If e varies directly as n and e/d = 10, then what is the value of e when d = 30?
A. 25
B. 0.12
C. 200
D. 78
E. 300
If a1=1 and an+1-3an+2 = 4n for every positive integer n, then a100 equals
A. 399-200
B. 399+200
C. 3100-200
D. 3100+200
If 3x – 5y = 5 and x/x + y = 5/7, then what is the value of x – y ?
A. 3
B. 4
C. 6
D. 9
E. None of these
If 2x + 3y -31, y – z - 4 and x + 2z – 11, then what is the value of x + y + z ?
A. 12
B. 13
C. 15
D. 16
If a = log2, b = log 3 and c = log 7 then find the value of log67 in terms of a, b and c.
A. b/(a+c)
B. c/(a+b)
C. a/(b+c)
D. None of these
If f (x+(y/8), x-(y/8)) = xy, then f (m, n) + f (n, m) = 0
A. only when m = n
B. only when m ≠ n
C. only when m = -n
D. for all m and n
If 3x – 4y + z = 7; 2x – z + 3y = 19; x + 2y + 2z = 24, then what is the value of z ?
A. 4
B. 5
C. 6
D. 8
The number of positive integers n in the range 12 ? n? 40 such that the product (n – 1) (n –2)…3.2.1 is not divisible by n is
A. 5
B. 7
C. 13
D. 14
Solve for real x: 6x2 + 5x - 6 ≥ 0
A. x€ R
B. x € R-(-3/2,2/3)
C. x€R-(-2/3,3/2)
D. x €(-3/2,2/3)
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.
A. (x1/2y1/3)/( x1/2+y1/3-1)
B. (xy)/(x+y-1)
C. (x1/3y1/2)/( x1/3+y1/2-1)
D. None of these
The cost of 8 Sharpeners and 12 Pens is Rs. 76/- What is the cost of 20 Sharpeners and 30 Pens?
A. 113. 172
B. Rs.186
C. Rs. 190
D. cannot be determined
E. None of these
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:
A. 31
B. 13
C. 5
D. 6
E. none of these
If (x + 4) (x + 6) (x +1) 2> 0, then the solution set for the inequality is
A. R
B. (-6,-4)
C. [-6,-4]
D. R-[-6,-4]
If 5x + 9 > 3x + 19, what is the range of values x can take?
A. [5,∞)
B. (-∞,5)
C. (5,∞)
D. (-∞,5]
The total number of integer pairs (x, y) satisfying the equation x + y = xy is
A. 0
B. 1
C. 2
D. None of the above
If a, b and c are the sides of a triangle and a4 + b4 + 2a2b2 = c4, then the triangle is
A. right-angled triangle
B. acute-angled triangle
C. equilateral triangle
D. obtuse-angled triangle
Which of the following is true?
A. The second round issues have a higher maturity than the first round for all dates.
B. The second round issue of any date has a lower maturity only when the first round notified amount exceeds that of the second round.
C. On at least one occasion, the second round issue having lower maturity received a higher number of competitive bids.
D. None of the above three statements is true
If 9c + 2d = 11 and z – 3d = 5, then what is the value of g?
A. 0.78
B. 78g
C. 0.678
D. 76
E. 2.0
If a sum of money at certain rate of interest doubles in 5 years and at a different rate of interest becomes 3 times in 12 years, the better rate of interest is
A. 20%
B. 10%
C. 162/3
D. 15%
H.C.F. of two polynomials is a + 5 and their L.C.M. is (a + 5) (a + 4) (a – 1). If one of the polynomial is a2+ 4a – 5,then the other polynomial is
A. a2+ 9a – 20
B. a2– 9a + 20
C. a2 + 9a + 20
D. a2– 9a – 20