This question tests general knowledge about prominent Indian sports personalities and their associated sports. To answer correctly, one needs to recall the sport Bembem Devi is famous for.
Correct Option: B) Football
If sin θ + cosec θ = 2, then find the value of sin2018 θ + cosec2018 θ
The problem provides an equation involving \(\sin \theta\) and \(\text{cosec } \theta\) and asks for the value of a similar expression with a high power. The key to solving this type of problem is to first find the value of \(\sin \theta\) (or \(\text{cosec } \theta\)) from the given equation. Since \(\text{cosec } \theta = 1/\sin \theta\), we can substitute this into the given equation to form a quadratic equation in terms of \(\sin \theta\).
Understand the given equation:
We are given the equation: \(\sin \theta + \text{cosec } \theta = 2\)
Substitute \(\text{cosec } \theta\):
Recall that \(\text{cosec } \theta = \frac{1}{\sin \theta}\). Substitute this into the given equation:
Form a quadratic equation:
Multiply the entire equation by \(\sin \theta\) (assuming \(\sin \theta \neq 0\), which must be true for \(\text{cosec } \theta\) to be defined):
Solve the quadratic equation:
This equation is a perfect square trinomial, which can be factored as:
Find \(\text{cosec } \theta\):
Since \(\sin \theta = 1\), then \[\text{cosec } \theta = \frac{1}{\sin \theta} = \frac{1}{1} = 1\].
Evaluate the required expression:
We need to find the value of \(\sin^{2018} \theta + \text{cosec}^{2018} \theta\).
Substitute the values of \(\sin \theta = 1\) and \(\text{cosec } \theta = 1\):
Correct Option: B) The value of \(\sin^{2018} \theta + \text{cosec}^{2018} \theta\) is 2. This is because the initial condition \(\sin \theta + \text{cosec } \theta = 2\) implies that \(\sin \theta = 1\). When \(\sin \theta = 1\), then \(\text{cosec } \theta = 1\). Any positive integer power of 1 is 1, so \(1^{2018} + 1^{2018} = 1 + 1 = 2\).
This problem involves the concept of work and time. We can calculate the total work in terms of "man-days". Then, we'll determine the work done before some men left and the remaining work. Finally, we'll find the time taken by the remaining men to complete the rest of the work.
Calculate the total work:
Given that 48 men can complete a work in 30 days.
Calculate the work done in the first 6 days:
48 men worked for 6 days.
Calculate the remaining work:
\[ \text{Remaining work} = \text{Total work} - \text{Work done in 6 days} \] \[ \text{Remaining work} = 1440 \text{ man-days} - 288 \text{ man-days} = 1152 \text{ man-days} \]Calculate the number of remaining workers:
After 6 days, 12 men left the work.
Calculate the time taken by remaining workers to complete the remaining work:
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Remaining men}} \] \[ \text{Days required} = \frac{1152 \text{ man-days}}{36 \text{ men}} = 32 \text{ days} \]B) 32 — The remaining work of 1152 man-days is completed by 36 men in 32 days.
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate the conclusions based on these diagrams. The key is to consider all possible valid diagrams for the statements.
B) Either I or II follows. This is because the two conclusions are contradictory and exhaustive. If "No bag is a paper" is true, then "Some bags are paper" must be false. If "Some bags are paper" is true, then "No bag is a paper" must be false. Given the statements, we cannot definitively say which one is true, but we know that one of them must be true.
When a number is rounded to a certain number of decimal places, it means the original number falls within a specific range. We need to determine this range for a number \(x\) that is 15.84 when rounded to two decimal places.
Correct Option: D) \(15.835 \le x < 15.845\)
This question tests knowledge of Mendelian genetics, specifically the dominant and recessive traits observed by Gregor Mendel in pea plants. To answer correctly, one must recall the specific characteristics Mendel studied and identify which one is recessive.
Correct Option: B) Wrinkled seed
Wrinkled seed shape is a recessive trait in pea plants, meaning it only appears when the plant inherits two copies of the allele for wrinkled seeds.
The problem asks us to find the measure of each angle in a quadrilateral where all four angles are equal. We will use the fundamental property that the sum of the interior angles of any quadrilateral is 360 degrees.
Correct Option: D) 90°
The question asks to identify the activist who received the Queen's Young Leader Award in 2017 for their work against hunger and malnutrition. This requires knowledge of prominent award recipients and their fields of work.
Correct Option: C) Ankit Kawatra is an Indian social entrepreneur who founded "Feeding India," an organization that redistributes excess food from events, hotels, and restaurants to feed the underprivileged. His efforts in fighting hunger and malnutrition earned him the Queen's Young Leader Award in 2017.
The question asks about the applicability of Newton's Universal Law of Gravitation. We need to recall the fundamental principle of this law to determine its scope.
Correct Option: D) Any pair of objects
The rise of Jainism and Buddhism saw religious unrest in India in the __________ century BC.
The question asks about the historical period when Jainism and Buddhism emerged, leading to religious unrest in India. This requires knowledge of ancient Indian history, specifically the timeline of major religious movements.
C) 6th century BC. Both Jainism, founded by Mahavira, and Buddhism, founded by Gautama Buddha, rose to prominence in the 6th century BC. This period was characterized by significant intellectual and religious ferment, as these new doctrines challenged existing Vedic rituals and social hierarchies, leading to what can be described as religious unrest.