Question

How many times was the issue of securities under-subscribed, i.e., how often did the total amount mobilized fall short of the amount notified?

• A. 0
• B. 1
• C. 2
• D. 3
• 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.
• A. Competitive bids received always exceed non-competitive bids received.
• B. The number of competitive bids accepted does not always exceed the number of non-competitive bids accepted.
• C. The value of competitive bids accepted on any particular date is never higher for higher maturity.
• D. The value of non-competitive bids accepted in the first round is always greater than that in the second round.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question defines under-subscribed for us: the total amount mobilized fell short of the amount notified.
So only two columns matter here, Notified Amount and Total Amount (both in Rs. Crore). We compare them for every issue, one row at a time.

Step 2: Compare the two columns row by row:
Write each row as notified / total. Each date has two rounds, so we list both rounds.
17-Jul-02: 40 / 16 and 30 / 30. 5-Aug-02: 50 / 50 and 20 / 20. 28-Aug-02: 50 / 50 and 20 / 20.
11-Sep-02: 40 / 40 and 30 / 30. 9-Oct-02: 40 / 40 and 30 / 30. 7-Nov-02: 40 / 40 and 30 / 30.
9-Apr-03: 40 / 40 and 50 / 50. 23-Apr-03: 50 / 50 and 20 / 20. 5-May-03: 60 / 60 and 30 / 30.
4-Jun-03: 30 / 30 and 60 / 60. 2-Jul-03: 50 / 50 and 30 / 30. 16-Jul-03: 60 / 60 and 30 / 30.
Every row has equal numbers except the first round of 17-Jul-02, where \(16 < 40\).

Step 3: Cross-check with the Total row:
The Total row shows 930 notified and 906 mobilized. The gap between them is
\[ 930 - 906 = 24 \]
The single short row gives a shortfall of \(40 - 16 = 24\). That one row explains the whole gap, so no other issue can be short.

Step 4: Why the other options fail:
Option (1), 0 times: wrong, because the first round of 17-Jul-02 clearly mobilized only 16 against 40.
Option (3), 2 times, and option (4), 3 times: wrong, because a second short row would add to the gap, and the total gap is already fully used up by the first row (24 out of 24).

Final Answer:
The issue was under-subscribed exactly once, which is option (2). \[ \boxed{\text{Option (2): 1 time}} \]

Answer 2

Step 1: Set up the pairs:
Each date has two rounds, listed one after the other. Call the upper row round 1 and the lower row round 2. Every statement compares the two rounds of the same date.
Maturity in years (round 1, round 2): 17-Jul-02 (15, 10), 5-Aug-02 (9, 24), 28-Aug-02 (15, 30), 11-Sep-02 (15, 20), 9-Oct-02 (11, 30), 7-Nov-02 (17, 24), 9-Apr-03 (20, 11), 23-Apr-03 (15, 29), 5-May-03 (10, 20), 4-Jun-03 (25, 9), 2-Jul-03 (11, 25), 16-Jul-03 (17, 29).
Round 2 has the lower maturity on three dates only: 17-Jul-02, 9-Apr-03 and 4-Jun-03.

Step 2: Check statement (1):
It says round 2 has the higher maturity on all dates. On 17-Jul-02 round 1 is 15 years and round 2 is only 10 years, so round 2 is lower.
One counter-example is enough, so (1) is FALSE.

Step 3: Check statement (2):
It says round 2 can have a lower maturity only if the round 1 notified amount is bigger than the round 2 notified amount. So we test the three dates from Step 1.
17-Jul-02: notified 40 and 30, round 1 is bigger, no problem. 9-Apr-03: notified 40 and 50, round 1 is smaller, yet round 2 has lower maturity (11 against 20).
This breaks the rule, so (2) is FALSE. (4-Jun-03 breaks it too, with 30 and 60.)

Step 4: Check statement (3):
Now look at the same three dates and compare competitive bids received in the two rounds.
17-Jul-02: 229 and 145, round 2 gets fewer. 9-Apr-03: 245 and 236, round 2 gets fewer. 4-Jun-03: 187 and 378, round 2 gets more.
On 4-Jun-03 the second round had the lower maturity (9 years against 25) and still received more competitive bids. So (3) is TRUE.

Step 5: Check statement (4):
Statement (4) says none of the first three is true. We just showed that (3) is true, so (4) is FALSE.

Final Answer:
Only statement (3) holds, which is option (3). \[ \boxed{\text{Option (3)}} \]

Answer 3

Step 1: What we must find:
The question asks for the statement that is NOT true. So three statements are true and one is false. We test each one against the table.

Step 2: Check statement (1):
It says competitive bids received are always more than non-competitive bids received. The smallest value in the competitive-received column is 91 (second round of 9-Oct-02). The largest value in the non-competitive-received column is 29.
Since \(91 > 29\), every competitive count beats every non-competitive count. So (1) is TRUE.

Step 3: Check statement (2):
It says the number of competitive bids accepted does not always exceed the number of non-competitive bids accepted. To make this true we need one row where competitive accepted is not bigger.
On 23-Apr-03, round 2, competitive accepted is 9 and non-competitive accepted is 19. So 9 is below 19 and (2) is TRUE. (4-Jun-03 round 1 with 15 and 19 and 16-Jul-03 round 2 with 12 and 22 also show it.)

Step 4: Check statement (3):
It says that on any one date the competitive value accepted is never higher for the higher maturity. Compare the two rounds of each date in this form: (higher maturity value, lower maturity value).
17-Jul-02: 15.21 and 29.88. 5-Aug-02: 19.81 and 49.68. 28-Aug-02: 19.61 and 48.92. 11-Sep-02: 29.44 and 38.93. 9-Oct-02: 29.52 and 39.22. 7-Nov-02: 29.70 and 39.71.
9-Apr-03: 39.53 and 49.40. 23-Apr-03: 19.39 and 48.98. 5-May-03: 29.58 and 59.69. 4-Jun-03: 28.50 and 59.09. 2-Jul-03: 28.64 and 49.05. 16-Jul-03: 29.32 and 57.00.
In every pair the higher-maturity value is the smaller one. So (3) is TRUE.

Step 5: Check statement (4):
It says the non-competitive value accepted in round 1 is always greater than in round 2. We compare the pairs (round 1, round 2).
17-Jul-02: 0.37 and 0.12, fine. 5-Aug-02: 0.33 and 0.19, fine. 28-Aug-02: 1.08 and 0.39, fine. 11-Sep-02: 1.07 and 0.56, fine. 9-Oct-02: 0.78 and 0.48, fine.
7-Nov-02: 0.29 and 0.31. Here round 1 is smaller, so the claim already fails. (5-May-03 with 0.31 and 0.42, and 2-Jul-03 with 0.95 and 1.36, fail as well.)
So (4) is FALSE, which makes it the statement that is NOT true.

Final Answer:
Statements (1), (2) and (3) are true, while statement (4) is not. The answer is option (4). \[ \boxed{\text{Option (4)}} \]