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?
correct ans:1/2
Sir please share the approach
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)
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
?
For an odd integer, k, which of the following can be a perfect square?
4k + 1
4k+2
4k+3
none of these
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)
125.008
124.875
121
11O
110
solution please
x+1/x =5
x^3 + 1/x^3 +3*5 = 125
x^3 + 1/x^3= 110
Find the number of integral solutions of the equation x3 + y3 = 14z2 + 3.
ans 0
approach?
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.
CAN THIS QUESTION BE DONE WITHOUT MAKING A GRAPH? iF YES, THEN APPROACH PLEASE.
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
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?
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
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)
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
40 ?
50
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
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
2.8 ?
8.4
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
Find the largest natural number which is divisible by all the numbers less than or equal to its square root?
16
36
24
24 is the answer its under root will b around 4.9 and natural no.s less than 4.9 are 4,3,2,1 and all are divisible by 24
I have got it as
8^3-1/8^3+1 ...... And so on but what to do next ?
How many three digit numbers of base-10 both start and end with 1 when represented in base-3, base-5 or base-7 representations?
Find the largest number that is divisible by all of positive integers less than it's cuberoot.
It has been told earlier 24 is the answer
this time we have cuberoot here
One way is to check the options if options are not given then only way is to fiddle with nos...
