23/10/2018 9:12 pm
Algebra
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aniket prajapati 23/10/2018 10:57 pm
while doing reciprocal in inequality sign changes
7/3<x/(x+5)<17/3
3/7> (x+5)/x > 3/17
3/7> 1+5/x > 3/17
subtracting 1 from each side
-4/7>5/x>-14/17
by doing reciprocal
-7/4<x/5<-17/14
-35/4<x<-85/14
-8.7<x<-6.01
hence x can take only two integer values i.e -7 and -8
0
24/10/2018 6:20 pm
Medha and Megha are sisters . Madhvi is Medha's daughter and 12 years younger than her aunt . Medha is twice as old as Madhvi . Four years ago, Medha was the same age as Megha is now , and Megha was twice as old as her niece. How old is Madhavi ?
correct ans: 30
solution please
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24/10/2018 6:20 pm
A bag contains 10 identical balls. All except one ball are of 10gm each. We can use a spring-balance, where we can hang the object in attached pan to know its weight. How many least number of times the spring-balance must be used to identify the faulty ball?
aniket prajapati 25/10/2018 7:11 pm
since it says least no. of times let one picks the faulty ball and he gets to know its weight but to know that it is a faulty he has to check 2 more so that he has 3 weights of which two are of the same weight and hence not faulty and the remaining one is faulty so total no of times spring balance used is 3
0
24/10/2018 6:24 pm
There exists a 10 digit number such that the 1st digit from left represents the number of 0's in the number, the2nd digit from left represents the number of 1's occurring in the number and so on until the 10th digit represents the number of 9's in the number.
The sum of the digits of the number is:
8
9
10
19
aniket prajapati 24/10/2018 11:41 pm
for this 10 digit one thing is for sure there will be more no. of zeros than any other no. so we will start by putting 10 zeroes but for that we need to keep no. 10 at first digit from left which is not possible
we will keep 9 on first and lets see
9000000000 (but we also need to fill no. of 9 at 9th place so this case is not possible)
8_ _ _ _ _ _ _ _ _ now we can keep 8 zeroes anywhere of the 9 places vacant but we have to keep 1 at 8th place because no, of "8" is 1 and if we do that we have to keep no. 1 at 2nd place so this case is also not possible
7 _ _ _ _ _ _ _ _ _ for this case we need 7 zeroes and we need 1 at 7th place and 1 at 2nd place also because 1 has appeared in 7th place so we get this 7100001000 but since 1 has occured two times we need to place 2 at the third place so this case is also not possible
6 _ _ _ _ _ _ _ _ _ for this case we need 6 zeroes and then we will keep 1 at 6th place and keep 1 at 2nd place and we will still left with one vacant place like this
61 _ 0010000 now since 1 has occured two times we need to write 2 at 2nd place so we rewrite as
62 _ 0010000 but now this no. suggests that 1 has been written two times and also that 2 has been written one time so we can rewrite as
6210010000 this is the answer
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25/10/2018 3:52 pm
A survey shows that 90% of graduates in metro cities like at least one of the following activities: going to the movies, playing sports, or shopping. It is known that 45% like the movies, 48% like sports, and 35% like shopping. Also, it is known that 12% like the movies and shopping both, 20% like only the movies, and 15% only shopping. What percent of graduates like all three activities?
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25/10/2018 5:54 pm
correct ans:1/2
aniket prajapati 26/10/2018 1:45 pm
for infine sum
S= lim n->∞ Sn
applying limits since 1/n is 0 if n tends to ∞
S= 1/2(1-0)
S=1/2 (answer)
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25/10/2018 5:54 pm
How many 10 digit numbers can be formed which have each digit distinct. Also in any number, 0 never comes before 1, 1 never comes before 2, 2 never comes before 3, 3 never comes before 4, 4 never comes before 5 but 5 always comes before 6.
ans:4320
0
25/10/2018 5:55 pm
For an odd integer, k, which of the following can be a perfect square?
4k + 1
4k+2
4k+3
none of these
TG Team 25/10/2018 6:16 pm
All perfect squares are of the form 8a , 8a + 4 or 8a + 1 .
4k +1 = 4 ( 2m +1) + 1 = 8m + 5
4k + 2 = 4 ( 2m + 1) + 2 = 8m + 6
4k + 3 = 4 ( 2m + 1) + 3 = 8m + 7
Hence, never a perfect square .
Option (D)
0
25/10/2018 5:56 pm
125.008
124.875
121
11O
0
25/10/2018 6:37 pm
Find the number of integral solutions of the equation x3 + y3 = 14z2 + 3.
ans 0
approach?
TG Team 25/10/2018 6:49 pm
Possible remainders when a perfect cube is divided by 7 are 1 , 6 or 0.
RHS is of the form 7k + 3 but LHS is never of the form 7k + 3 Hence no integral solution.
0
25/10/2018 7:10 pm
CAN THIS QUESTION BE DONE WITHOUT MAKING A GRAPH? iF YES, THEN APPROACH PLEASE.
aniket prajapati 27/10/2018 3:42 pm
Hi Richa,
You can always go by options
Putting x=-4 we get (12,16,-16) Max of them is 16
Putting x=-2 we get (0,8,-8) Max of them is 8
Putting x=1 we get (-3,-4,4) Max of them is 4
Putting x=0 we get (-4,0,0) Max of them is 0
So min of (16,8,4,0) is 0 which we get by putting x= 0
Hence option 4th
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27/10/2018 3:30 am
Approach please.
I have come down to:
x^2 - 4 = root(4-x)
Stuck here. what to do next to reach to an answer option?
aniket prajapati 27/10/2018 8:48 am
You can do by checking options
1st and last doesn't satisfy your equation
And your equation suggests that x^2>4 and x<4
4<x^2<16 check 2nd and 3rd by squaring them only 3rd follows hence option 3rd
0
27/10/2018 3:31 am
aniket prajapati 27/10/2018 10:06 am
This post was modified 6 years ago by aniket prajapati
Since 5001 is odd term the sequence will end with 1 written (n+1) times where (n+1) is odd
Sum will be something like
1 +2(1)+3(1)..... n times
+ 7(1) + 7(2)......n times And then 1 will be written 2n+1 times which would be a odd no.
= n(n+1)/2 + 7{n(n+2)/2} +2n+1
= 4n(n+1) +2n+1
= Even + odd= odd.
Since 5001 can't be the answer other option which is odd is (c)
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27/10/2018 11:27 am
Out of 120 students of a class all of the students engage in at least one of the five games: hockey, football, cricket, badminton and tennis. It is known that exactly 80 students play cricket, 70 play football, 60 play hockey, 40 play tennis and 20 play badminton. What can be the maximum number of students who play only cricket?
40
48
50
aniket prajapati 27/10/2018 4:16 pm
70 play football and every student plays at least one sports so Same 70 can play all other sports also.....we are left with 50 students so they will play only cricket hence 50 is the answer
0
27/10/2018 11:28 am
Find the sum of all possible solutions of x[x[x]] = 14 where [x] is greatest integer less than or equal to x.
2.8
5.6
8.4
aniket prajapati 27/10/2018 10:09 pm
Raman sir ,
is this solution right ?
only 2.8 satisfies the equation
since it is a 3rd degree polynomial x will have three values and all the three values will be 2.8 hence sum of all solutions = 2.8+2.8+2.8=8.4