If a is a prime number and a [(a - 1)! + 1] is divisible by 2a, then a^a is
Select one:
a. 4
b. 27
c. 256
d. More than one solution exists
e. None of the above
How to solve this type ?
A = {1, 4, 7, 10, ..., 2004th term}
B = {9, 16, 23, 30, ..., 2004th term}
PFA
An ANT is located at the upper rim of a cylindrical jar( ie on the circle edge). It notices a speck of its favorite food at the opposite lower corner. The radius of cylinder is 343mm and height is 7mm.. Find the shortest possible route. explain plz!!!!!!!!!!
IF K = (99^77 - 89^77)/(99^76 + 89^76) then k>10.. can somebody pls expail the solution to this question?
number of distinct terms in the expansion of (a+b+c)^20 ?
231
253
242
210
228
consider obtuse angled triangles with sides 8,15 and x . if x is an integer, then how many such triangles exist ?
5
21
10
15
14
how to solve
number of non negative solutions of a+b+c+d=40 such that a>b>c>d
If two adjacent sides of a parallelogram are given along with one of the diagonals as 16,20 and 18; what would be the quickest way to find the other diagonal ?
concentration of Oxygen in mixtures(having Oxygen and Nitrogen) A,B and C is 20%, 40% and 80% respectively; now 20%of mixture X is transferred to mixture B and after that 40% from mixture B is transferred to mixture C; find resultant %concentration of Oxygen and Nitrogen in C ?
N is a positive integer, which when divided by 16, 17 and 18 leaves remainders of 6, 7 and 8 respectively. Find the remainder when N2 + 5N + 6 is divided by 12.
The least value of N is LCM(16, 17, 18) - 10.
In general, N is 10 lesser than any integer multiple of LCM(16, 17, 18)
Hence, N = (m * LCM(16,17,18)) - 10; where m is a natural number.
Now, (N^2) + 5N + 6 = (N+2) * (N+3)
Substituting the general format of N, we get
(m*LCM(..) - 8) * (m*LCM(..) -7)
LCM(..) = 2*2*2*2*3*3*17
Note that LCM(..) is a multiple of 12.
Hence, the expression becomes
(12p - 8) * (12q - 7) = a multiple of 12 + 56.
Hence, the expression will leave a reminder of 8 upon division by 12.
Whew!!! That was the generic solution
OR
In the exam, one could have just done the following:
1. Figure out that the number is 10 lesser than a multiple of 2448
2. Take that number to be 2438
3. Figure out that the expression is (2438 + 2) * (2438 + 3)
4. Divide the expression by 12 to figure it out to be (12p + 4) * (12q + 5) = (12m + 20). Hence, final reminder is 8.
Hope that helps. Thanks!
A survey of 200 people in the community who watch at least 1 of the three channels BBC ,DD CNN
BBC=22%. DD=80% and CNN 30%.
If 5% of people watched DD and CNN and 10 % watched DD and BBC then what % of people watched
BBC and CNN only?
Hi Puys....Please suggest!!
which strategy do you feel should be worked out for CAT....whether we should :
> for section I: solve QA first then DI or vice-versa
>for section II: solve all LR first and then English
>solve serially and noting down questions we need to re-look irrespective of QA/DI/LR/VA
pls share your views on this...TIA😠👍
Since it is exam time...I would request all members not to post wrong answer for their question , if he/she has confusion he must say but he/she should not be stubborn in saying a clearly wrong option as right one bcoz confidence dent ho jata hai baanki logon ka and earlier studied concepts ko negative asar karta hai 😁
A group of exactly four absent minded professors from a "Well Known Institute of Management in Western India" met one evening for a get together. If at the get together there were a total of 43 handshakes, then which of the following statements is definitely true?
1)Each professor shook hands at least 21 times.
2)Each professor shook hands at most 21 times.
3)At most two professors shook hands 22 times or more.
4)
At least one professor shook hands at least 22 times.
kindly explain the approach too.
Finding Number of FunctionsA = ( a,e,i,o,u ), B = ( 1,2,3)
1. No. of Functions from A to B - Distributing 5 distinct Balls in 3 Distinct boxes.
2. No. of Onto functions from A to B - Distributing 5 distinct Balls in 3 Distinct boxes such that none of the box is empty.
3. No. of Into functions from A to B - Distributing 5 distinct Balls in 3 Distinct boxes such that atleast one of the box is empty. A = ( a,e,i ), B = ( 1,2,3,4,5)
4. No. of One to One functions from A to B - Distributing 3 distinct Balls in 5 Distinct boxes such that none of the boxes has more than 1 ball.
5. No. of Many to One functions from A to B - Distributing 3 distinct Balls in 5 Distinct boxes such that atleast one of the boxes has more than 1 ball.
a + b + c = 7 ; find Maximum value of a^2. b^3. c^4
Other than AM GM concept ??
sawal.
plz discuss approach. i dont have oa😉😉
There are 8436 steel balls, each with a radius 1 cm stacked in a pile with 1 ball on top, 3 balls in the 2nd layer, 6 in the 3rd layer and so on. The number of horizontal layers?
1) 30
2) 42
3) 36
4) 45