What is the area of the largest semicirle that can be drawn inside a square of side 1cm?
@ravi.theja said:a^3 or a*ba^3 => a=2 ,3 [ 2 values]a*b = 2* b ===> all primes values of b less than 50 and greater than or equal to 5 ==> total no.'s = 12a*b = 3*b ==> all prime values of b less than 33 and greater than 3. ==> 5 ,7.....31 ==> total = 9a*b = 5*b ==> all primes values of b less than 20 and greater than 5 ==> 7,11,13,17,19==> 5 valuesa*b = 7*b ==> all prime values of b greater than 7 and less than 14...11,13 ==> 2 valuestotal = 2+12+9+5+2 = 30 .#Ravi Theja
can you help me with this approach i am not able to understand
@catahead said:What is the area of the largest semicirle that can be drawn inside a square of side 1cm?
pie/2
@ravi.theja said:a^3 or a*ba^3 => a=2 ,3 [ 2 values]a*b = 2* b ===> all primes values of b less than 50 and greater than or equal to 5 ==> total no.'s = 12a*b = 3*b ==> all prime values of b less than 33 and greater than 3. ==> 5 ,7.....31 ==> total = 9a*b = 5*b ==> all primes values of b less than 20 and greater than 5 ==> 7,11,13,17,19==> 5 valuesa*b = 7*b ==> all prime values of b greater than 7 and less than 14...11,13 ==> 2 valuestotal = 2+12+9+5+2 = 30 .#Ravi Theja
value for the bold one shud be 13.
5=
total 13 values.
@bs0409 said:V anand and G kasparov play a series of 5 chess games. the prob that anand wins a game is 2/5 and kasparov is 3/5. there is no prob of draw . the series will be won by a person who wins 3 matches . find prob that Anand wins the series( The series ends the moment w/n any of the two wins 3 matches)
Ending after 3 matches ==> Anand wins all the three = (2/5)^3= 8/125
Ending after 4 matches ==> _ _ _ A in the first three matches Anand has to win 2 matches 3c1 * (2/5)^3 * 3/5 = 9*8/625 = 72/625. * 2/5
Ending after 5 matches ==> _ _ _ _ A in the first four anand and kasprov has to win 2 matches respectively ==> 4c2 (2/5)^2 (3/5 ) ^2 = 216/625 .*2/5
Total ways = 8/125 + 144/3125 + 432/3125 =776/3125
Ending after 4 matches ==> _ _ _ A in the first three matches Anand has to win 2 matches 3c1 * (2/5)^3 * 3/5 = 9*8/625 = 72/625. * 2/5
Ending after 5 matches ==> _ _ _ _ A in the first four anand and kasprov has to win 2 matches respectively ==> 4c2 (2/5)^2 (3/5 ) ^2 = 216/625 .*2/5
Total ways = 8/125 + 144/3125 + 432/3125 =776/3125
@iLoveTorres said:ans 24?. It is a A.P with common difference 6.
@The_Loser said:how many 4 digit no's are there that does not contain more than 2 distinct digits?
it shud be 25
=THTU
2*2*2*2 - 2 different digits(from 0 to 9) 10c2 ways of chosing two digits .... and 8*9 ways with
0 as first digit to be eliminated...this will include single digits too 1111 2222
10c2*16 -8*9
please correct me if i m wrong..
find possible value of the sum of the squares of roots of the eqn
x^2 - (a-3)x + 5-a=0
a) -3
b) -8
c) -7
d) -9
@raopradeep said:find possible value of the sum of the squares of roots of the eqnx^2 - (a-3)x + 5-a=0a) -3b) -8c) -7d) -9
-3.
let x and y be the roots ==> x^2 + y^2 = (x+y)^2 - 2*x*y = (a-3)^2 -2 *(5-a)
= a^2 - 6a+9 -10+2a = a^2 -4a -1 = (a-2)^2 -5
here (a-2)^2 is always +ve..so minimum value is -5 ..so only -3 is greater than -5 .... so its -3
let x and y be the roots ==> x^2 + y^2 = (x+y)^2 - 2*x*y = (a-3)^2 -2 *(5-a)
= a^2 - 6a+9 -10+2a = a^2 -4a -1 = (a-2)^2 -5
here (a-2)^2 is always +ve..so minimum value is -5 ..so only -3 is greater than -5 .... so its -3
need help!
i dont know whether this is the right forum to ask this question...
please suggest some quant books other than quantum cat and arun sharma...
thanks in advance..
@coonal2006 said:can anyone please post detailed sol of this question -Q. Number of 5 digit numbers with only 3 distinct digits.Thanks
10c1*(5!/2!)*9C3 ----Will contain all 5 digit numbers with 2 same digits and 3 distinct digits..
however we will need to eliminate the ones with 0 as first digit from left
case1: two 0
9c3*4!
case 2: one 0
9c1*(4!/2!)9c2
is the approach right or am i doing something wrong???
find out the missing term(x):
1.4,6,13,13,x,28,121,59 options 26,35,40,45
2.5,6,9,15,x,40 options:21,25,27,33
3.2,26,x,124,214,342 options:14,56,64,118
Please mention the approach along with the answers.
Find the value of the expression:
(1+17)(1+17/2)(1+17/3).....(1+17/19)
--------------------------------------------------------
(1+19)(1+19/2)(1+19/3).......(1+19/17)
options:1, 17/19, 19/17, 2/19
(1+17)(1+17/2)(1+17/3).....(1+17/19)
--------------------------------------------------------
(1+19)(1+19/2)(1+19/3).......(1+19/17)
options:1, 17/19, 19/17, 2/19
@anitito123 said:Find the value of the expression:
(1+17)(1+17/2)(1+17/3).....(1+17/19)
--------------------------------------------------------
(1+19)(1+19/2)(1+19/3).......(1+19/17)
options:1, 17/19, 19/17, 2/19
for (1+17)(1+17/2)(1+17/3).....(1+17/19) expression,
denominator = 19!
for (1+19)(1+19/2)(1+19/3).......(1+19/17) expression,
denominator = 17!
=> value of the whole expression = (18*19*20*21....36/19!)/(20*21*22*23.....36/17!)
= 18*19/19*18 = 1
The surface of the water of a swimming pool is a rectangle 26m long and 10m wide and the depth of the water increases uniformly from 1.6m at one end to 4.4m at the other end .Volume (meter cube) of the pool is . options :364, 390, 780, 1560
Please mention the approach.
@anitito123 said:The surface of the water of a swimming pool is a rectangle 26m long and 10m wide and the depth of the water increases uniformly from 1.6m at one end to 4.4m at the other end .Volume (meter cube) of the pool is . options :364, 390, 780, 1560Please mention the approach.
780????
10*26*(4.4+1.6)/2
10*26*(4.4+1.6)/2