Simplify  

$$\begin{gathered} 1.53 + 4.73 + 3.83 - 3 x 1.5 x 4.7 x 3.81.52 + 4.72 + 3.82 - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8 \\ \end{gathered}$$

$$\begin{gathered} [(K-L)2-K+L2]4K = ab \\ K2+L2-2KL-K2+L2+2KL4K= ab \end{gathered}$$

=> - 4KL/4K = a/b

=> L = - a/b

=> bL = -a

Let the price of each note book be Rs.x.

Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.

Hence xy = 300

=> y = 300/x

(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy

=>5(300/x) - 10x - 50 = 0 => -150+x2+5x

multiplying both sides by -1/10x

=> x2+15x-10x-150=0

=> x(x + 15) - 10(x + 15) = 0

=> x = 10 or -15

As x>0, x = 10.

Half of the cloth = 37.5/2
From 1 meter he will make 8 pieces
=> in 37.5/2 ---- ?

37.5/2 x 8

= 150.

2172+1832

= 200+172+200-172

It is in the form of a+b2+a-b2=2a2+b2

= 2(40000 + 289) = 80578.

Let the integer be x. Then,

x2 - 20x = 96

(x + 4)(x - 24) = 0

x = 24

(2000 + 3)(2000 + 4) - (2000 + 1)(2000 + 2) = ?
Since (2000 x 2000) - (2000 x 2000) is equal to zero. ?
= (8000 + 6000 + 12) - (4000 + 2000 + 2)
=> 14012 - 6002 = 8010.

Let number of 20 ps coins = x and

number of 25 ps coins = y

Given total coins in the bag = 50

x + y = 50.......(1)

But the total money in the bag = Rs. 10.25

0.20x + 0.25y = 10.25

20x + 25y = 1025.........(2)

Now multiplying (1) by 25 we get

25x+25y=1250.............(3)

By solving (2) and (3)

20x + 25y = 1025;

=> x = 45;

Then, the no. of 20 ps coins are 45.

Draw the two chords as shown in the figure. Let O be the center of the circle. Draw OC
perpendicular to both chords. That divides the two chords in half.
So CD = 10 and AB = 14. Draw radii OA and OD, both equal to radius r.
We are given that BC = 5, the distance between the two chords. Let
OB = x.

We use the Pythagorean theorem on right triangle ABO

AO² = AB² + OB²
r² = 14² + x²

We use the Pythagorean theorem on right triangle DCO

DO² = CD² + OC²

We see that OC = OB+BC = x+5, so

r² = 10² + (x+5)²

So we have a system of two equations:

r² = 14² + x²
r² = 10² + (x+5)²

Since both left sides equal r², set the right sides
equal to each other.

14² + x² = 10² + (x+5)²
196 + x² = 100 + x² + 10x + 25
196 = 125 + 10x
71 = 10x
7.1 = x

r² = 14² + x²
r² = 196 + (7.1)²
r² = 196 + 50.41
r² = 246.41
r = √246.41
r = 15.69745202 cm