This is a logical reasoning problem involving scheduling. We need to determine the exam schedule for seven students (D, F, G, H, S, T, V) over seven days of a week (Monday to Sunday) based on the given clues. We will use a table to organize the information and deduce the schedule step-by-step.
Set up the table: Create a table with days of the week from Monday to Sunday.
| Day | Student |
|---|---|
| Monday | |
| Tuesday | |
| Wednesday | |
| Thursday | |
| Friday | |
| Saturday | |
| Sunday |
Fill in direct information:
| Day | Student |
|---|---|
| Monday | |
| Tuesday | |
| Wednesday | V |
| Thursday | |
| Friday | H |
| Saturday | |
| Sunday |
Use the clue: V's exam is on the day immediately after T's exam.
Since V's exam is on Wednesday, T's exam must be on Tuesday.
| Day | Student |
|---|---|
| Monday | |
| Tuesday | T |
| Wednesday | V |
| Thursday | |
| Friday | H |
| Saturday | |
| Sunday |
Use the clue: D's exam is on the day immediately before G's exam.
This means D and G must be in consecutive slots. Possible pairs are (Monday, Tuesday), (Thursday, Friday), (Saturday, Sunday). Since Tuesday and Friday are already filled, the only remaining consecutive slots are (Saturday, Sunday).
| Day | Student |
|---|---|
| Monday | |
| Tuesday | T |
| Wednesday | V |
| Thursday | |
| Friday | H |
| Saturday | D |
| Sunday | G |
Use the clue: Only one student has an exam between D and F.
D's exam is on Saturday. If there is one student between D and F, F's exam must be on Thursday (Saturday - 1 day - Thursday). This fits the condition.
| Day | Student |
|---|---|
| Monday | |
| Tuesday | T |
| Wednesday | V |
| Thursday | F |
| Friday | H |
| Saturday | D |
| Sunday | G |
Check the remaining clue: F's exam is neither on Monday nor on Saturday.
Our placement of F on Thursday satisfies this condition.
Fill the last remaining slot: The only remaining student is S, and the only remaining day is Monday.
| Day | Student |
|---|---|
| Monday | S |
| Tuesday | T |
| Wednesday | V |
| Thursday | F |
| Friday | H |
| Saturday | D |
| Sunday | G |
Answer the question: Who has an exam on Thursday?
From the completed table, F has an exam on Thursday.
Correct Option: B) F
To find the day of the week on 17 September 2015, given that 5 August 2012 was a Sunday, we need to calculate the total number of odd days between these two dates. Odd days are the remainder when the total number of days is divided by 7. Each odd day shifts the day of the week forward by one.
Therefore, 17 September 2015 will be a Thursday.
B) Thursday is the correct answer because adding 4 odd days to Sunday results in Thursday.
This problem involves the concept of pipes and cisterns, which is a variation of time and work problems. We need to calculate the individual rates of filling and emptying, then determine the amount of tank filled in the initial phase, and finally calculate the time required to fill the remaining part of the tank when both pipes are open.
Calculate the filling rate of Pipe A:
Pipe A fills the tank in 15 minutes. So, in 1 minute, Pipe A fills \(\frac{1}{15}\) of the tank.
Calculate the emptying rate of Pipe B:
Pipe B empties the tank in 20 minutes. So, in 1 minute, Pipe B empties \(\frac{1}{20}\) of the tank.
Calculate the amount filled by Pipe A in the first 5 minutes:
Pipe A is opened for 5 minutes initially. Amount filled by Pipe A in 5 minutes is:
Calculate the remaining part of the tank to be filled:
Remaining part \[= 1 - \frac{1}{3} = \frac{2}{3}\] of the tank.
Calculate the combined rate when both pipes A and B are open:
Pipe A fills and Pipe B empties, so their combined effect is the difference between their rates:
Calculate the time to fill the remaining \(\frac{2}{3}\) of the tank:
Time \[= \frac{\text{Remaining part}}{\text{Combined rate}}\]
Therefore, the remaining tank will be filled completely in 40 minutes.
C) 40
The question asks about the nature of the graph obtained when plotting voltage (V) against current (I). This relationship is described by Ohm's Law for ohmic conductors.
D) an inclined straight line is obtained. This is consistent with Ohm's Law, which states that V is directly proportional to I, resulting in a straight line passing through the origin with a slope equal to the resistance (R).
The problem presents a number series with a missing term. We need to identify the pattern in the given numbers to find the missing value. A common approach for such series is to look for differences between consecutive terms, squares, cubes, or combinations of these operations.
C) 47 is the correct number that fits the pattern in the series.
The problem requires us to modify a given set of numbers according to specific rules and then count how many of the modified numbers satisfy a divisibility condition. For each number, we need to add 1 to its first digit and subtract 1 from its last digit. After this modification, we check if the new first digit is exactly divisible by the new last digit.
The numbers where the first digit is exactly divisible by the last digit after modification are 242, 864, and 264. There are 3 such numbers.
C) 3 is the correct answer because three numbers (242, 864, 264) satisfy the given condition after modification.
The problem asks us to identify a set of three numbers that follows the same relationship as the given sets: (28, 33, 48) and (67, 72, 87). We need to find the pattern or rule governing the numbers within these sets.
Both given sets follow the same pattern: the second number is 5 more than the first number, and the third number is 15 more than the second number.
We will now check each option to see which one follows this pattern.
D) (29, 34, 49)
This set follows the established pattern (\(+5, +15\)).
First difference: \(72 - 57 = 15\). This does not match the required \(+5\).
First difference: \(38 - 25 = 13\). This does not match the required \(+5\).
First difference: \(150 - 125 = 25\). This does not match the required \(+5\).
The problem asks us to identify the relationship between the letter-clusters in the given pairs and then find an option that follows the same logic. We need to analyze the positional values of the letters in the English alphabet.
The logic here is that each letter in the first cluster is shifted forward by 4 positions to get the corresponding letter in the second cluster.
This pair also follows the same logic: a shift of +4 for each letter.
A) XYZ : BCD
This option follows the same +4 shift logic, wrapping around the alphabet.
The shifts are not consistent (+2, +8, +1), so this option is incorrect.
This option uses a +3 shift, not +4, so it is incorrect.
This option uses a -3 shift (backward by 3), not +4, so it is incorrect.
Simplify: \(\frac{6+6\times6}{3\times3+5}\div\frac{\frac{1}{2}\div\frac{1}{2}\ \mathrm{of}\ \frac{1}{2}}{\frac{1}{2}\div\frac{1}{2}\times\frac{1}{2}}\)
\( \frac{1}{3} \)
\( \frac{4}{3} \)
3
\( \frac{3}{4} \)
To simplify the given expression, we will use the BODMAS/PEMDAS rule (Brackets, Orders/Exponents, Division, Multiplication, Addition, Subtraction). We will simplify each part of the expression separately and then combine them.
D) \( \frac{3}{4} \). The step-by-step simplification leads to the result \( \frac{3}{4} \).
The question asks to identify which of the given options is NOT a fundamental right in the Constitution of India. To answer this, we need to recall the list of fundamental rights enshrined in Part III of the Indian Constitution and identify the option that is no longer or never was a fundamental right.
Correct Option: B) Right to Acquire Property is NOT a fundamental right in the Constitution of India. It was removed from the list of fundamental rights by the 44th Amendment Act of 1978 and made a legal right under Article 300A.