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Frequently Asked GRE Latest Exam Pattern - GRE Sample Question with Solutions Page 40

(#M40151741) GRE QUESTION Inequalities Keep an EYE

Let f and g be twice-differentiable real-valued functions defined on R. If f’(x) > g’(x) for all x > 0, which of the following inequalities must be true for x > 0?
(A) f(x) > g(x)
(B) f”(x) > g”(x)
(C)f(x) – f(0) > g(x) – g(0)
(D) f’(x) – f’(0) > g’(x) – g’(0)
(E) f”(x) – f”(0) > g”(x) – g”(0)

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(#M40151738) GRE QUESTION xy-plance base question Keep an EYE

What is the volume of the solid formed by revolving about the x-axis the region in the first quadrant of the xy-plane bounded by the coordinate axes and the graph of the equation y = 1/(Sqrt(1+x^2).
(A) Pi/2
(B) Pi
(C) Pi^2/4
(D) Pi^2/2
(E) Infinite

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(#M40151735) GRE QUESTION Triangular region Keep an EYE

What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
(A) 1/2
(B) 1
(C) Sqrt 2
(D) Pi
(E) (1 + Sqrt 2)/4

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(#M40151734) GRE QUESTION Intersection with parabola Keep an EYE

Which of the following circles has the greatest number of points of intersection with the parabola x^2 = y + 4
(A) x^2 + y^2 = 1
(B) x^2 + y^2 = 2
(C) x^2 + y ^2 = 9
(D) x^2 + y^2 = 16
(E) x^2 + y^2 = 25

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(#M40151732) GRE QUESTION 2-Dimensional Keep an EYE

If V and W are 2-dimensional subspaces of R^4, what are the possible dimensions of the subspace V Intersection W?
(A) 1 only
(B) 2 only
(C) 0 and 1 only
(D) 0, 1, and 2 only
(E) 0, 1, 2, 3, and 4

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(#M40151731) GRE QUESTION Tangent to the graph Keep an EYE

Which of the following is an equation of the line tangent to the graph of y = x + e^x at x = 0 ?
(A) y = x
(B) y = x + 1
(C) y = x + 2
(D) y = 2x
(E) y = 2x 1

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(#M40151730) GRE QUESTION xy-plance base question Keep an EYE

The xy-plane, the curve with parametric equations x = cost and y = sin t, 0 =< t =< Pi has length
(A) 3
(B) Pi
(C) 3 Pi
(D) 3/2
(E) Pi/2

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(#M40151727) GRE QUESTION Population in category Keep an EYE

Population Category -------- Population(millions) -------------- Number of States
A ------------------------------------------------------ 0.0-19 ----------------------- 15
B ------------------------------------------------------ 2.0-3.9 ---------------------- 9
C ------------------------------------------------------ 4.0-5.9 ---------------------- 12
D ------------------------------------------------------ 6.0-7.9 ---------------------- 3
E ------------------------------------------------------- 8.0-9.9 ---------------------- 4
F ------------------------------------------------------- 10.0-11.9 ------------------- 1
G ------------------------------------------------------ 12.0-13.9 ------------------- 2
H ------------------------------------------------------ 14.0 and over ------------- 4

In 2000 the population of West Virginia was 1.8 million. If the ratio of the population of Georgia to that of West Virginia was 9 to 2, in which population category was Georgia?
(A) B
(B) C
(C) D
(D) E
(E) F

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(#M40151724) GRE QUESTION Property Tax Keep an EYE

Question
Steve’s property tax is $140 less than Patricia’s property tax. If Steve’s prop-
erty tax is $1,960, then Steve’s property tax is what percent less than Patricia’s property tax, to the nearest 0.1 percent?
(A) 6.7%
(B) 7.1%
(C) 7.5%
(D) 7.9%
(E) 8.3%

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(#M40151723) GRE QUESTION In the xy-plane Keep an EYE

Question
In the xy-plane, points R and S have coordinates (2, 1) and (4, 7)respectively. If
point P is the midpoint of line segment RS, what are the coordinates of point P?
(A) (-1, -3)
(B) (1,- 4)
(C) (1, -3)
(D) (2,- 4)
(E) (3,- 4)

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