Explanation

Geometric Series

Given series: 8 + 4 + 2 + ... to infinity

This is a geometric series with first term a = 8 and common ratio r = 1/2.

S = 8/1 - 1/2 = 8/1/2 = 8 × 2 = 16

Explanation

Normal Line to a Circle

Given circle equation: x² + y² = 25

This is a circle with center (0,0) and radius 5.

Given point: (2,3)

The normal line at a point on the circle is the line passing through the center and the point.

The slope of the line joining (0,0) and (2,3) is 3/2.

The equation of the line passing through (0,0) and (2,3) can be found using point-slope form y = mx, where m is the slope.

So, y = (3/2)x

Multiplying both sides by 2 to get rid of the fraction: 2y = 3x

Rearranging: 3x - 2y = 0

Explanation

Explanation

Passage

Once upon a time there was cap seller who used to go to other towns to sell caps. One day he was going to a town. There happened to be a forest on his way he decided to have a short nap under a shady tree as he felt tired. He placed his bundles of caps beside him as he lay down he feel a sleep.

There lived monkeys in that forest the monkeys are mischievous creature they came down when they saw the cap seller sleeping.

They started picking the caps from the bundle the monkeys wore caps and started playing jumping, here and there.

When the cap seller wake up he found all the caps missing the bundle was lying empty seeing this he became worried as ware the caps had gone.

اوپر دیے گے پیرے کو پڑھیں اور نیچے دیے گے سوالات کے جواب دیں 

Q.1 Why did the cap seller decide to take a short nap?

A.      He was hungry.

B.      He was lazy.

C.      He was tired.

D.      He had sold all the caps so decided to take rest.

Q.2 Where did he place the bundle of caps before lying down?

A.      On a nearby tree

B.      Under a heavy stone

C.       In a cave

D.      Beside him

Q.3 Why did the cap seller become worried when he woke up?

A.   His money was stolen

B.   He had forgotten the way to the town

C.    His caps were missing

D.   He was late.

Q.4 Which characteristic of monkeys is mentioned in the paragraph?

A.   Shy

B.   Cruel

C.    Naughty

D.   Creative

Explanation

Matchless means بے نظیر

Common means عام

Explanation

Front means سامنے

Back means واپس

Explanation

Free means غلام 

Slave means آزاد

Explanation

Explanation

A jewel is typically shiny, just as a demon is typically portrayed as evil.

Both show a common characteristic-to-subject relationship.

Explanation

A nightmare is a type of dream, just as a wrench is a type of tool.

Shows the relationship specific : general category.