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Factorise:

$4a^{2}b-9b^3$

Factorise :

$x^2-36$

Find the value of: 5.06 $\times$ ${10}^{-4}$

Find the value of $x$ in the following figure.

Find a two digit number which is three times the sum of its digits.

What is the square root of 14.44?

Question 60

In case of gain, $CP=\frac{100\times SP}{100+Loss\%}$

Ajay's father asks him to find the area covered by the grass in his garden. Ajay is informed that the shape of the area covered by the grass is square which has a diagonal length of $16\sqrt{2}$ meters. What is the area calculated by Ajay is ___ $m^2$.

Count the vertices in the following shape:

Find the compound interest at the rate of $10\%$ per annum for four years on the principal which in four years at the rate of $4\%$ per annum gives $Rs.1600$as simple interest.

Given the universal set = $\{-7,-3,-1,0,5,6,8,9\}$, find :

Question 37

In the following question, fill in the blanks to make the statements true.

$5^5\times 5^{-5}$ =

Let A = {x such that x belongs to N and x+1 < 8} and B = {x such that x belongs to N and x+3≤5}. Then find A union B?

Find the value of $(1+\sqrt{2}{)}^2$.

Express $(\frac{2}{3}{)}^{-4}$ with positive exponent.

Simplify:
$\frac{m^2+3m}{m^2+4m+3}\times \frac{m^2-2m-3}{m^2-9}$

The population of a town is $50,000$. It decreases by $20$ per thousand per year. Find out the population after $2$ years.

A shop keeper sells sugar in such a way that the selling price of 950gm is the same as the cost price of one kg. Determine his profit percentage.

Divide :~

1. $6x^3{y}^2{z}^{2}by3x^{2}yz$

2. $15m^2{n}^{3}by5m^2{n}^2$

3. $24a^3{b}^{3}by-8ab$

4. $-21ab{c}^{2}by7abc$

5. $72xy{z}^{2}by-9a^2{b}^2{c}^3$

Match the following with their square roots.

$\begin{array}{cc}Numbers& Squareroots\\ 1.289& a.22\\ 2.1225& b.17\\ 3.196& c.35\\ 4.484& d.14\end{array}$

${11}^3$ can be represented as a sum of how many consecutive odd numbers?

You are given the measurement of two sides of a right angled triangle such that these sides enclose the right angle. What else do you need in order to draw a triangle?

Evaluate the following products without multiplying directly:
$95\times 96$

The equation of the circle whose radius is 5 and which touches the circle $x^2+y^2-2x-4y-20=0$ externally at the point (5, 5), is

Adjacent sides and adjacent angles are equal in ______ .

If 20a3 is a 4-digit number and a multiple of 3, then sum of the possible values of a is

When we insert 3 rational numbers at equal intervals between 13 and 14, two of the numbers are 13.5 and 13.25. Find the third number.

What is meant by the mean of a given set of observations?

Question 114

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.

Question 13
The positive solutions of the equation ax + by + c = 0 always lie in the:

A) Ist quadrant
B) IInd quadrant
C) IIIrd quadrant
D) IVth quadrant

Prepare bank reconciliation statement as on December 31, 2009. On this day, the pass book of Mr Himanshu showed a balance of Rs. 7,000.

(i) Cheques of Rs. 1,000 directly deposited by a customer.

(ii) The bank has credited Mr Himanshu for Rs. 700 as interest.

(iii) Cheques for Rs. 3000 were issued during the month of December but of these cheques for Rs. 1,000 were not presented during the month of December.

Find the value of $\frac{(1.2{)}^3}{\sqrt[3]{30.216}}$

Following is the Balance Sheet of Ravi, Navin and Sudhir as on 31st March, 2015. Their profit sharing ratio is 2 : 2 : 1.
$\begin{array}{ccccc}\text{Liabilities}& & \text{Amount}& \text{Assets}& \text{Amount}\\ & & \text{(Rs)}& & \text{(Rs)}\\ \text{Creditors}& & 24,000& \text{Bank}& 36,000\\ \text{Bills Payable}& & 16,000& \text{Stock}& 28,000\\ \text{General Reserve}& & 12,000& \text{Debtors}& 16,000\\ \text{Capital Accounts :}& & & \text{Land and Building}& 2,00,000\\ \text{Ravi}& 1,20,000& & \text{Profit and Loss A/c}& 64,000\\ \text{Navin}& 1,20,000& & & \\ \text{Sudhir}& \underset{–}{52,000}& \underset{–}{2,92,000}& & \\ & & 3,44,000& & \overline{3,44,000}\end{array}$

Navin died on 30th June 2015. The partnership deep provided for the following on the death of partner.

(i) Goodwill of the firm was valued at 2 years' purchase of the average profit of the last 5 years. The profit for the year ended 31st March, 2014; 31st March, 2013; 31st March 2012 and 31st March, 2011 were Rs 20,000; Rs 32,000; Rs 44,000 and Rs 88,000 respectively.

(ii) Navin's share of profit or loss till the date of his death was to be calculated on the basis of profit or loss for the year ended 31st March 2015. Prepare Navin's Capital Account till the time of his death to be presented to his executors.

A church clock gains half a minute during the daylight hours and loses one third of a minute during the night. At dawn,may first , it has been set right. When will it be five minutes fast?

Factorise

27y³ - 343x³

Which of the following can be the cube root of -132651?

$1528+A\underset{–}{}15B0\underset{–}{}$
A =___ and B =___

Mohan lends Rs. 4800 to John for $4\frac{1}{2}$ years and Rs. 2500 to Shyam for 6 years and receives a total sum of Rs. 2196 as interest. Find the rate percent per annum, it being the same in both the cases.

Evaluate :${101}^2$

Factorize

a²+4ab+b^b2