This unique section will help to tackle objective type problems in physics, chemistry, mathematics and mental ability
within the specified time limit of 45 seconds. This section is immensely helpful the general science of general studies paper
in preliminary. For aspirants from non science background it is indispensible.It will be highly beneficial to students who opt
physics, mechanical engineering and chemistry as their optional in preliminary examination.
Furthermore the questions tackled here are frequently asked in IIT, engineering and medical entrance examinations.

N.B: We suggest the use of short cut methods only after grasping the underlying theories and concepts and discourage blind following of short cuts.
 Sample question: A stone dropped from a tower covers 7/16 of it's total height in the last second of it's fall. Find the height of the tower ? (Consider g= 9.8 m/s2)
Normally the solution for this question is quiet lengthy and involves the specific equation sⁿth
 We are about to explain a different scientific approach,
 short cut will then follow, based on this approach.
 Equation used s=ut+1/2 at² (equation of motion)
 s=ut+1/2 gt²..............s in the last sec.
 s=unknown
 u=unknown...............u is the initial velocity in the last sec fall.
t=last one sec.
s=ut+1/2 gt²
 s_∞ t²  (s proportional to t²)when u=0,since g=constant.
But here u ≠0,since there is some initial velocity in the time under consideration.
so we can conclude that 7 parts of the distance out off the total 16 parts are covered in the last second.
It means that 9 parts out of the total 16 parts is covered in the initial phase.(1 - 7/16=9/16)
This initial phase has initial velocity=0 since it includes the phase at which the stone is dropped ie u=0
Then s∞t² as u=0
9/16∞t²
 t∞ √9/16
 t∞3/4
Means 3/4 of the total time is consumed in the initial phase
so 1/4 is the remaining time and is consumed in the last second of fall.
Last sec means last one second. Then 1/4 t=1 sec, t=4 sec
Total height is the distance covered in this 4 seconds,1/2 gt²
1/2× 9.8 t² = 1/2 × 9.8×4² =4.9× 16 =
Height of the tower =4.9 × 16 =78.4 m

These details were mentioned to explain the way by which we derive the short cut
Now 7/16 in last second ie 9/16 in the initial phase where u=0
t∞9/16 ie t∞3/4
3/4 t is used initially ie 1/4 t in the last sec
1/4 t=last one sec ie 1 sec
t=4 seconds
s=1/2 g × t² =78.4 m
For ease of calculation g can be considered as 10m/s²
It usually is sufficient to get the answer from the options,
unless the options are too close like 78.4m,78.6m,79m,78.8 etc

 N.B: Some faulty short cuts are seen to be applied in such questions
like, when 7/16 in last second, take the square root of the denominator i.e. √16=4,  t=4,   s=4.9×16=78.4m 
 **This method is faulty and should not be followed,
Even though it is alright with some problems it is unscientific .
Consider :body dropped covers 7/16 in the last 2 seconds
Find the height of tower ?
If the above method is followed then square root of 16 =4 ,
 height =4.9×16=78.4 m ,And the answer is wrong.
 By the short cut we explained 7/16 in last 2 seconds i.e. 9/16 in
  initial  phase where u=0  , t ∞ √ 9/16 , t ∞ 3/4
 3/4 t consumed initially,1/4 t=last 2seconds , then t=8 sec
 s= 5 × 8 ² =320 m
 Also try  16/25 in the last second, Find the height of the tower ?
 Then 9/25 distance  in the initial phase
 Time initially consumed = √9/25=3/5
 So 2/5 in last one sec i.e. 2/5t=1 second, t=5/2=2.5 second
 Now h= 5× 2.5 ²=31.25 m
Now check whether you can arrive at the answer with that faulty short cut.
Even if short cuts are practised it should  be scientific .
Since the short cut we explained is scientific, it satisfies every questions.
Trial questions
(1)A body dropped from a tower covers 9/25 of it's total heightb in the last sec of it's fall.
Find the height of the tower ?
(2)A body dropped from a tower covers 5/9 of it's total height in the last sec of it's fall.
Find the height of the tower ?
(3)A body dropped from a tower covers 11/36 of it's total height in the last sec of it's fall.
Find the height of the tower ?
(4)A body dropped from a tower covers13/49 of it's total height in the last sec of it's fall.
Find the height of the tower ?
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