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Write the cubes of 5 natural numbers of the form 3n + 2 (i.e. 5 , 8 , 11, ..... ) and verify the ffollowing
'The cube of a natural number of the form 3n + 2 is a natural number of the same form i.e. when it is divideend by 3 the remainder is 2.

By what least number should the given number be multiplied to get a perfect square number? In each case, find the number whose square is the new number.
(i) $3675$
(ii) $2156$
(iii) $3332$
(iv) $2925$
(v) $9075$
(vi) $7623$
(vii) $3380$
(viii) $2475$

Factorise: $1-16(x-2y{)}^2$.

Question 5(iii)

Give expression for the following case.

5 times y to which 3 is added.

Which of the following is true about a line graph?

If $\frac{n}{n+15}=\frac{4}{9}$, then n = ?

(a) 4

(b) 6

(c) 9

(d) 12

Draw a figure of a cylinder in which a cone of same height is removed. [2 MARKS]

A class is 7 m long, 6 m board and 3.5 m high. Doors and windows occupy an area of 17 $m^2$. What is the cost of white-washing the walls at the rate of Rs. 1.50 per $m^2$.

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice, as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Choose an appropriate question tag for the blank.

If I need anything, I can just tell the bell boy, ______ I?

A factor that divides two or more expression is called___

If you have AB = 3 cm, BC = 4 cm, CD = 5 cm & and DA = 6 cm, can you draw quadrilateral ABCD? If you can, will this quadrilateral be unique?

In which quadrant or on which axis do each of the points (-2,4), (3, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane

The number -1728 is the cube of the number ______ .

If the interest is compounded half yearly, calculate the amount if the principle is $Rs.7,400$, the rate of interest is $5\%$ per annum & the duration is one year

Factorise:
$36a^2+36a+9$

Rahul found 3 pairs of wooden ice-cream sticks in which the sticks in each pair are of the same length as shown below.

Rahul took one stick each from each pair and made a triangle. Likewise, his friend Arjun made another triangle which looked exactly same with the remaining sticks. They realized both these triangles have the same perimeter and are congruent under the ___________ criterion of congruence.

At what rate % p.a. compound interest, compounded annually, will Rs 2209 amount to Rs 2601 in 2 years?

1. 643

The value of $\sqrt[3]{3\sqrt[2]{20.000729}}$ is ______.

Question 95

Find the area enclosed by the following figure:

A man invests ₹ 5000 at a certain rate of interest, compounded annually. At the end of one year, it amounts to ₹ 5600. The rate of interest per annum is

Ram appeared in his mid-term examination and his marks in different subjects were:-

$$\begin{array}{cc}\text{Subject}& \text{Marks}\\ \text{Science}& 75\\ \text{Maths}& 85\\ \text{Hindi}& 75\\ \text{English}& 75\\ \text{Social Science}& 65\end{array}$$

What is the mode of marks obtained by Ram?

The sum of all the angles of a triangle is

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$\%$ ?

Question 92 (xx)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$y^4-625$

Which of the following is a like term of $10x^2$?

Sonia went to a bank with $Rs.2,000,00$. She asked the cashier to give her $Rs.500$ and $Rs.2000$ currency notes in return. She got $250$ currency notes in total. Find the number of each kind of currency note.

How to find the square of 31 without actual multiplication?

If the present age of a grandfather is 72 years while his grandson's age is 12 years then find the ratio of their age after 8 years.

The sum of two numbers is 70. Their difference is 16 . Find the numbers.

Draw a bar graph for the following information. [3 MARKS]

$\begin{array}{ccc}\text{Name}& \text{Practice Test}& \text{Test}\\ \text{Ram}& 30& 40\\ \text{Rajat}& 82& 90\\ \text{Sandeep}& 32& 56\\ \text{Ranga}& 15& 45\end{array}$

80 min = ___ hr.

Select the statements that hold true.

The compound interest on Rs.30000 at 1% per annum is Rs.909 .The period in years (approximately) is

Divide Rs. 15600 into two parts such that the simple interest on one at 5 percent for 5 years is equal to interest on remaining at 6% per annum for 4.5 years.

Mr. Choudhury opened a savings bank account at SBI on 1st Apr 2007. The entries of 1 year as shown in his pass book are given below. If the bank pays interest 5% per annum, find the interest paid on 1st April 2008. (correct to nearest re.)

Pass necessary Journal entries for the following in case of Revaluation :

(a) The value of furniture is to be increased by Rs 25,000 (Book value is Rs 10,000).

(b) Stock is found undervalued by Rs 4,000 (Book value is Rs 20,000).

(c) An office equipment of Rs 6,000 is unrecorded in the books.

(d) Machinery is taken over by B for Rs 25,000 (Given book value of machinery is Rs 21,000).

(e) there is a liability of Rs 3,000 included in Bills Payable, that is not likely to arise.

(f) Rent of Rs 3,000 still outstanding.

Solve and find value of y.

$\frac{3x}{2}-\frac{5y}{3}=-2$ ; $\frac{x}{2}+\frac{y}{2}=\frac{13}{6}$

Coefficient of $x{y}^2$ in the term $-\frac{4x{y}^2}{9}$ is:

A company issued 10% debentures of the face value Rs. 1,20,000 at a discount of 6% on January 1, 2001. The debentures are payable by annual drawings of Rs.40,000 commencing from the end of third year.

How will you deal with discount on debentures?

Show the discount on debentures account in the company ledger for the period of duration of debentures. Assume accounts are closed on December 31.