• Placement Questions
• /
• Numerical Ability

Placement Papers with Solutions

(#M40151777) GRE QUESTION Decimal representation Keep an EYE

For how many positive integers k does the ordinary decimal representation of the integer k! end in exactly 99 zeros?
(A) None
(B) One
(C) Four
(D) Five
(E) Twenty-four

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Number System

(#M40151776) GRE QUESTION Minimum value of the expression Keep an EYE

What is the minimum value of the expression x + 4z as a function defined onR^3 , subject to the constraint x^2 + y^2 + z^2 =< 2 ?
(A) 0
(B) 2
(C) – Sqrt(34)
(D) – Sqrt(35)
(E) -5 Sqrt(2)

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (1)   (0) Submit Your Solution Algebra

(#M40151775) GRE QUESTION Subset of the real line Keep an EYE

If A is a subset of the real line R and A contains each rational number, which of the following must be true?
(A) If A is open, then A = R.
(B) If A is closed, then A = R.
(C) If A is uncountable, then A = R .
(D) If A is uncountable, then A is open.
(E) If A is countable, then A is closed.

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (2) Submit Your Solution Permutation and Combination

(#M40151774) GRE QUESTION Matrix Keep an EYE

Let A be a real 2*2 matrix. Which of the following statements must be true?
I. All of the entries of A^2 are nonnegative.
II. The determinant of A^2 is nonnegative.
III. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Data Sufficiency

(#M40151773) GRE QUESTION Isomorphism Keep an EYE

Up to isomorphism, how many additive abelian groups G of order 16 have the property that x+x+x+x = 0
for each x in G ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Algebra

(#M40151772) GRE QUESTION Consider the theorem Keep an EYE

Consider the theorem: If f and f’ are both strictly increasing real-valued functions on the interval (0, infinite) then lim f(x) = infinite (x -> infinite). The following argument is suggested as a proof of this theorem.
(1) By the Mean Value Theorem, there is a c1 in the interval (1, 2) such that
f’(c1) = {f(2)-f(1)}/ (2-1) = f(2) – f(1) > 0.
(2) For each x > 2, there is a c(x) in (2, x) such that {f(x) – f(2)}/(x-2) = f’{c(x)}
(3) For each x > 2, {f(x)-f(2)}/(x-2) = f’(c(x)) > f’(c1) since f’ strictly incrasing
(4) For each x > 2, f(x) > f(2) + (x-2) f’(c1)
(5) lim f(x) = infinite (x -> infinite)
Which of the following statements is true?
(A) The argument is valid.
(B) The argument is not valid since the hypotheses of the Mean Value Theorem are not satisfied in (1) and (2).
(C) The argument is not valid since (3) is not valid.
(D) The argument is not valid since (4) cannot be deduced from the previous steps.
(E) The argument is not valid since (4) does not imply (5).

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (1) Submit Your Solution Data Sufficiency

(#M40151771) GRE QUESTION xyz-space Keep an EYE

Let F be a constant unit force that is parallel to the vector (-1, 0, 1) in xyz-space. What is the work done by F on a particle that moves along the path given by (t, t^2, t^3) between time t = 0 and time t = 1?
(A) – 1/4
(B) – 1/4 Sqrt(2)
(C) 0
(D) Sqrt(2)
(E) 3 Sqrt(2)

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Geometry

(#M40151770) GRE QUESTION Complex number Keep an EYE

Let G be the group of complex numbers {1, i, -1, -i} under multiplication. Which of the following statements are true about the homomorphism of G into itself?
I. z -> z defines one such homomorphism, where z denotes the complex conjugate of z,
II. z -> z^2 defines one such homomorphism.
III. For every such homomorphism, there is an integer k such that the homomorphism has the form z -> z^k .
(A) None
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Data Sufficiency

(#M40151769) GRE QUESTION Circular region divide 5 sector Keep an EYE

A circular region is divided by 5 radii into sectors. Twenty-one points are chosen in the circular region, none of which is on any of the 5 radii. Which of the following statements must be true?
I. Some sector contains at least 5 of the points.
II. Some sector contains at most 3 of the points.
III. Some pair of adjacent sectors contains a total of at least 9 of the points.
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Data Sufficiency

(#M40151768) GRE QUESTION Greatest probability Keep an EYE

A fair coin is to be tossed 100 times, with each toss resulting in a head or a tail. If H is the total number of heads and T is the total number of tails, which of the following events has the greatest probability?
(A) H = 50
(B) T >= 60
(C) 51 =< H =< 55
(D) H >= 48 and T >= 48
(E) H =< 5 or H >= 95

Asked In GRE Aashu (10 years ago)

Unsolved

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Probability