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Factorise :

$x^2-y^2-2y-1$

$\text{A jeweller allows a discount of}16\%\text{to his customers and still gains}20\%.\text{Find the marked price of a ring which costs the jeweller Rs.1190.}$

Ajit buys a motocycle for Rs. 17600 inclusing value added tax. If the rate of VAT is $10\%$, what is the sale price of the motorcycle?

“Did you understand?” Jack asked. At this, Jacob said, “I understood what mode is. Give me any question, I can find the mode of the observations.” Jack smiled at him and said- “Okay, I will give you a question and 3 hrs to solve it.” Jacob felt strange as for finding mode, 3 minutes would be enough, why was he given 3 hrs? Then Jack gave the problem:

What is the mode of the following set of observations?

9 13 5 9 6 9 9 17 13 11 12 13 19

13 0 9 13 21 7 13 7 17 9 0 7 11

If 14 is the HCF of 4p and 21q, then the minimum value of p and q, given p and q are natural numbers are:

Which of the following is a rectangle-

Knowing the location of 0, you started to connect the dots in your mind. Everything started to make sense now. Everything was planned brilliantly. -1 started the fight, not because it liked 0 but because it wanted to become the king. In the world of integers, it has been nobody just like number 1, but in the world of negative integers, it would become king, if and only if 0 was removed from the picture somehow. So, it constructed the wall with 0 inside it, without anybody knowing about it.....

The only way to show the truth is to break the wall. So you, along with your friend -13 and some others, break the wall at night. And there it is!!!!!! You found 0. The moment 0 came, the number line was restored to its proper order-

Krishna deposited $‘x^{\prime }$ number of $‘2000$ notes, $‘y^{\prime }$ number of ${}^{\prime }500$ notes, $‘z^{\prime }$ number of $‘100$ notes in a bank and Arjun deposited $‘3x{y}^{\prime }$ times the amount of what Krishna had deposited. How much did Arjun deposit in the bank?

Subscriptions received during the year ending 31.12.2012 are as follows:

$\begin{array}{cc}\text{Subscriptions Receipts:}& Rs\\ \text{For 2011}& 320\\ \text{For 2012}& 16,880\\ \text{For 2013}& 680\\ & \underset{–}{\overline{17,880}}\end{array}$

There are 450 members each paying on annual subscription of 50, 200 were in Arrears for 2011 at the beginning of 2012. Calculate the amount of subscription to be credited to Income and Expenditure account for the year ending 31.12.2012.

a gardener wishes to plant 8289 plants in the form of square founded that there were 8 plants left how many plants planted in each row ?

If a^2+b^2+4c^2=ab+2bc+2ca,prove that a=b=2c.

You have deposited ₹1000 in the bank.There is a 7% on it every year. How much money will you have after 5 years

The measures of angles of hexagon are x°, x-5°, 2x-5°,

2x+20°.

Find x.

1.Write the expansion of ( x- y ) square. Using the identity factorise 4x square-12x+9

Rajendra purchases a pair of chappals from a Bata shop worth Rs 99.95. The rate of sales tax is 7% . Calculate the total amount to be paid by him.

A water tank is in a form of cube with edge 2 m. Find its volume.

Find the square roots of each of the following numbers by Division method: $2304$

Reema borrowed ₹ 60,000 for 4 years at 10% per annum compound interest. Calculate the interest paid by her for the third year.

Following histogram represents the height of the students in a class.:

(i) Find the number of students whose height falls in the range 145 - 160

(ii) Find the height range with the highest frequency.

If a + b + c = 5

4a + 2b + c = 11

9a + 3b + c = 19

Find the value of $a\times b\times c$.

If the difference between an exterior angle of an (n - 1) sided regular polygon and an (n + 1) sided regular polygon is $9^{\circ }$, the value of ‘n’ is

Given the length of two diagonals of a parallelogram, we need measurement of at least

A quadrilateral with only one pair of parallel sides is a ______ .

Which of the following quadrilaterals has equal length of diagonals?

i)Rhombus

ii) Rectangle

iii) Square

iv) Kite

v) Parallelogram

To draw a square inside a circle, the diameters must be _______ .

Does (2, 1) lie on the line x-2y =0?

The length of a rectangle is twice its width. If its perimeter is 54 cm; find its length.

Number of cookie boxes sold by Riya is:

Each pair of interior angles formed by two parallel lines and their traversals are ............... angles. ?

A, B and C can alone complete a work in 10, 12 and 15 days respectively. A and C started the work and after working for 4 days, A left and B joined. In how many days the total work was completed?

Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter; find :
(i)the S.P. and the C.P. of the scooter for Rahim.
(ii) the S.P. and the C.P. of the scooter for Rajesh.

What was the percentage of people who voted in the 6^th Lok Sabha election?

In a basket, there are 10 mangoes and 30 oranges. The ratio of the number of oranges to the number of mangoes is:

The frequency for class mark 42.5 is?

If a+b+c=6, a^2+b^2+c^2=14, a^3+b^3+c^3=36, find abc

A number is first increased by $20\%$ and the resulting number is then decreased by $10\%$. Find the overall change in the number as percent.

Question 94 (iv)

Carry out the following division:

$-121p^3{q}^3{r}^3÷(-11x{y}^2{z}^3)$

If the areas of two similar triangles are equal, prove that they are congruent. [3 MARKS]

Question 26
Factorise the following:
(i) $4x^2+20x+25$

(ii) $9y^2–66yz+121z^2$

(iii) ${(2x+\frac{1}{3})}^2-{(x-\frac{1}{2})}^2$

Which number is in the middle if $\frac{-1}{6},\frac{4}{9},\frac{6}{-7},\frac{2}{5}and\frac{-3}{4}$ are arranged in descending order?

Find the area of the figure below which is made of two equal trapeziums. Two parallel sides of a trapezium are of lengths $57cm$ and $39cm$. The distance between the parallel sides $AB$ and $FC$ is $28cm$.

If 4- digits number greater that 5000 are randomly formed the digits 0,1,3,5 and 7, then what is the probability of forming a number divisible by 5, when

(i) the digits may be repeated?

(ii) the repetition of digits in not allowed?

Or

A card is drawn from a deck of 52 cards . Find the probability of getting

(i) an ace.

(ii) a king or a heart or a red card.

Which of the following expression will give the answer as 36:

If a + b = 8 and ab = 15, find : $a^3+b^3$.