To determine how many times the hands of a clock are at right angles in a week, we first need to calculate the frequency of this event in a 12-hour period, then extend it to a 24-hour day, and finally to a full week.
A) 308 â The hands of a clock are at right angles 22 times in 12 hours, and thus 44 times in 24 hours. Over 7 days (a week), this occurs \(44 \times 7 = 308\) times.
This problem involves calculating simple interest for two different scenarios and then equating them to find the ratio of the principal amounts. The formula for simple interest is \(SI = \frac{P \times R \times T}{100}\), where \(P\) is the principal, \(R\) is the rate of interest per annum, and \(T\) is the time in years.
Calculate Simple Interest for the first investment:
Principal (\(P_1\)) = âšx
Rate (\(R_1\)) = 8% per annum
Time (\(T_1\)) = 5 years
Simple Interest (\(SI_1\)) is given by:
\[ SI_1 = \frac{x \times 8 \times 5}{100} = \frac{40x}{100} = \frac{2x}{5} \]Calculate Simple Interest for the second investment:
Principal (\(P_2\)) = âšy
Rate (\(R_2\)) = 7.5% per annum
Time (\(T_2\)) = 6 years
Simple Interest (\(SI_2\)) is given by:
\[ SI_2 = \frac{y \times 7.5 \times 6}{100} \]\[ SI_2 = \frac{y \times \frac{15}{2} \times 6}{100} \]\[ SI_2 = \frac{y \times 15 \times 3}{100} = \frac{45y}{100} = \frac{9y}{20} \]Equate the two simple interests:
According to the problem, \(SI_1 = SI_2\).
\[ \frac{2x}{5} = \frac{9y}{20} \]Find the ratio x : y:
To find the ratio \(x : y\), we rearrange the equation:
\[ \frac{x}{y} = \frac{9}{20} \times \frac{5}{2} \]\[ \frac{x}{y} = \frac{9 \times 5}{20 \times 2} \]\[ \frac{x}{y} = \frac{45}{40} \]\[ \frac{x}{y} = \frac{9}{8} \]Therefore, \(x : y = 9 : 8\).Correct Option: C) 9 : 8
Select the most appropriate term for the given set of items. 
The question asks for the most appropriate term that categorizes the given set of items shown in the diagram. The diagram includes images of a sun with clouds, a cloud with lightning, and a snowman.
Correct Option: C) Seasons
The chart shows men and women's average daily earning in company X. The difference between the average daily earning between men and women over the successive years is:
decreasing
equal
increasing
both, increasing and decreasing in different years
To determine the trend in the difference between men's and women's average daily earnings over successive years, we need to analyze the data presented in the bar chart.
Correct Option: C) increasing
Select the option that means 'Big Clever Parrot' according to the following Venn diagram.
To solve this problem, we need to identify the region in the Venn diagram that represents the intersection of all three categories: 'Big', 'Clever', and 'Parrot'. Each shape in the diagram corresponds to one of these categories.
Therefore, the correct option that represents 'Big Clever Parrot' is the region labeled 'C'.
Correct Option: C) C
To determine the number of valence electrons in an atom, we need to know its atomic number, which allows us to write its electronic configuration. Valence electrons are the electrons in the outermost shell of an atom.
Therefore, an atom of phosphorus has 5 valence electrons.
D) 5 â As determined from its electronic configuration, phosphorus has 5 electrons in its outermost shell (the third shell), making them its valence electrons.
Select the option that depicts the correct mirror image of the following figure if the mirror is placed at MN.
To determine the correct mirror image of a figure, we need to consider how each element of the figure would appear if reflected across the specified line. The mirror image is essentially a lateral inversion of the original figure.
Correct Option: B) The mirror image correctly swaps the positions of the heart, arrow, and rectangle, maintaining their orientations as per the original figure.
To determine the work done, we need to understand the definition of work in physics. Work is done when a force causes a displacement in the direction of the force. If there is no displacement, or if the displacement is perpendicular to the force, no work is done.
Even if the passenger were walking horizontally, the work done by the passenger on the suitcase against gravity would still be zero because the force (upwards) would be perpendicular to the displacement (horizontal), making \(\theta = 90^\circ\) and \(\cos(90^\circ) = 0\).
A) 0 J â As calculated, since there is no displacement of the suitcase while the passenger is standing, the work done is 0 Joules.
The question asks to identify the host country for the 2018 Asian Games. This is a factual question related to major international sporting events, which is a common topic in general knowledge sections of competitive exams.
Correct Option: C) Indonesia was indeed the host country for the 2018 Asian Games, with events primarily held in Jakarta and Palembang.
Select the option that fits in the blank space in the following figure.
The question involves selecting the correct pattern to complete the given figure. Observing the arrangement and orientation of lines and curves is crucial to solving this type of problem.
Correct Option: D) The pattern correctly completes the figure by aligning the diagonal lines and curve with the existing sections.
