List of top Questions asked in XAT- 2008

For each \(p > 1\), a sequence \(A_n\) is defined by \(A_0 = 1\) and \(A_n = np + (-1)^n A_{n-1}\) for \(n \geq 1\). For how many integer values of \(p\) is 1000 a term of the sequence?

If \(F(x, n)\) denotes the number of ways of distributing \(x\) toys to \(n\) children so that each child gets at most 2 toys, then what is the value of \(F(4, 3)\)?

ABCD is a quadrilateral whose diagonals intersect at point P. The area of triangle APD is 27 and the area of triangle BPC is 12. If the areas of triangles APB and CPD are equal, then the area of triangle APB is

Directions: Each question below is followed by two statements, I and II. Decide whether the data in the statements is sufficient to answer the question, using these options:
(AA) Statement I alone is sufficient.
(BB) Statement II alone is sufficient.
(CC) Statements I and II together are sufficient, but neither alone is sufficient.
(DD) Either statement I alone or statement II alone is sufficient.
(EE) Statements I and II together are not sufficient.

A, B, C, D, E and F are six integers such that \(E < F\), \(B > A\), and \(A < D < B\). C is the greatest of the six integers. Is A the smallest integer?
I. \(E + B < A + D\)
II. \(D < F\)

In a cricket match, Team A scored 232 runs without losing a wicket. The score was made up of byes, wides and runs scored by the two opening batsmen, Ram and Shyam. The runs scored by the two batsmen are 26 times the wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram and Shyam is \(6:7\), then the runs scored by Ram is ______?

Let \(X = \{a, b, c\}\) and \(Y = \{l, m\}\). Consider the following four subsets of \(X \times Y\):
\(F_1 = \{(a, l), (a, m), (b, l), (c, m)\}\)
\(F_2 = \{(a, l), (b, l), (c, l)\}\)
\(F_3 = \{(a, l), (b, m), (c, m)\}\)
\(F_4 = \{(a, l), (b, m)\}\)
Which one, among the choices given below, is a representation of functions from \(X\) to \(Y\)?

Rajiv is a student at a business school. After every test, he calculates his cumulative average score. QT and OB were his last two tests. Scoring 83 in QT increased his average by 2. Scoring 75 in OB further increased his average by 1. If his next test is Reasoning and he scores 51 in it, his new average will be

Directions: Each question below is followed by two statements, I and II. Decide whether the data in the statements is sufficient to answer the question, using these options:
(AA) Statement I alone is sufficient.
(BB) Statement II alone is sufficient.
(CC) Statements I and II together are sufficient, but neither alone is sufficient.
(DD) Either statement I alone or statement II alone is sufficient.
(EE) Statements I and II together are not sufficient.

The base of a triangle is 60 cm, and one of its base angles is \(60^{\circ}\). What is the length of the shortest side of the triangle?
I. The sum of the lengths of the other two sides is 80 cm.
II. The other base angle is \(45^{\circ}\).

In the figure, the number in any cell is obtained by adding the two numbers in the cells directly below it. For example, the 9 marked in the figure is obtained by adding the 4 and 5 directly below it.

The value of X - Y is

In the second year, students at a business school opt for exactly one of three electives: Systems, Operations, or HR.

The number of girls who opted for Operations plus the number of boys who opted for Systems is 37. Twenty-two students opted for the Operations elective. Twenty girls opted for the Systems and Operations electives put together. The number of students who opted for the Systems elective plus the number of boys who opted for the Operations elective is 37. Twenty-five students opted for the HR elective.

If 20% of the girls opt for the HR elective, then the total number of boys in the second year is

\(ABCD\) is a square with \(AB = 2\). \(P\) is the midpoint of \(AB\). The line through \(A\) that is perpendicular to \(DP\) meets the diagonal \(BD\) at \(Q\) and meets side \(BC\) at \(R\). Find the length of \(PR\).

\(ABCD\) is a rectangle with \(AD = 10\). \(P\) is a point on \(BC\) such that \(\angle APD = 90^{\circ}\). If \(DP = 8\), find the length of \(BP\).

In the second year, students at a business school opt for exactly one of three electives: Systems, Operations, or HR.

The number of girls who opted for Operations plus the number of boys who opted for Systems is 37. Twenty-two students opted for the Operations elective. Twenty girls opted for the Systems and Operations electives put together. The number of students who opted for the Systems elective plus the number of boys who opted for the Operations elective is 37. Twenty-five students opted for the HR elective.

The number of students in the second year is

Directions: A statement is followed by three conclusions. Choose the answer from the options below.
(AA) Using the given statement, only conclusion I can be derived.
(BB) Using the given statement, only conclusion II can be derived.
(CC) Using the given statement, only conclusion III can be derived.
(DD) Using the given statement, all conclusions can be derived.
(EE) Using the given statement, none of the three conclusions I, II and III can be derived.

An operation # is defined by \(a \# b = 1 - \dfrac{b}{a}\).
Conclusion I: \((2 \# 1) \# (4 \# 3) = -1\)
Conclusion II: \((3 \# 1) \# (4 \# 2) = -2\)
Conclusion III: \((2 \# 3) \# (1 \# 3) = 0\)

Directions: A statement is followed by three conclusions. Choose the answer from the options below.
(AA) Using the given statement, only conclusion I can be derived.
(BB) Using the given statement, only conclusion II can be derived.
(CC) Using the given statement, only conclusion III can be derived.
(DD) Using the given statement, all conclusions can be derived.
(EE) Using the given statement, none of the three conclusions I, II and III can be derived.

A, B, C and D are whole numbers such that:
\(A + B + C = 118\)
\(B + C + D = 156\)
\(C + D + A = 166\)
\(D + A + B = 178\)
Conclusion I: A is the smallest number and A = 21.
Conclusion II: D is the largest number and D = 88.
Conclusion III: B is the largest number and B = 56.

The graph below shows the percentage returns of Stock X and Mutual Fund Y over sixteen days of a month. Study the graph and pick the statement that correctly describes the relationship between the returns of Stock X and Mutual Fund Y.

If \([XX]\) denotes the greatest integer less than or equal to \(X\), find the value of \[ \left[\frac{1}{3}\right] + \left[\frac{1}{3}+\frac{1}{99}\right] + \left[\frac{1}{3}+\frac{2}{99}\right] + \cdots + \left[\frac{1}{3}+\frac{98}{99}\right] \]

Four digits of the number \(29138576\) are removed so that the remaining four digits, kept in their original order, form the largest possible number. Which removed digit has the largest value?