@pirateiim478 said:Both are same!! Try other question in same post.One more question=> How many right angled triangles are there in which 1. One leg is 122. Hypotenuse will be 12
1.1 2.0
@ravi.theja said:Find the remainder when the sum 2^100+2^200+2^300..+...+..2^10000 is divided by 7a) 2b) 0c) 1d) 6 e) None of these.
2^3 mod 7 = 1
=> 2^100 mod 7 = 2
Also, 2^200 mod 7 = 4
And, 2^300 mod 7 = 1
So, here we will have [ 2*34 + 4*33 + 1*33 ] mod 7
=> 68 + 132 + 33 mod 7
=> 233 mod 7
=> 2 mod 7
Remainder = 2 :roll:
@ravi.theja said:Find the remainder when the sum 2^100+2^200+2^300..+...+..2^10000 is divided by 7
a) 2
b) 0
c) 1
d) 6
e) None of these.
c) 1..??
@ravi.theja
Should be 2..
Rem[2^1/7]= 2, Rem[2^2/7] = 4, Rem[2^3/7]=1, Rem[2^4/7]= 2...Hence the cycility of power of 2 with 7 as divisor is 3..
Hence, Rem[2^100/7] = 2, Rem[2^200/7] = 4, and, Rem[2^300/7] = 1..
Thus, 2^100+2^200+2^300 is divisible by 7..These can be grouped as a single unit..
Since the maximum is ten thousand, which can be defined as, 3*3,333 + 1, Thus, the answer wil be Rem [2^1/7]...Since the coupled power "9,999=2^100+^200+....+2^9,999" will be divisible by 7..
Hence, the answer is 2..
@pirateiim478 said:Check again 1st one.It will be 4. 2nd is correct
a^2-c^2 = 144 = 72*2 , 36*4 , 18*8,..?? 
( 20,16) ,( 13,5) (37,35)
getng 3 😃 4th one???
( 20,16) ,( 13,5) (37,35)
getng 3 😃 4th one???
@ravi.theja said:Find the remainder when the sum 2^100+2^200+2^300..+...+..2^10000 is divided by 7a) 2b) 0c) 1d) 6 e) None of these.
ans is 2.
2^3=1Mod 7
2^100=2mod7
2^200=4mod7
and so on...
Which of the followinf is not a perfect square
100856, 325137, 945729? how to find quickly?
@vbhvgupta
Any perfect square will have 0,1,4,5,6 n 9 as the Unit digit..For the starters we can luk..Here..Option B ends with 7..Hence it wont be..
Q.
A train overtakes two persons who are walking in the same direction in which the train is going,at the rate of 2kmph and 4kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?
Please share logical aprroach in detail ,please.
@vbhvgupta said:Which of the followinf is not a perfect square100856, 325137, 945729? how to find quickly?
always square of any number ends with 1,4,9,6,5 and 0... in this case optn B ends with 7 so B is the ans
@rayus how about this way..2 (100+200+...10000)..now treating 100, 200 to 10000 as an AP sum would be 505000..now 2*505000/7..remainder would be 6..what say!
@pirateiim478 said:Both are same!! Try other question in same post.One more question=> How many right angled triangles are there in which 1. One leg is 122. Hypotenuse will be 12
1. 4 (37,35), (20, 16), (15,9), (13,5)
2. 0
@nirzone said:@rayus how about this way..2 (100+200+...10000)..now treating 100, 200 to 10000 as an AP sum would be 505000..now 2*505000/7..remainder would be 6..what say!
depends on personal choice bro..
always ,Square of any number ll end with 1,4,9,,6,5 or 0 as the unit digit..here in optn B unit digit is 7 😃 so ans : B
@vbhvgupta said:Which of the followinf is not a perfect square100856, 325137, 945729? how to find quickly?
@cadmium said:Q.
A train overtakes two persons who are walking in the same direction in which the train is going,at the rate of 2kmph and 4kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?
Please share logical aprroach in detail ,please.
Is it 50 metres??
Let the length of the traing be l and it's speed be v mps
=> l/(v - 5/9) = 9
and l/(v - 10/9) = 10
therefore, l = 9v - 5
and l = 10/9*(9v - 10)
Solve both equations, l comes out to be 50 metres
@nirzone said:@cadmium Arun sharma can help you out decently with these basic question..
Thanks for the suggestion.
I would be more thankful if you can share the logical approach.
Regards.
@cadmium said:Q.A train overtakes two persons who are walking in the same direction in which the train is going,at the rate of 2kmph and 4kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?Please share logical aprroach in detail ,please.
D=S*T ==> L (length of train ) = [ s (train ) + s (person) ]* time
==> L = ( s - 2 *5/18) * 9 ; L= (s-4* 5/18)*10 ==> on solving we get s= 110/18 ==> L= 50 metres
==> L = ( s - 2 *5/18) * 9 ; L= (s-4* 5/18)*10 ==> on solving we get s= 110/18 ==> L= 50 metres