When x5– 5x4+ 9x3– 6x2– 16x + 13 is divided by x2 – 3x + a, the quotient and the remainder are x3 2x2+ x + 1 and – 15x + 11, respectively. The value of a is equal to
1
2
3
4
If 4x + 5y = 83 and 3x/2y = 21/22, then y-x = ?
7
11
If 3x – 4y + z = 7; 2x – z + 3y = 19; x + 2y + 2z = 24, then what is the value of z ?
5
6
8
If X and Y are positive integers and X + Y = 1, what is the least value of (X+1/X)2 + (Y+1/Y)2 ?
24
12.5
20
None of these
The number of solutions of x2 - 5|x| + 6 = 0 is
Which of the following value of x do not satisfy the inequality (x² - 3x + 2 > 0) at all?
1 ≤ x≤ 2
-1 ≥ x≥ -2
0 ≤ x≤ 2
0 ≥ x≥ -2
Solve the following equation 3s + 5 = s – 1
63
– 3
-56
62
10
The total number of integer pairs (x, y) satisfying the equation x + y = xy is
0
None of the above
Find the number of pairs of real numbers x, y such that (x2 + 8x +17)(y2 − 2y + 6) = 5
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
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
85
2.0
If o = 4/3 and h = 6 then h/o + 4/o2 =
2/9
7/4
A pole has to be erected on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrical opposite fixed gates A and B on the boundary is 7 meters. The distance of the pole from one of the gates is:
8 meters
8.25 meters
5 meters
None these
If l(s) = 3s2 + 3s + 3, which of the following is equal to l(-3.5)?
L7
84
l(2.5)
78l
s/l
if (64)2 - (36)2 = 10x, then x = ?
200
220
210
280
If α, β are the roots of (x –√ 3) (x –√ 5) =√ 7, the roots of (x –α) (x –β) +√ 7= 0 are
√3,√ 7
√3 ,√ 5
√5 ,√ 7
√3+ √5 ,√ 5 +√ 7
If a + b + c = 3, a2 + b2 + c2 = 9, a3 + b3 + c3 = 24 , Then find a4 + b4 + c4
27
69
36
none of these
If a + b = 0, then (1 + xa)-1 + (1 + xb)-1 - xa+b =
x
ab
If x + y > 4 and x < 3, then y > 1 is true. Is this statement true?
Always
Only if x < 0
Only if x > 0
Never
If l + m + n=0, which of the following conditions must l, m and n satisfy so that the system of simultaneous linear equations x + 3y -4z = l, 2x - y - z = m, x + y - 2z = n has at least one ?
3l - 2m + 7n = 0
3l - 2m - 7n = 0
3l + 2m - 7n = 0
2l + 3m + 7n = 0
2l + 3m - 7n = 0
n4 − 20n2 + 4 = k where k is a prime number and n is an integer. How many such k exist?
A father with 8 children takes 3 children at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. Then:
number of times he will go to zoological garden is 56.
number of times each child will go to the zoological garden is 21.
number of times a particular child will not go to the zoological garden is 35.
All of the above.
If ( p - q) 2 = ( x – y ) 2, then x =
p–q+y
y – p + q
Both ( a) and (b)
The cost of 8 Sharpeners and 12 Pens is Rs. 76/- What is the cost of 20 Sharpeners and 30 Pens?
113. 172
Rs.186
Rs. 190
cannot be determined
Simplify the expression (1+i)6+(1+i)4 .
-4 - 8i
4 – 8i
8 – 4i
8 + 4i
If 2x – ky + z = 0 is a factor of 9y2– z2 – 2xz + 6xy, then the value of k is equal to
-3
-1
If a * b – 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to:
22
26
28
The sum of X and Y's age is 105. When X was Y's age, she was 1.5 times Y's age then what are their present ages?
45: 60
30: 40
50: 60
60: 45
The L.C.M. of 6x2 – 5x – 6 and 12x2 + 11x + 2 is
(3x – 2) (2x – 3) (4x – 1)
(3x – 2) (2x – 3) (4x + 1)
(3x – 2) (2x + 3) (4x + 1)
(3x + 2) (2x – 3) (4x + 1)