If Ramu and Krishna work on alternate days to complete a work, then the work gets completed in exactly 24 days. If R and K denote the number of days required by Ramu and Krishna respectively to complete the work independently, then how many ordered pairs of integral values of R and K are possible? (a)14, (b)8, (c)15, (d)7,(e)16
X+y+2z=-9Then find x^2+y^2+2z^2+2yz =???
76^203+ 21^203/97, remainder? any short method?
last digit of 999^9999! ???
please give expanation.
ax^2+ bx + c = 0 is a quadratic equation with rational coefficients such that a + b + c = 0, then which
of the following is necessarily true?
(a) Both the roots of this equation are less than 1.
(b) One of the roots of the equation is c.
(c) One of the roots of the equation is c/a.
(d) Exactly one of the roots is 1
IF p, q, r are in A.P. and are positive, the roots of the quadratic equation p*x^2 + q*x + r=0 are all real for -
a. |r/p - 7| >= 4 * (3)^1/2
b. |r/p - 7|
c. All p and r
d. No p and r
A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before he will have result that will end with 3 zeroes?
a) 11 (b) 10 (c) 6 (d) 5
€‹In a survey, the following information was gathered about the people reading different kinds of books. The total number of people reading fiction or biography is 80 and the number of people reading fiction and Biography is 10. Also, the number of people reading biography is 40 and that reading science is 30. What is the number of people reading all three kinds of books?I. Nobody reads only science books.II. Number of people reading only two kinds of books is 30.(ds question )
if x, y and z are positive then the minimum value of x^(logy-logz) + y^(logz-logx) + z^(logx-logy) is-
a. 3
b. 1
c. 9
d. 16
the sum of the products of the ten numbers +-1, +-2 , +-3, +-4 , +-5 taking two at a time is-
a. 165
b. -55
c. 55
d. NOTA
There are five consecutive integers a, b, c, d and e such that a
What is/are the possible value(s) of b?
(a) 0 (b) 11 (c) 0 and–11 (d)–1 and 11
let N be a four digit number say abcd. Then the maximum value of N/(a+b+c+d) is equal to -
a. 1000
b. 9999/4
c. 800
d. NOTA
In a class of 50 students, 26% students play only cricket, 18% students play only badminton, 10% students play only football, 20% students play only badminton and cricket, 12% students play only cricket and football and 8% students play only football and badminton, 6% students play all three games.Total how many students play cricket?(a) 26 (b) 19 (c) 23 (d) 32
If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have?
1)5/3
2)13/3
3)19^(1/2)
4)None of these
A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw
A professor was to demonstrate an experiment to 10 student. If she can show the experiment to only 4 student at a time in how many ways can she make the group for the experiment?(a) 210 (b) 220 (c) 320 (d) 240
A can do a piece of work in 7 days of 9 hours each whereas B can do the same work in 6days of 7 hours each. How long will it take to complete the work together working 8 2/5 hrs aday?(a) 2 days (b) 3 days (c) 3 1/7 days (d) 4 2/5days
A can do a piece of work four hours faster than B. They worked together for two hours and then the remaining part of the work was done by A in an hour. How many hours would B take to complete the job if he were to work alone?
a) 8 b) 6 c) 4 d) 3 e) 2
Please solve attached .
In a tournament, there are n teams T1 , T2 , ..., Tn, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common:T1 & T2 , T2 & T3 , ... , Tn-1 & Tn, and Tn & T1No other pair of teams has any player in common. How many players are participatingin the tournament, considering all the n teams together?
n (k - 1)
k (n - 1)
n (k - 2)
k (n - 2)
(n - 1) (k - 1)
Year of Exam : CAT - 2007