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If the
circumference of a circular sheet is 154m, find its radius. Also find
the area of

the sheet.
(Takeπ)

Question 28

In the following question, out of the four options, only one is correct. Write the correct answer.

${\left(\frac{3}{4}\right)}^5÷{\left(\frac{5}{3}\right)}^5$ is equal to

(a) ${(\frac{3}{4}÷\frac{5}{3})}^5$

(b) ${(\frac{3}{4}÷\frac{5}{3})}^1$

(c) ${(\frac{3}{4}÷\frac{5}{3})}^0$

(d) ${(\frac{3}{4}÷\frac{5}{3})}^{10}$

If A = {set of even prime number}, then A is

'5ab + 2b - 12bc + 4' is a

In the figure given below, a ray OC extends from a point O on a straight line AB, If ∠AOC = 135°, then $\frac{\angle BOC}{3}$ is equal to:

Ravi had ${\frac{5}{6}}^{\text{th}}$ of a cake with him. He ate ${\frac{2}{3}}^{\text{rd}}$ of it. What part of the cake did he eat ?

Two candles are of different lengths and thicknesses. The short and the long ones can burn respectively for 3.5 hour and 5 hours. After burning for 2 hour, the lengths of the candles become equal in length. What fraction of the long candle’s height was the short candle initially?

Amita has $12$ marbles and Reeta has $8$ marbles. Reeta says that she has $x/y$ times the marbles that Amita has, where x and y are co-prime numbers.

Then $x+y=$

Question 59

Fill in the blanks to make the statement true.

When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ___ sign before quotient.

Explain, why

ΔABC ≅ ΔFED

The temperature recorded at 12 noon was 15 degrees celsius above 0. it decreases at the rate of 3 degree Celsius per hour until midnight ,at what time would the temperature be 9 degree Celsius below zero. What t would be the temperature at midnight?

During the year, a machine costing ₹ 25,000 (accumulated depreciation thereon ₹ 15,000) was sold for ₹ 13,000.

Calculate Cash Flow from Investing Activities on the basis of the above information.

Question 5

In the following question out of the four options only one is correct, write the correct answer:

If $\frac{5x}{3}-4=\frac{2x}{5},$ then the numerical value of 2x-7 is:

(a) $\frac{19}{13}$

(b) $\frac{-13}{19}$

(c) 0

(d) $\frac{13}{19}$

Find the equation of the horizontal line that is drawn through the point $(5,7).$

The length of a rope is 2 m and its diameter is 1 cm. The ratio of the length of the rope to its diameter is _____.

The largest two-digit multiple of 19 is ___ .

Solve the following.

Find the mean proportion between 9 and 49.

1. 3

Question 77

Shiv works in a mall and gets paid Rs. 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.

To keep system of 3 charges in equilibrium as shown in figure, $q_0$ must be

Question 32

In the following question, fill in the blanks with correct symbol >, < or =.

$\frac{3}{7}$ ___ $\frac{-5}{6}$

Which are the points to be considered while calculating simple interest?

The given pie chart shows the distribution of different types of plants in a garden in Chicago.



If the garden has a total of 60 plants, how many apple plants does it have?

Peter has $12$ pens, and Sheldon has $15$ pens. They wanted to make bundles of pens, having the same number of pens in each bundle. How many maximum possible pens can be included in each bundle if all the bundles are identical?

What is the sum of the rational numbers $\frac{2}{5}$ and $\frac{-3}{7}$?

Ram has certain number of chocolates. If he gets the same number of chocolates from his friend, then how many chocolates does he have in total ?

What is the value of the product $567\times 982?$