 × 2ab2 is equal to

(a) 2a3b4
(b) 2a3b5
(c) 2ab
(d) a3b5

(b) 2a3b5

Question 7:

4a2b3 × 3ab2 × 5a3b is equal to

(a) 60a3b5

(b) 60a6b5

(c) 60a6b6

(d) a6b6

(c) 60a6b6

Question 8:

If 2x2y and 3xy2 denote the length and breadth of a rectangle, the its area is

(a) 6xy
(b) 6x2y2
(c) 6x3y3
(d) x3y3

(c) 6x3y3

Area of the rectangle = Length $×$ Breadth
=

Question 9:

In a room there are x2 rows of chairs and each two contains 2x2 chairs. The total number of chairs in the room is

(a) 2x3
(b) 2x4
(c) x4
(d) $\frac{{x}^{4}}{2}$

(b) 2x4
Total number of chairs in the room = Number of rows $×$ Number of chairs in each row
= x2 $×$ 2x2 = 2x4

Question 10:

a3 × 2a2b × 3ab5 is equal to

(a) a6b6
(b) 23a6b6
(c) 6a6b6
(d) None of these

(c) 6a6b6
a3 × 2a2b × 3ab5

Question 1:

Write the following using numbers, literals and sings of basic operations. State what each letter represents:

(i) The diameter of a circle is twice its radius.
(ii) The area of a rectangle is the product of its length and breadth.
(iii) The selling price equals the sum of the cost price and the profit.
(iv) The total amount equals the sum of the principal and the interest.
(v) The perimeter of a rectangle is two times the sum of its length and breadth.
(vi) The perimeter of a square is four times its side.

(i) Let r and d be the radius and diameter of the circle, respectively.

$\therefore$ d = 2r

(ii) Let l and b be the length and breadth of the rectangle, respectively.

$\therefore$ Area of rectangle = lb

(iii) Let s, c and p be the selling price, cost price and profit, respectively.

$\therefore$ s = p

(iv) Let T, p and i be the total amount, principal and interest, respectively.

$\therefore$ T = p + i

(v) Let l and b be the length and breadth of the rectangle, respectively.

$\therefore$ Perimeter of rectangle = 2(b)

(vi) Let a be the side of the square.

$\therefore$ Perimeter of  the square = 4a

Question 2:

Write the following using numbers, literals and sings of basic operations:

(i) The sum of 6 and x.
(ii) 3 more than a number y.
(iii) One-third of a number x.
(iv) One-half of the sum of number x and y.
(v) Number y less than a number 7.
(vi) 7 taken away from x.
(vii) 2 less than the quotient of x by y.
(viii) 4 time x taken away from one-third of y.
(ix) Quotient of x by 3 is multiplied by y.

(i) The sum of 6 and x is 6 + x.
(ii) 3 more than a number y means y + 3.
(iii) One-third of a number x is $\frac{x}{3}$.
(iv) One-half of the sum of numbers x and y is $\frac{\left(x+y\right)}{2}$.
(v) Number y less than a number 7 means 7 $-$ y.
(vi) 7 taken away from x means x $-$ 7.
(vii) 2 less than the quotient of x by y is $\frac{x}{y}-2$.
(viii) 4 times x taken away from one-third of y is  .
(ix) Quotient of x by 3 is multiplied by y means:

Question 3:

Think of a number. Multiply it by 5. Add 6 to the result. Subtract y from this result. What is the result?

Let the number be x.

On multiplying the number by 5, we get:
5x

​Further, adding 6 to 5x, we get:
5x + 6

Finally, on subtracting y from 5x + 6, we get:
5x + 6 $-$ y

Question 4:

The number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor. If the first floor has x rooms, how many rooms does the ground floor has?

Let the number of rooms on the ground floor be y.

It is given that the ​number of rooms on the first floor is x; therefore, we have:

y = 2 $×$ x $-$ ​12
= 2x $-$ 12

Thus, the number of rooms on the ground floor is 2$-$ 12.

Question 5:

Binny spends Rs a daily and saves Rs b per week. What is her income for two weeks?

It is given that Binny spends Rs. in one day.

$\therefore$ Money spent by him in one week = 7 $×$ a = 7a

It is further given that he saves Rs. in one week; therefor we have:

Total income in one week = Total expenditure in one week + Total saving in one week
= 7a + b

$\therefore$ Binny's total income in 2 weeks = 2 $×$ (7a + b) = Rs. (14a + 2b)

Question 6:

Rahul scores 80 marks in English and x marks in Hindi. What is his total score in the two subject?

Question 7:

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

It is given that Rohit covers x cm in one step.

$\therefore$ Distance covered by him in ​y steps = x $×$ y = xy cm

Question 8:

One apple weighs 75 grams and one orange weighs 40 grams. Determine the weight of x apples and y oranges.

Question 9:

One pencil costs Rs 2 and one fountain pen costs Rs 15. What is the cost of x pencils and y fountain pens?