This is a syllogism problem. We can solve it using Venn diagrams or by applying the rules of logical deduction. We will draw Venn diagrams for the given statements and then check if the conclusions logically follow from these diagrams.
Based on the statements, we can visualize concentric circles:
This implies a hierarchy: Chairs \(\subset\) Desks \(\subset\) Chalks \(\subset\) Boards.
Since all desks are chalks, and all chalks are boards, it logically follows that all desks are boards. If all desks are boards, then 'some boards are desks' must be true (as the set of desks is a subset of boards). This conclusion follows.
We know that all chairs are desks, and all desks are chalks. This means that all chairs are chalks. If all chairs are chalks, then 'some chalks are chairs' must be true (as the set of chairs is a subset of chalks). This conclusion follows.
Following the chain: All chairs are desks, all desks are chalks, and all chalks are boards. Therefore, all chairs are boards. If all chairs are boards, then 'some boards are chairs' must be true (as the set of chairs is a subset of boards). This conclusion follows.
D) All the conclusions follow. As determined in the step-by-step analysis, all three conclusions (I, II, and III) logically follow from the given statements.
The following chart shows the percentage of students enrolled in different streams in a university. The total number of students enrolled in the university is 15200. Study the chart and answer the question.
How many students are enrolled in Medical, Engineering, and Law streams taken together?
To find the total number of students enrolled in the Medical, Engineering, and Law streams, we need to calculate the sum of the percentages of these streams and then apply it to the total number of students in the university.
\[ \text{Total percentage} = 15\% + 11\% + 9\% = 35\% \]
\[ \text{Number of students} = \frac{35}{100} \times 15200 = 5320 \]
Therefore, the total number of students enrolled in Medical, Engineering, and Law streams is 5320.
Correct Option: B) 5320
The equation x2+7x+6=0 can be written as:
(x−1)(x−6)=0
(x+1)(x+6)=0
(x−1)(x+6)=0
(x+1)(x−6)=0
To write the given quadratic equation in factored form, we need to find two numbers that multiply to the constant term (6) and add up to the coefficient of the x term (7). This method is known as factoring by splitting the middle term.
This is the factored form of the given quadratic equation.
Correct Option: B) The factored form of the equation \(x^2 + 7x + 6 = 0\) is \((x+1)(x+6)=0\), as derived by finding two numbers (1 and 6) that multiply to 6 and add to 7.
To find the diameter of the cylinder, we first need to determine its radius. We can do this by using the formula for the volume of a cylinder, as the volume and height are given. Once the radius is found, the diameter can be calculated by doubling the radius.
The volume \(V\) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]where \(r\) is the radius of the base and \(h\) is the height of the cylinder.
Using the approximation \(\pi = \frac{22}{7}\):
\[ 5500 = \frac{22}{7} \times r^2 \times 70 \]Simplify the equation:
\[ 5500 = 22 \times r^2 \times 10 \] \[ 5500 = 220 r^2 \]Divide both sides by 220 to find \(r^2\):
\[ r^2 = \frac{5500}{220} \] \[ r^2 = \frac{550}{22} \] \[ r^2 = 25 \]Take the square root of both sides to find \(r\):
\[ r = \sqrt{25} \] \[ r = 5 \text{ m} \]The diameter \(D\) is twice the radius:
\[ D = 2r \] \[ D = 2 \times 5 \text{ m} \] \[ D = 10 \text{ m} \]A) 10 m is the correct diameter calculated from the given volume and height of the cylinder.
Study the given diagram carefully and answer the question. The numbers in different sections indicate the number of persons.
Which of the following statements is correct on the basis of the above diagram?
The number of coffee lovers who are both graduates and soldiers is 90.
The number of graduates who are also coffee lovers but not soldiers is 65.
The number of soldiers who are neither coffee lovers nor graduates is 193.
The number of soldiers who are also coffee lovers is 27.
The problem involves analyzing a Venn diagram to determine the correct statement about the groups of coffee lovers, graduates, and soldiers.
Correct Option: B) The number of graduates who are also coffee lovers but not soldiers is 65.
The equivalent fraction of 4.2222… is:
\(\frac{38}{100}\)
\(\frac{38}{9}\)
\(\frac{42}{99}\)
\(\frac{422}{99}\)
To convert a repeating decimal into a fraction, we can use an algebraic method. We assign the repeating decimal to a variable, multiply it by a power of 10 to shift the repeating part, and then subtract the original equation from the new one to eliminate the repeating digits.
B) The equivalent fraction of \(4.2222\ldots\) is \(\frac{38}{9}\).
The question asks to identify the field of study associated with Geomorphology, a branch of Physical Geography. We need to recall the definitions of different branches of geography and environmental sciences.
C) Study of landforms. Geomorphology is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or near the Earth's surface.
The question tests knowledge of basic chemical reactions, specifically oxidation and reduction reactions involving copper. We need to evaluate each statement based on known chemical properties of copper and its compounds.
D) Both the statements are true. As explained in the step-by-step analysis, heating copper powder in air forms black copper(II) oxide, and subsequently passing hydrogen gas over this heated black oxide reduces it back to reddish-brown copper metal.
The question asks to identify the state government that presented a "Children's Budget" for the first time as part of its annual financial plan in March 2022. This requires knowledge of recent state budget initiatives in India.
D) Madhya Pradesh. In March 2022, Madhya Pradesh became the first state in India to present a "Children's Budget" as part of its annual financial plan for the fiscal year 2022-23. This initiative aimed to ensure specific allocation and tracking of funds for child-centric programs and schemes.
This question asks to identify devices that operate based on the heating effect of electric current. We need to analyze each device listed and determine if its primary function relies on heat generated by electrical resistance.
Based on this analysis, both the incandescent lamp and the electric geyser rely on the heating effect of electric current for their primary function.
C) Both (i) and (ii) — As explained, both incandescent lamps and electric geysers utilize the heating effect of electric current to produce light and heat, respectively.