Sainik Awayasiya Mahavidyalaya Games

Algebra

100

Quadratic Equation Standard Form:

ax2+bx+c=0.

200

nth Term of an Arithmetic Progression (AP):
 

 a + (n-1)d

300

Sum of n Terms of an AP:
 

Sn=n/2[2a+(n−1)d]

400

Sum of n th term in G.P

S_n=a(rⁿ-1)/r-1

500

Roots of Quadratic Equation:
 

 (-b ± √ (b2 - 4ac) )/2a

Geometry

100

Pythagoras Theorem: 

h²=p²+b²

200

sin(90∘−θ)

 =cosθ

300

sinθ in terms of ratio 

p/h

400

Height and Distance Relation:
 

tan θ=Height/ distance 

500

Length of an Arc:

l=θ/360∘×2πrl

Mensuration

100

Volume of Sphere:
 

V=4/3πr³

200

• Volume of Cylinder:
   

πr²h

300

Volume of Cone:
 

1/3πr²h

400

Curved Surface Area (CSA) of a Hemisphere:

2πr²

500

TSA of cone:

πr²+πrl

Probability / Indices

100

Probability Formula:
P(E)

=Number of favorable outcomes/Total number of outcomes

200

Probability of Intersection (for Independent Events):

P(A∩B)=P(A)×P(B)

300

• Probability of Union (for Mutually Exclusive Events):
  
  

P(A∪B)=P(A)+P(B)

400

(x^a)/x^b in terms of indices 

x^a-b

500

a⁰

1

Circle Theorem

100

Relation of central Angle and inscribed angle

central angle is double of inscribed angle standing on same arc

200

Relation of cyclic quadrilateral to opposite sides 

Opposites sides of a cyclic quadrilateral are supplementary 

300

Relation of cyclic quadrilateral to the exterior angle 

exterior angle of cyclic quadrilateral is equal to the opposites sides of cyclic quadrilateral 

400

Is inscribed angle standing on same arc equal ?

Yes 

500

What is the relation of inscribed angle made at semi-circle?

Inscribed angle of a semicircle is one right angle