The Reserve Bank of India was nationalised with effect from 1st January, ______.
This question tests knowledge about the historical timeline of the Reserve Bank of India (RBI), specifically its nationalisation. Candidates need to recall the exact year when the RBI was nationalised.
Correct Option: C) 1949
If 0.72\(\overline{45}\) = \( \frac{a}{b} \), where the HCF of a and b is 1, then what is the value of (b − a)?
To solve this problem, we need to convert the given recurring decimal into a fraction in its simplest form. Once we have the fraction \( \frac{a}{b} \) where \( \text{HCF}(a, b) = 1 \), we can find the value of \( (b - a) \).
Let \( x = 0.72\overline{45} \). This can be written as \( x = 0.72454545... \).
We can write \( x \) as:
\[ x = 0.72 + 0.00\overline{45} \]
Let's convert \( 0.00\overline{45} \) to a fraction first. Let \( y = 0.00\overline{45} \).
\[ y = rac{1}{100} imes 0.\overline{45} \]
To convert \( 0.\overline{45} \) to a fraction:
Let \( z = 0.\overline{45} = 0.454545... \)
Multiply by 100:
\[ 100z = 45.454545... \]
Subtract \( z \) from \( 100z \):
\[ 100z - z = 45.4545... - 0.4545... \]
\[ 99z = 45 \]
\[ z = rac{45}{99} = rac{5}{11} \]
Now substitute \( z \) back into the expression for \( y \):
\[ y = rac{1}{100} imes rac{5}{11} = rac{5}{1100} = rac{1}{220} \]
\[ x = 0.72 + y \]
\[ x = rac{72}{100} + rac{1}{220} \]
Simplify \( rac{72}{100} \):
\[ rac{72}{100} = rac{18}{25} \]
So, \( x = rac{18}{25} + rac{1}{220} \)
Find a common denominator, which is \( \text{LCM}(25, 220) \). \( 25 = 5^2 \), \( 220 = 2^2 imes 5 imes 11 \). So, \( \text{LCM} = 2^2 imes 5^2 imes 11 = 4 imes 25 imes 11 = 100 imes 11 = 1100 \).
\[ x = rac{18 imes 44}{25 imes 44} + rac{1 imes 5}{220 imes 5} \]
\[ x = rac{792}{1100} + rac{5}{1100} \]
\[ x = rac{792 + 5}{1100} = rac{797}{1100} \]
We have \( rac{a}{b} = rac{797}{1100} \).
Here, \( a = 797 \) and \( b = 1100 \).
We need to check if \( \text{HCF}(797, 1100) = 1 \). \( 797 \) is a prime number. \( 1100 \) is not divisible by \( 797 \).
Thus, \( \text{HCF}(797, 1100) = 1 \).
Now, calculate \( (b - a) \):
\[ b - a = 1100 - 797 = 303 \]
C) 303
This is a circular seating arrangement problem. We need to deduce the positions of all six people (K, L, M, N, O, P) around a circular table based on the given clues and then identify who is seated second to the right of L.
D) M is seated second to the right of L.
To find the approximate value, we will round off each number in the equation to the nearest whole number. Then, we will perform the operations (division, addition, and subtraction) in the correct order according to the BODMAS/PEMDAS rule.
Thus, the approximate value is 13.
Correct Option: A) 13
The question asks to identify which substances can be separated using distillation. Distillation is a separation technique used for mixtures whose components have different boiling points.
B) Water and liquid ink. Distillation is an effective method to separate water from the non-volatile components of ink due to their significant difference in boiling points.
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(13, 16, 21)
(28, 34, 45)
(35, 12, 59)
(64, 26, 90)
(37, 18, 46)
(72, 45, 27)
The problem asks us to identify a set of three numbers that follow the same pattern or relationship as the given sets: (13, 16, 21) and (28, 34, 45). We need to find the mathematical operations connecting the numbers within these sets and then apply the same logic to the given options.
The patterns \(+3, +5\) and \(+6, +11\) are different. Let's re-examine the relationship. Perhaps there's a different pattern or a common underlying logic. Let's try to find a relationship between the differences themselves or a relationship involving the first and third numbers.
Let's consider the differences again:
This looks like a consistent pattern! The relationship is: if the numbers are \(A, B, C\), then \(B - A = X\) and \(C - B = Y\), where \(Y = 2X - 1\).
