**Question 1:**

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is \(35\frac{7}{{17}}\). What was the number erased?

[1] 7

[2] 8

[3] 9

[4] None of these

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**Question 2:**

The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:

r_{1}= Number of runs scored in completed innings

n_{1}= Number of completed innings

r_{2}= Number of runs scored in incomplete innings n_{2}= Number of incomplete innings

A = \(\frac{{{{\rm{r}}_1} + {{\rm{r}}_2}}}{{{{\rm{n}}_{\rm{1}}}}}\)

To better assess a batsman’s accomplishments, the ICC is considering two other measures MBA_{1}and MBA_{2}defined as follows:

\({\rm{MB}}{{\rm{A}}_1} = \frac{{{r_1}}}{{{n_1}}} + \frac{{{n_2}}}{{n1}}\max \left[ {0,\left( {\frac{{{r_2}}}{{{n_2}}} - \frac{{{r_1}}}{{{n_1}}}} \right)} \right]\)

\({\rm{MB}}{{\rm{A}}_2} = \frac{{{r_{1 + }}{r_2}}}{{{n_1} + {n_2}}}\)

Based on the above information which of the following is true?

[1] MBA

_{1}≤ BA ≤ MBA

_{2}

[2] BA ≤ MBA

_{2}≤ MBA

_{1}

[3] MBA

_{2}≤ BA ≤ MBA

_{1}

[4] None of these

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**Question 3:**

The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:

r_{1}= Number of runs scored in completed innings

n_{1}= Number of completed innings

r_{2}= Number of runs scored in incomplete innings n_{2}= Number of incomplete innings

A = \(\frac{{{{\rm{r}}_1} + {{\rm{r}}_2}}}{{{{\rm{n}}_{\rm{1}}}}}\)

To better assess a batsman’s accomplishments, the ICC is considering two other measures MBA_{1}and MBA_{2}defined as follows:

\({\rm{MB}}{{\rm{A}}_1} = \frac{{{r_1}}}{{{n_1}}} + \frac{{{n_2}}}{{n1}}\max \left[ {0,\left( {\frac{{{r_2}}}{{{n_2}}} - \frac{{{r_1}}}{{{n_1}}}} \right)} \right]\)

\({\rm{MB}}{{\rm{A}}_2} = \frac{{{r_{1 + }}{r_2}}}{{{n_1} + {n_2}}}\)

An experienced cricketer with no incomplete innings has BA of 50. The next time he bats, the innings is incomplete and he scores 45 runs. It can be inferred that

[1] BA and MBA

_{1}will both increase

[2] BA will increase and MBA

_{2}will decrease

[3] BA will increase and not enough data is available to assess change in MBA

_{1}and MBA

_{2}

[4] None of these

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**Question 4:**

Let b be a positive integer and a = b

^{2}– b. If b ≥ 4 , then a

^{2}– 2a is divisible by

[1] 15

[2] 20

[3] 24

[4] All of these

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**Question 5:**

Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

[1] 11

[2] 12

[3] 13

[4] None of these

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