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In order to represent a rational number on a number line, _____ of the rational number tells the number of parts that should be considered when the first unit is divided into equal parts.

Question 80

In the following question, state whether the statement is True (T) or False (F):

The value of $(a+1)(a-1)(a^2+1)$ is $a^4-1$.

In a single throw of a coin, what is the probability of getting a tail ?

Find the area of a trapezium whose parallel sides are $24cm$ and $20cm$ and the distance between them is $15cm.$

In which of the following quadrants does the point P(3, 6) lie ?

(a) I (b) II (c) III (d) IV

If we have 15 boys and 5 girls in a class which carries a higher probability? Getting a copy belonging to a boy or a girl. Can you give it a value?

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$. What is the original fraction equal to ?

Question 134

Solve the following question:

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Question 67

Using the frequency table, answer the following:

$\begin{array}{ccccccc}\text{Marks(Obtained out of 10)}& 4& 5& 7& 8& 9& 10\\ \text{Frequency}& 5& 10& 8& 6& 12& 9\end{array}$
The frequency of more than 8 marks is 21 ?

Find the greatest common factors (GCF / HCF) of the following polynomials :

$x^3,-y{x}^2$

Question 61

In questions which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) Number of students in a hostel and consumption of food.
(ii) Area of the walls of a room and the cost of whitewashing the walls.
(iii) The number of people working and the quantity of work.
(iv) Simple interest on a given sum and the rate of interest.
(v) Compound interest on a given sum and the sum invested.

Question 63 (iv)

How many faces does the following solid have?

Octahedron

After all these questions, William mentioned that the chart looks like a chart of several bars. Jack could relate to it as he knew that William was going to invent them in future!

To return to the future, he needed to charge the super batteries. Though nobody knew how to generate electricity there, Jack, with the help of magnets and superconductor wires, successfully built a micro hydro generator.

He went to the church and started charging the super batteries every day. Meanwhile, Jack played the game of Ludo with William to pass time. This game is played by throwing a 6 faced die with numbers from 1 to 6 on its 6 faces. To win, Jack had to get a 4. What is the probability that he will win the game?

$(a+b+c)(a+b-c)=(a^x+2ab+b^y-c^z)$

then, x+y+z=___

($\frac{a}{b}$) will be __________number if two variables a and b are whole numbers.

Here is a histogram which is made up of bricks. 1 brick = 10,500. Carefully observe the histogram and answer the question that follows:

By selling a radio for Rs. 950, a man loses 5 %. What per cent shall he gain by selling it for Rs. 1040 ?

(a) 4 %

(b) 4.5 %

(c) 5 %

(d) 9 %

(n-10) (n-10) +(10-n)

Which of the following is a 'Euler’s formula'?

solve and find the value of ' x '

x+3 - (2x+8) / 3 = 7x - 2 / 24

What must be added to each term of the ratio 2 : 3, so that it may become equal to 4 : 5?

Question 122

In the given figure, $\Delta AEC$ is right angled at E, B is a point on EC, BD is the altitude of $\Delta ABC$, AC = 25 cm BC = 7 cm and AE = 15 cm. Find the area of $\Delta ABC$ and the length of DB.

Question 1

A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also, find the area of the garden in hectares.

The diagonal of a quadrilateral shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m²).

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The total time taken for the work to be completed was

The marks obtained by a student in a subject in three different tests were 20, 12, (-4). What are the total marks obtained by the student in that subject? What is the minimum number of marks he needs to score in the 4th test if the passing marks are 40?
[2 MARKS]

Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with :

(i) 7 sides (ii) 10 sides (iii) 250 sides

If a coin is tossed 2 times, what is the probability of getting at least one tail?

Ravi has purchased a vehicle at ₹ 60,000. He sold it at a price $30\%$ less than its value to Amit. Amit spent $5\%$ of the amount he purchased in repairs. Find the percentage decrease of the price of the vehicle, including the repair price also.

What sum of money borrowed on 24th May will amount to Rs. 10210.20 on 17th October of the same year at 5 percent per annum simple interest.

Draw a line segment BC = 4 cm. Construct angle ABC = ${60}^{\circ }$.

The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find : (i) its marked price (ii) its selling price (iii) the profit percent.

The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:

$(a+b+c)(a+b-c)$ = ___.

Which of the following is a binomial?

Arrange the following rational numbers in the ascending order
$\frac{5}{4},\frac{2}{3},\frac{6}{8},\frac{8}{5},\frac{9}{2}.$

Evaluate : ${27}^{\frac{2}{3}}+(\frac{81}{16}{)}^{\frac{-1}{4}}$

$2x^2-3x+4$, when $x=-2$.

X + 1/2 = 12 , find the value of X - 1/x

${\left(2\right)}^5\times {\left(4\right)}^5$ = _____

A farmer has enough food to feed 20 cattle for 6 days. The number of days food will last if there were 10 more cattle is

If 2/3 is multiplicative inverse of -4 2/3 then why is it so or why not

The cube root of the number 15625 is a perfect square of __________.

Expanded form of 432 is:

Construct a quadrilateral ABCD in which AB = 2.7 cm, BC = 3.5 cm, CD = 4 cm, AD = 6 cm and $\angle B={90}^{\circ }$ [4 MARKS]