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First, find the initial velocity (v) of the ball as it leaves the machine, using the kinematic equation for maximum height:
v² = u² + 2as ⇒ 0 = v² - 2gh_max
v² = 2gh_max = 2 * 10 * 20 = 400
v = 20 m/s.
Now, apply the work-energy theorem to the ball while it is being pushed by the machine. The work done by the constant force F equals the change in kinetic energy of the ball.
Work done W = F * d
Change in K.E. = (1/2)mv² - 0
F * 0.2 = (1/2) * 0.15 * (20)²
F * 0.2 = (1/2) * 0.15 * 400 = 0.15 * 200 = 30
F = 30 / 0.2 = 150 N.

Of course. You do have full-time GIS courses at top colleges at different levels, which provide you with the best possible learning resources and practical exposure to GIS applications, spatial analysis, and satellite mapping. You can take up BTech Civil Engineering (GIS and Remote Sensing) at Galgotias University, MTech in GIS and RS at NIT Warangal, MNNIT Allahabad, SRM IST, IIRS Dehradun, and Amity University, or go for a PGD in GIS at Jamia Millia Islamia, BHU and Lucknow University.

You can take up free GIS courses, which can be of a few hours' duration or stretch up to a few weeks/months. Some of the GIS & Remote Sensing courses online for free are given here:

Available at Coursera:

• Introduction to GIS Mapping
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Available at Esri Training Academy:

• Going Places with Spatial Analysis
• ArcGIS Online Basics

( (1+i)/ (1-i) )^ (m/2) = ( (1+i)/ (i-1) )^ (n/3) = 1
⇒ ( (1+i)²/2 )^ (m/2) = ( (1+i)²/ (-2) )^ (n/3) = 1
⇒ (i)^ (m/2) = (-i)^ (n/3) = 1
⇒ m/2 = 4k? and n/3 = 4k?
⇒ m = 8k? and n = 12k?
Least value of m = 8 and n = 12
∴ GCD = 4
∴ GCD = 4

The height of capillary rise is given by the formula:
h = (2T cosθ) / (rρg)
Given: h = 15 cm = 0.15 m, r = 0.015 cm = 1.5 × 10? m, ρ = 900 kg/m ³, g = 10 m/s², and θ ≈ 0° (so cosθ ≈ 1).
We need to find the surface tension, T.
T = (h r ρ g) / (2 cosθ)
T = (0.15 * 1.5 × 10? * 900 * 10) / 2
T = 0.10125 N/m
The answer is required in milliNewton m? ¹, so we multiply by 1000.
T = 101.25 mN/m.

The time required to prepare for the GIS course entrance exams cannot be said with any certainty as it differs on the basis of the specific exam you're preparing for, but you should start your preparation as early as possible. Generally, it is better to start at least 6 to 8 months before the final exam date so that you have enough time in hand to cover the entire exam syllabus, have a look at the previous year question papers, take up mock tests, and plan a good revision in the last month.

(0.16)^log? (1/3 + 1/3² + . to ∞)
= (4/25)^log? (1/2)
= ( (5/2)? ² )^log? /? (1/2) = (5/2)^ (-2 log? /? (1/2)
= (5/2)^ (log? /? ( (1/2)? ² ) = 4

GATE exam scores are very important for admission to the M.Tech in GIS and Remote Sensing course at top colleges like NIT Warangal & MNNIT Allahabad. There is high competition with multiple students like you giving the exam to get admission to an M.Tech specialisation of their choice.

Other colleges also accept GATE exam scores or may conduct their own university level exams for giving admission. You can have a look at the college websites to have better clarity on the individual admission requirements for M.Tech in GIS course.

lim_ (x→0) (1/x? ) {1 - cos (x²/2) - cos (x²/4) + cos (x²/2)cos (x²/4)} = 2?
⇒ lim_ (x→0) ( (1 - cos (x²/2) (1 - cos (x²/4) / x? ) = 2?
⇒ 2? = 2? ⇒ k = 8

GIS technology can help greatly in agriculture-related decisions, as it can help map soil types, moisture levels, and overall soil suitability for various crops through drones. It can also help in mapping and keeping a check on crop health and crop yields across different geographical locations.

This information can help farmers manage irrigation, minimize the spread of pests and diseases, and ensure sustainable farming practices.

∴ center lies on x + y = 2 and in 1st quadrant center = (a, 2-a) where a > 0 and 2-a > 0 ⇒ 0 < a < 2
∴ circle touches x = 3 and y = 2
⇒ |3-a| = |2 - (2-a)| = radius
⇒ |3-a| = |a| ⇒ a = 3/2
∴ radius = a
⇒ Diameter = 2a = 3.

Kindly go through the solution

GIS full form is Geographic Information System, a powerful framework or tool technology that is used to manage, analyze and map all sorts of visual spatial data. One of the most widely used examples of GIS visualization is Google Maps, which we use almost every day to look for the best routes and journey times.

A = [ x 1 ]
[ 1 0 ]
A² = [ x 1 ] [ x 1 ] = [ x²+1 x ]
[ 1 0 ] [ 1 0 ] [ x 1 ]
A? = [ x²+1 x ] [ x²+1 x ]
[ x 1 ] [ x 1 ]
= [ (x²+1)²+x² x (x²+1)+x ]
[ x (x²+1)+x²+1 ]
a? = (x² + 1)² + x² = 109
⇒ x = ±3
a? = x² + 1 = 10

After burning, heat exchange occurs between helium and atmospheric. Hence, irreversible, isothermal process.