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A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

The area of a square field is 60025sq.m. A man cycles along it's boundary at 18km per hour. In how much time he return at starting point

In the following figure, three equal rhombuses are arranged.

What additional information do you depict about the interior angles of rhombuses?

Which of the following combinations get South facing rooms?

Pawan is a cashier in a bank. He has currency notes of denominations 1000 and 100 respectively. The ratio of the number of these notes is 4:10. If the total cash with Pawan is Rs.5,00,000, how many notes of Rs.1000 denomination does he have?

The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.

Question 5 (iv)
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

1825

For a polyhedron having 5 faces and 3 vertices, find the number of edges.

If the addition of numbers 2A and 33 gives 5B, where A and B are digits then find A and B. Given that number 2A is divisible by 10.

Question 3(i)
You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913.

Which congruence criterion is used in the following?

Given: $\angle MLN=\angle FGH,\angle NML=\angle HFG,ML=FG$
So, $\Delta LMN\cong \Delta GFH$

$\text{If a=b, show that abc=bac.}$

The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu.dm. Find its dimensions.

$\text{The marked price of a T.V. is Rs.18500.A dealer allows two successive discounts of}20\%and5\%.\text{For how much is the TV available?}$

Factorise :
$x^2-ax-bx+ab$

A village, having a population of 4000, requires 150 litres water per head per day. It has a tank which is 20 m long, 15 m broad and 6 m high. For how many days will the water of this tank last?

Bhagwanti inherited Rs 12000.00. She invested part of it as 10% and the rest at 12%. Her annual income from these investments is Rs 1280.00. How much did she invest at each rate ?

A publisher gives $32\%$ discount on the printed price of a book to booksellers. What does a bookseller pay for a book whose printed price is $Rs.275$?

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is $8316c{m}^3$, find the total surface area of the cylinder.

Question 99

Find the area of the shaded region:

A line is rotated by an angle of ${360}^{\circ }$ about one of its extreme end. The resultant shape is

A shopkeeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.

Factorise : $75(x+y{)}^2-48(x-y{)}^2$

The following data gives the amount spent of the construction of a house. Draw a pie diagram.
$\begin{array}{ccccccc}\text{Item}& \text{Cement}& \text{Timber}& \text{Bricks}& \text{Labour}& \text{Steel}& \text{Miscellaneous}\\ \text{Expenditure (in thousand Rs)}& 60& 30& 45& 75& 45& 45\end{array}$

Simplify:$(\frac{(\frac{1}{5}{)}^{-3}-(\frac{1}{3}{)}^{-4}}{(\frac{1}{4}{)}^{-3}})$

Question 82

In the following question, state whether the given statements are true (T) or false (F).

$\frac{x^m}{y^m}={\left(\frac{y}{x}\right)}^{-m}$

Find discount per cent when: MP $=Rs.625$ and SP $=Rs.562.50$

Question 4 (x)
Find the square roots of the following numbers by the Prime Factorization method:
8100

A garden has 2000 trees. 12% of these are mango trees, 18% lemon and the rest are orange trees. Find the number of orange trees.

Factorize $8a^3+27b^3+36a^{2}b+54a{b}^2$

In Fig. ABCD is a trapezium in which AB||DC. E is the mid-point of AD. A line l through E is parallel to AB show that l bisects the side BC.[3 MARKS]

Multiply:

$(5x+3)by(7x+2)$

Sohan bought a second-hand refrigerator for ₹ 2500 and spent ₹ 1500 on its repair. He then sold it for ₹ 3300. What is the gain or loss%?

The number of coins,each of radius 0.75 cm and thickness 0.2 cm,to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is

(a) 460

(b) 500

(c) 600

(d) 640

➡️The adjacenct sides of a parallelogram are 21cm and 28cm. If one diagonal is 35 cm ; find the area of the parallelogram.

Find the value of n such that $2(4n-1)-1(5n-1)=n+5$

Which of the following represents the factorisation of $y^2+yz+9y+9z$?

Question 3(i)
Simplify:
$(x^2-5)(x+5)+25$

The geometrical shapes that do not have thickness or depth are known as ___ dimensional objects.

Show that the following integers are cubes of negative integers. Also, find the integer whose cube is the given integer:
(i) -5832 (ii) -2744000