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Factorise:
$x^2-22x+117$

Your school has decided to introduce Mass Media Studies as a subject under the vocational stream. This is going to help students who want to pursue a career in films, its production and other attached fields. Write a notice for your school notice board informing all students who are studying in class X regarding the course.

Writing a notice A notice is information regarding an important event that is about to happen or that has happened. It is publicly displayed -- a kind of information for others to know and follow:

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  The notice must contain complete information

  
  


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  The message with essential details includes:

  
  

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  an eye-catching caption - preferably a phrase and not a sentence

  
  


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  important details

  
  


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  the name of the body / organisation organising the event

  
  

Sum of three consecutive numbers is 39. Find the numbers.

PQ and RS are two parallel chords of a circle whose centre is O and radius is 5 cm. If PQ = 8 cm and RS = 6 cm.The distance between PQ and RS if they lie on the same side of the centre is ___ cm

Without adding, find the sum:

1 +3 + 5+7 + 9 +11 +13+ 15 + 17+19 + 21 + 23

PQRS is a quadrilateral in which $PQ=5\sqrt{2}cm$, $QR=5\sqrt{2}cm$, $RS=8cm$, $SP=6cm$, $\angle PSR=\angle PQR={90}^{\circ }$. Then its area is

What will be the cost of the Minimum spanning Tree (MST) of such a graph with n nodes

The length of a rectangular field is twice its breadth. If the perimeter of the field is 288 m, find the dimensions of the field.

A footpath of uniform width runs all around the inside of a rectangular field 28 m long and 22 m wide. If the path occupies 600 $m^2$, what is the width of the path?

Question 74

Solve the following:

$\frac{3t-2}{3}+\frac{2t+3}{2}=t+\frac{7}{6}$

A cubical tank has a volume of 8000 $m^3$. What is the height of the tank (in cm)? ___

Find the multiplicative inverse of ${10}^{-7}$.

One
of the two digits of a two digit number is three times the other
digit. If you interchange the digit of this two-digit number and add
the resulting number to the original number, you get 88. What is the
original number?

In the given construction,

• PQ is the perpendicular bisector AX


• RS is the perpendicular bisector AY


• XA is the angle bisector of the $\angle LXY$


• YA is the angle bisector of the $\angle MYX$

Then find the value of $\angle CAB$.

A company issued debentures of the face value of Rs. 5,00,000 at a discount of 6% on January 1, 2001. These debentures are redeemable by annual drawings of Rs.1,00,000 made on December 31st each year. The directors decided to write off discount based on the debentures outstanding each year.

Calculate the amount of discount to be written-off each year. Give journal entries also.

A bag contains $25$ pieces of candies. There are $10$ grapes, $7$ cherries, $3$ lemons, $5$ strawberries. What are the odds against drawing a lemon?

In an examination a student has to secure 40percent marks to pass Rahul gets 178 Marks and fails by 32 marks what are the maximum marks?

In which of the following quadrilaterals, diagonals bisect each other?

i) Parallelogram

ii) Rhombus

iii) Rectangle

iv) Square

v) Kite

Superman can fly at speeds almost equal to $2.6\times {10}^7$ m/s. A supersonic jet on the planet Krypton can fly at a maximum speed of 130000 m/s.

Question 2 (ii)

Find the number of digits in the square root of each of the following numbers (without any calculation):

144

Question 6 (i)

For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:

252

The product of two whole numbers is always a:

What is octet and duplet?

Find the value of A , if 42A8 is divisible by 4

Find the
smallest number by which each of the following numbers must be
divided to obtain a perfect cube.

(i) 81

(ii) 128

(iii) 135

(iv) 192

(v) 704

If the side of a square is $a$, then area and perimeter can be found by using the formulae _____.

In a class of 40 students, 20% are selected for a trip to Goa. Find the number of students going for the trip.