C) (37, 18, 46)
Let's re-examine the original sets. It seems I made a mistake in the analysis of the given sets. The numbers are \(A, B, C\).
The pattern of differences is not directly \(+X\) and \(+(2X-1)\) as \(5 \neq 2 \times 3 - 1\) and \(11 \neq 2 \times 6 - 1\). My previous calculation was incorrect. Let's re-evaluate.
Let's look for a different pattern. What if the pattern involves the sum or product of the first two numbers, or some other combination?
Consider the relationship between the first and third numbers, or the sum of the first two numbers.
Let's look at the differences again:
There doesn't seem to be a simple arithmetic progression in the differences. Let's try to find a relationship between the first number and the differences.
What if the pattern is related to the sum of digits? The problem explicitly states: "Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.\
The question asks to identify the plant part that primarily stores food. We need to recall the functions of different plant parts to determine which one is specialized for food storage.
B) Root — Roots are specialized organs for absorbing water and nutrients, but many plants also use their roots as primary storage sites for carbohydrates (food) produced during photosynthesis. Examples include carrots, radishes, sweet potatoes, and beets, which are all root vegetables known for their stored food reserves.
An electric pump can fill a tank in 5 hours. Due to a leakage in the tank, it takes 7\( \frac{1}{2} \) hours to fill the full tank. How much time will its leakage take to empty the full tank if water does not get in or out of the tank through any other point during this period?
This problem involves concepts of work and time, specifically dealing with pipes and cisterns. We will calculate the rate of work (filling or emptying) for the pump and the net rate when both the pump and leakage are active. From these rates, we can determine the time taken by the leakage alone to empty the tank.
The pump fills the tank in 5 hours. So, in 1 hour, the pump fills \(\frac{1}{5}\) of the tank.
\[ \text{Pump's filling rate} = \frac{1}{5} \text{ tank/hour} \]Due to leakage, it takes \(7\frac{1}{2}\) hours to fill the tank. Convert this mixed fraction to an improper fraction:
\[ 7\frac{1}{2} = \frac{(7 \times 2) + 1}{2} = \frac{15}{2} \text{ hours} \]So, in 1 hour, the net filling (pump - leakage) is \[\frac{1}{\frac{15}{2}}\] of the tank.
\[ \text{Net filling rate} = \frac{2}{15} \text{ tank/hour} \]The net filling rate is the pump's filling rate minus the leakage rate. Let \(R_L\) be the leakage rate.
\[ \text{Pump's filling rate} - \text{Leakage rate} = \text{Net filling rate} \]\[ \frac{1}{5} - R_L = \frac{2}{15} \]Now, solve for \(R_L\):
\[ R_L = \frac{1}{5} - \frac{2}{15} \]Find a common denominator, which is 15:
\[ R_L = \frac{3}{15} - \frac{2}{15} \]\[ R_L = \frac{1}{15} \text{ tank/hour} \]This means the leakage empties \(\frac{1}{15}\) of the tank in 1 hour.
If the leakage empties \(\frac{1}{15}\) of the tank in 1 hour, then to empty the full tank (which is 1 unit), it will take the reciprocal of the leakage rate.
\[ \text{Time taken by leakage} = \frac{1}{\text{Leakage rate}} \]\[ \text{Time taken by leakage} = \frac{1}{\frac{1}{15}} = 15 \text{ hours} \]Correct Option: D) 15 hours
When numbers leave the same remainder upon division by a certain number, the differences between these numbers must be perfectly divisible by that number. Therefore, to find the largest such number, we need to find the Highest Common Factor (HCF) of the differences between the given numbers.
Correct Option: B) 4
In Fleming’s left-hand rule, the thumb, forefinger and centre finger respectively represent:
Direction of current, magnetic field and force experienced
Direction of force experienced, magnetic field and current
Direction of magnetic field, current and force experienced
Direction of magnetic field, force experienced and current
Fleming's left-hand rule is a mnemonic used in physics to determine the direction of the force on a current-carrying conductor placed in a magnetic field. It relates the directions of the magnetic field, the electric current, and the resulting force.
B) Direction of force experienced, magnetic field and current
This option correctly aligns the thumb with force, the forefinger with the magnetic field, and the centre finger with the current, as per Fleming's left-hand rule.