Practice Questions

r = 1.5 cm
𝚹 = 240° = ∏/180 x 240 = 4∏/3
l= r𝚹
= 1.5 x 4∏/3
=6.28 cm

Radius = r₁
𝚹₁ = 65° = ∏/180 x 65 = 13∏/36
Radius -= r₂
𝚹₂ = 110 ° = ∏/180 x 110 = 22∏/36
l = r₁𝚹 ₁= r₂𝚹₂
r₁/r₂ = 𝚹₂ /𝚹₁ = 22∏/36 x 36/13∏ = 22/13
r₁ : r₂ = 22 : 13

1 minute = 360 revolution
1 second = 360/60 = 6 revolutions
1 revolution :
360° = 2∏ radian
6 revolution = 6 x 2∏ = 12 ∏ radian

l = 37.4cm
𝚹=60° = ∏/180 x 60 = ∏/3
r= l/𝚹 
=37.4 x 3/∏
=37.4 x 3 x 7 / 22
=35..7 cm

Degree measure = 180 / ∏ x radian measure
= 180 / ∏ x 6 (∏= 22/ 7)
= 180 x 7 x 6 / 22 = (180 x 11 )/ 22

sinA = 1/2
A= 30
cosB = 1/2
B= 60
A+B= 30 + 60 = 90°

cotA = √3
cotA= cot 30
A = 30°
C= 60°
B=90°
sinAcosC + cosAsinC = sin (A+C) = sin(30+60) = sin 90 = 1

4 × 0.5 + 440 × 25 + 12 × 12.5 

= 4 × 1/2 + 440 × 100/4 × 12 × 100/8

= 2 + 11000 + 150

= 11152

440 × 25

= 440 × 100/4

= 110 × 100

= 11000

divident = (divisor x quotient) + reminder 
divident - remainder = (divisor x quotient )

ans = x-1

p(x)=ax²+bx+c
a(0)²+b(0)+c=4
c=4
a(1)²+b(1)+4=9
a(-1)²+b(-1)+4=5
a+b=5
a-b=1
2a=6 ; a=3
b=5-3 = 2

ans: 3x² + 2x + 4

x² - (ɑ+β) x + ɑβ
ɑ+β=1
ɑβ = -12
x²-x-12

(x-1) ia factor of p(x), if p(a)=0
p(1)=0
k(1)²-3(1)+k=0
2k-3 = 0
k=3/2

(x-a) is a factor of p(x) if p(a)=0
p(-2) = 3(-2)³-4(-2)²-6(-2)+7 = 21
p(2) = 3(2)³-4(2)²-6(2)+7 = 3
p(-1) = 3(-1)³-4(-1)²-6(-1)+7 = 6
p(1) = 3(1)³-4(1)²-6(1)+7 = 0
therefore ans (x-1)

x²-1 = (x+1)(x-1)
p(1)=1⁴⁷=1 = 1+1 = 2
p(-1)=(-1)⁴⁷+1=-1+1=0
let reminder = Ax + B
p(x) = (x+1)(x-1)q(x)+Ax+B
2=A+B
0=-A+B
2=2B ; B=1; A=1
reminder = Ax + B = x+ 1

p(x) ÷ (x-a) , then the reminder is p(a).
2x-1 = 0 ; 2x = 1 ; x= 1/2
reminder = p(1/2) 
=4(1/2)³ + 2(1/2) + 1/2 + 1/2 
=1/2 + 1/2+ 1/2+ 1/2 = 4/ 2 = 2

Let p(x) = x³-ax²+6x-a
reminder p(a) = a³ - a(a²) + 6a -a 
=a³ - a³ + 6a -a 
= 5a

Total number of students is 2800. Find the total number of students who play hockey and tennis

= 2800 ×40/100

= 1120

pERCENTAGE = M3/M5× 100

= 18/36 × 100

= 50%

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