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Question 23
Which of the following are reflections of each other?

a)

b)

c)

d)

It is given that the sum of three rational numbers is $\frac{2}{3}$. Among the three numbers, two numbers are $\frac{5}{6}$ and $\frac{1}{4}$, find the third one.

Solve the following.

Antony and Budenmia invests Rs. 24,000 and Rs. 36,000 in a partnership (Small scale industry). At the end of the year, they get Rs.10,000 in the form of profit. What is the amount of profit each gets?

1.25 converted to fraction in its simplest form gives

Find the square of the following numbers using the formula:

(a − b)² = a² − 2ab + b²

A motorbike was sold by a showroom for Rs. 80,000. The owner then sold this bike at Rs. 60,000. Find the percentage of profit or loss.

Question 29

State whether the given statements are true (T) or false (F).

The ratio of 4 : 16 is in its lowest form.

Relative error =

Explain the relationship between AC and MC. Can the AC curve fall when MC curve is rising? Explain it with the help of diagram.

A train 175 m long crosses a bridge which is 125m long in 60s. What is the speed of the train?

The sum of 2 rational numbers is $-5$. If one of them is $\frac{5}{2}$ find the other.

Which of the following number cannot be multiplied on both sides?

Find the
number from each of the following expanded forms:

(a) 8 ×
10⁴ + 6 × 10³
+ 0 × 10² + 4 ×
10¹ + 5 × 10⁰

(b) 4 ×
10⁵ + 5 × 10³
+ 3 × 10² +
2 × 10⁰

(c) 3 ×
10⁴ + 7 × 10²
+ 5 × 10⁰

(d) 9 ×
10⁵ + 2 × 10²
+ 3 × 10¹

Select the correct multiplication statement. There can be more than one.

1. 6

Which is the numerical co-efficient in 4x²y?

In sexagesimal system of angle measurements, $1^{\circ }=$and $1^{\prime }=$

The product of two digit two-numbers is 2700 and their L.C.M is 180,then what is the sum of the two numbers?

राजप्पा ने नागराजन का टिकट-अलबम अँगीठी में क्यों डाल दिया?

Tap the sandwich which is divided into fourths.

A pack of 2 kg of sugar contains $8\times {10}^6$ crystals and a sack contains 3 packs of sugar. How many crystals would 12 sacks contain?

If

Solve the following problems and draw Venn diagrams for each of them.

It was observed that $150$ vehicles crossed a particular location of a highway in a duration of $30$ minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the number of times headway is greater than $5$ seconds in the above observation ?

1. 98.85

Fill in the blanks to make each of the following a true statement :

(i) $A\cup A^{\prime }=........$ (ii) ${\Phi }^{\prime }\cap A=......$

(iii) $A\cap A^{\prime }=......$ (iv) $U^{\prime }\cap A=......$

A die is thrown 325 times. The frequency of the outcomes of the event 1, 2, 3, 4, 5 and 6 are recorded in the following frequency distribution table.

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 50& 65& 45& 34& 55& 76\end{array}$

Find the probability of the occurrence of an (i) even number (ii) odd number.

Simplify:

(1) $2+(-4)-(+3)$

(2) $-5+4-(-2)$

(3) $10+(-5)-(-4)$

(4) $12-(+6)+(-3)$

(5) $-15+(-4)-(+3)$

Which of the following are rational numbers?

If the order of rorational symmetry of a figure is 1, then the figure has ___

What is the area of the rhombus ABCD below if AC = 6 cm and BE = 4 cm?

The length of a table is 2 m and its breadth is 50 cm. Find the ratio of the length of the table to its breadth.

Bisect the given angles and measure the bisected angles in the following:

∠LMN = 90°

Arrange the values of the following expressions in increasing order from bottom to top.

Parts exiting an assembly line are inspected and categorized as good or bad (defective). In a batch of 100 parts, 8 were found to be defective.
What is the probability that a part drawn at random is defective?

Question 48

Answer True/False.

In the equation 7k - 7 = 7, the variable is 7.

Find the sum of the interior angles of an octagon.

Add the following rational numbers :

(i) $\frac{-2}{5}$ and $\frac{4}{5}$ (ii) $\frac{-6}{11}$ and $\frac{-4}{11}$ (iii) $\frac{-11}{8}$ and $\frac{5}{8}$

(iv) $\frac{-7}{3}$ and $\frac{1}{3}$ (v) $\frac{5}{6}$ and $\frac{-1}{6}$ (iv) $\frac{-17}{15}$ and $\frac{-1}{15}$

What is (5x-7) when x = -1?