Five persons, P, Q, R, S and T travelled in different months of the same year viz. January, February, March, April and May.
R travelled in February. Only one person travelled between R and S. Only three people travelled between Q and T. T travelled in a month after S. Who among them travelled in May?
This is a logical reasoning problem involving arrangement. We need to deduce the travel month for each person based on the given clues and then identify who travelled in May. We will create a table or list of months and fill in the persons as we get definitive information.
| Month | Person |
|---|---|
| January | |
| February | R |
| March | |
| April | |
| May |
Since R is in February, S can be in April (February -> March -> April) or S can be in December (February -> January -> December), but December is not in the list of months. So S must be in April.
| Month | Person |
|---|---|
| January | |
| February | R |
| March | |
| April | S |
| May |
The available slots are January, March, May. If Q is in January, then there are three months (February, March, April) between January and May. So T would be in May. If Q is in March, there are only two months (April, May) after it, so T cannot be placed with three people between them. If Q is in May, there are no months after it. Thus, Q must be in January and T in May.
| Month | Person |
|---|---|
| January | Q |
| February | R |
| March | |
| April | S |
| May | T |
From our current arrangement, S is in April and T is in May. May comes after April, so this condition is satisfied.
The only remaining person is P and the only remaining month is March.
| Month | Person |
|---|---|
| January | Q |
| February | R |
| March | P |
| April | S |
| May | T |
Correct Option: C) T
The question describes a unicellular organism with specific characteristics: a definite shape, a fixed feeding spot, and movement of food using cilia. We need to identify the organism that matches these features from the given options.
Correct Option: A) Paramecium is a unicellular organism with a definite, slipper-like shape. It has an oral groove lined with cilia that sweep food particles (like bacteria and detritus) into a fixed feeding spot called the cytostome (cell mouth). The cilia are also used for locomotion. All the characteristics mentioned in the question accurately describe Paramecium.
The question asks for the period covered by India's First Five Year Plan and its primary focus. To answer this, one needs to recall the historical timeline of India's Five Year Plans and their objectives.
Correct Option: D) 1951 to 1956
India's First Five Year Plan was indeed implemented from 1951 to 1956. Its main objective was to address the problems arising from partition and the food crisis, hence it prioritized the development of the primary sector, particularly agriculture, along with irrigation and power projects.
The question asks about the gases evolved during the complete decomposition of ferrous sulphate crystals. This is a classic example of a thermal decomposition reaction. We need to recall the balanced chemical equation for the thermal decomposition of ferrous sulphate to identify the gaseous products.
Correct Option: A) Both SO₂ and SO₃
During the complete thermal decomposition of ferrous sulphate, it breaks down into ferric oxide (\(\text{Fe}_2\text{O}_3\)), sulphur dioxide (\(\text{SO}_2\)), and sulphur trioxide (\(\text{SO}_3\)). Both \(\text{SO}_2\) and \(\text{SO}_3\) are gases.
This problem can be solved by using the fundamental relationship between the product of two numbers, their Highest Common Factor (HCF), and their Least Common Multiple (LCM). The relationship states that for any two positive integers, the product of the numbers is equal to the product of their HCF and LCM.
Product of the two numbers \( = 25 \)
HCF of the two numbers \( = 5 \)
For any two numbers, say \(a\) and \(b\), the following relationship holds:
\[ a \times b = \text{HCF}(a, b) \times \text{LCM}(a, b) \]Let the two numbers be \(a\) and \(b\). We are given \(a \times b = 25\) and \(\text{HCF}(a, b) = 5\). Let \(\text{LCM}(a, b) = L\).
\[ 25 = 5 \times L \]To find \(L\), divide the product of the numbers by their HCF:
\[ L = \frac{25}{5} \]\[ L = 5 \]If the HCF is 5, both numbers must be multiples of 5. If the product is 25, the only pair of positive integers that are multiples of 5 and multiply to 25 is \(5\) and \(5\).
For numbers 5 and 5:
This confirms our calculated LCM is correct.
Correct Option: D) 5 — The LCM of the two numbers is 5, as calculated using the formula \(\text{Product} = \text{HCF} \times \text{LCM}\).
Select the combination of letters that when placed from left to right in the same sequence in the blanks of the given series will complete the series.
XY_YZ, _XYY, _ABXY, _ZAB, YYZA
Find the area of a trapezium (in sq. units) with parallel sides of length 3 units and 5 units and the shortest distance between its parallel sides is 6 units.
To find the area of a trapezium, we use the standard formula which involves the lengths of its parallel sides and the perpendicular distance between them (height).
C) 24 is the correct answer because, by applying the formula for the area of a trapezium with the given dimensions, the calculated area is 24 square units.
Which is the correct formula for median of grouped data?
Consider:
L = lower limit of median class
CFâ‚€ = cumulative frequency of preceding class
F = frequency of median class
H = class width
N = the total of frequency
\(\frac{\frac{N}{2}-CF_0}{F}\times H\)
\(L+\frac{\frac{N}{2}-CF_0}{F}\times H\)
\(L+\frac{\frac{N}{2}-CF_0}{F}\)
\(L+\frac{N}{2}-CF_0-F\times H\)
The question asks for the correct formula to calculate the median of grouped data. The median for grouped data is found using a specific formula that involves the lower limit of the median class, the cumulative frequency of the preceding class, the frequency of the median class, the class width, and the total frequency. We need to identify the formula that correctly combines these components.
B) \[L+\frac{\frac{N}{2}-CF_0}{F}\times H\] — This option perfectly matches the standard formula for calculating the median of grouped data. It correctly adds the lower limit of the median class to the product of the class width and the ratio of the difference between half the total frequency and the cumulative frequency of the preceding class, to the frequency of the median class.
To find the missing number in the series, we need to identify the pattern or the rule governing the sequence of numbers. We will examine the differences between consecutive terms to find a consistent progression.
Thus, the missing number in the series is 127.
Correct Option: B) 127
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate each conclusion based on these diagrams. We must assume the statements are true, even if they contradict common knowledge.
C) Only conclusions I and III follow. Both conclusions I and III are logically derived from the given statements.