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1. 36

A cylindrical rod of height 10 m and radius 7m is melted into 7 identical cylindrical pistons of radius 14m and height $\frac{5}{14}$ m.

Decide whether or not the following assertions are correct:

(1) The volume of the cylindrical rod is equal to the sum of the volume of all 7 pistons.

(2) The total surface area of the cylindrical rod is equal to the sum of total surface area of the cylindrical piston.

Which of the following form a pair of equivalent rational numbers?

The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, the sum of their ages will be 70 years. Find their present ages.

Area of a segment = Area of the sector Area of the triangle. Insert the correct operation.

Question 44

State whether the following statement is true (T) or false (F).

If 6x=18, then 18x=54.

What are the angles of an equilateral triangle?

The point of intersection of axes is called __.

If x + (1/x) = 6, find x² + (1/x²) and x⁴ +

Estimate the square root of 536 to its nearest whole number.

What is meant by new profit sharing ratio in case of admission of a partner ?

Select the pairs that give equal values after computation.

Integers comprise of:

If (4a2) is exactly divisible by 3, then the value of 'a' from the given options is :

Factorise

$63a^2-112b^2$

Which of the following regions represents 3x?

Question 56

When a die is thrown, outcomes 1,2,3,4,5,6 are equally___.

The angles of a triangle are in the ratio 7 : 9 : 2 . The measure of the smallest angle is _______.

PQR is a right-angled triangle with the right angle at Q and k being the length of the perpendicular from Q on PR. If l, m and n are the lengths of sides PQ, QR, and PR respectively, then which of the following holds true?

Find ten rational numbers between $\frac{-2}{5}$and $\frac{1}{2}$.

Question 4

Express 0.99999…in the form $\frac{p}{q}$. Are you surprised by your answer? Discuss why the answer makes sense.

In a science experiment, the weights of different body masses were measured at a specific height from the sea level as tabulated below.



Mass (kg)
Weight $\left({\text{kg}\times \text{m/second}}^2\text{or Newton (N)}\right)$

Question 1

Construct the Quadrilateral LIFT where

LI=4 cm, IF = 3 cm, TL = 2.5 CM, LF = 4.5 cm , IT = 4 cm

The number of pairs of opposite faces in a cube is:

Two friends A and B start a joint business with a capital s 60,000. If A’s share is twice that of B, how much have each invested?

(i) Obtain the range of monthly household expenditure on food.

(ii) Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure.

(a) find x
+ y + z

(b) find x
+ y + z + w

The histogram below represents the Mathematics marks of the students.

In marks interval ___ and ___ , number of students is same.

Question 1 (e)

State whether true or false.

(e) All kites are rhombuses.

How many different combinations of product can be obtained by multiplying three numbers from $12,13,14,15,16,19$ without using same number twice?

If 2x - 3 = x + 2, then x = ?

(a) 1

(b) 3

(c) 5

(d) 7

For how many hours did maximum number of students watch TV?

The forest department conducted a survey for two types of trees oak and pine in the years 2005, 2008 and 2011. The data obtained is shown below.

The year in which the no. of pine trees is more than oak trees is:

The following are the marks scored in a unit test (out of 25). Prepare a frequency distribution table, taking the class intervals as 0-4, 5-9, 10-14, 15-19, 20-24:

21, 14, 3, 7, 23, 18, 24, 16, 18, 17, 20, 10, 17, 18, 21, 23, 19, 12, 14, 9, 16, 18, 12, 14, 11.

From the table (i) find the mid-points of each class interval; (ii) find the class interval having maximum frequency; (iii) find the range of the scores.

1. 5

In the diagram when the supply and demand coincide?

If a+b+c=5 and ab+bc+ca=10 then prove that a^3+b^3+c^3-3abc=-25

Please send answers with steps