If x2 + 1/x2 = 51 , then the value of x-1/x is
±5
±7
±6
±9
Madhu has received admission in all schools listed above. She wishes to select the highest overall ranked school whose a) annual tuition fee does not exceed $23,000 and b) median starting salary is at least $70,000. Which school will she select?
University of Virginia
University of Pennsylvania.
Northwestern University
University of California - Berkeley
Ujakar and Keshab atternplted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?
(6, 1)
(-3, -4)
(4, 3)
(-4, -3)
For prime numbers p and q, p + q = 102 and p > q. What is the least possible value of p − q?
2
4
8
12
16
If (c – 5) = 4c – 7, then which of the following could be the value of c?
985
784
364
89
The ratio of ages of a father and son is 17:7 respectively. 6 years ago the ratio of their ages was 3:1 respectively. What is the father's present age?
64
51
48
54
If x=1+2a+3a2+4a2+……( -1 < a < 1 ) and y=1+3b+6b2+10b3+……( -1 < b < 1 )then find 1+ab+(ab)2+(ab)3+….. in terms of x and y.
(x1/2y1/3)/( x1/2+y1/3-1)
(xy)/(x+y-1)
(x1/3y1/2)/( x1/3+y1/2-1)
None of these
Solve the following equation 3 (x + 2) + 5 (x + 6) = 56
5/2
4/7
6/3
9/1
2/5
A ship 55 kms. From the shore springs a leak which admits 2 tones of water in 6 min; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink.
5.5km/h
6.5km/h
7.5km/h
8.5km/h
The difference in the money between A and B is Rs.1450.C has money twice of B and difference in the money between A and C is Rs.700.So the amount with A is?
750 Rs
2200Rs
800Rs
Find the number of triplets of real numbers (x, y, z) which satisfy (x + y)3 = z (y + z)3 = x (z + x)3 = y
0
1
3
none of these
If a = log2, b = log 3 and c = log 7 then find the value of log67 in terms of a, b and c.
b/(a+c)
c/(a+b)
a/(b+c)
(xn - an) is completely divisible by (x - a), if
n is an even natural number
n is and odd natural number
n is any natural number
n is prime
A singles tennis tournament is held, in which 30 men participated. If a player is eliminated as soon as he loses a match, how many matches are required to determine the winner
29
30
31
32
If x + y = 2, xy = 1, then the values of x and y are respectively
0 and 2
1/2 and 3/2
1 and 1
– 1 and 3
Find the number of solutions in positive integers (k; a1, a2, . . . , ak; b1, b2, . . . , bk) to the equation a1(b1) + a2(b1 + b2) + · · · + ak(b1 + b2 + . . . + bk) = 7
14
35
17
The largest value of min (2 + x², 6 - 3x) when x > 0 is
If o = 4/3 and h = 6 then h/o + 4/o2 =
6
2/9
24
85
7/4
n4 − 20n2 + 4 = k where k is a prime number and n is an integer. How many such k exist?
If p and q are real numbers; p ≠ 0, then the equation 3x – 5 + q = px + 1 has no solution, if
p = – 3
p = 0
p = 3
p = 6
The number of solutions of x2 - 5|x| + 6 = 0 is
If f (x+(y/8), x-(y/8)) = xy, then f (m, n) + f (n, m) = 0
only when m = n
only when m ≠ n
only when m = -n
for all m and n
If n(x) = x2 - 10x, then n(-10) =
2.3
9.0
5.9
20.0
s varies directly as the square of p. When s = 3.5, p = 0.5 If s = 90, then c would be equal to
2 √2
76
97
10
Let x and y be consecutive integers. Suppose m be the number of solutions of x3 − y3 = 3k2 and n be the number of solutions of x3 − y3 = 2t2,where k, t are integers. Then m + n equals:
13
5
If the interest on Rs. 800 exceeds that on Rs. 600 by Rs. 15.50 in 6 months, find the rate percent p.a
15 I/2 %
18 1/2 %
14%
5%
What is the minimum value of x for which the expression x3 – 7x2 + 11x – 5 gives positive values
If 7s + 2e = 14 and s – 2e = 5, then what is the value of s?
3.42
89.52
6.45
2.0
If a + b = 0, then (1 + xa)-1 + (1 + xb)-1 - xa+b =
x
ab
If 1 + 2 + 22 + 23 +.......+ 250 is divided by 7, what will be the remainder?