This is an analogy question. We need to identify the relationship between the first pair of words and then find a word that shares the same relationship with the third word.
Correct Option: C) Modern — "Contemporary" is to "Historic" as "Modern" is to "Ancient". Both pairs represent a contrast between the present/recent past and the distant past.
Project Loon is a research project by ______ for providing internet access to rural and remote areas using high-altitude helium-filled balloons. (as of 2016)
The question asks to identify the company behind "Project Loon," a research project aimed at providing internet access to rural and remote areas using high-altitude helium-filled balloons, specifically as of 2016.
A) Google — Project Loon was indeed a research and development project by Google (under its parent company Alphabet's X division) aimed at providing internet access to remote and rural areas using high-altitude balloons. It was launched in 2013 and was active in 2016.
The question asks to identify the communication satellite launched by India in November 2015. This requires knowledge of specific satellite launches by ISRO (Indian Space Research Organisation) around that time.
ISRO launched GSAT-15, a communication satellite, on November 11, 2015, from Kourou, French Guiana, using an Ariane 5 rocket. It was designed to provide C-band and Ku-band services.
B) GSAT-15 was indeed a communication satellite launched by India (ISRO) on November 11, 2015. It was launched aboard an Ariane 5 rocket from Kourou, French Guiana.
We are given the HCF of two numbers and two other factors of their LCM. We need to find the smaller of the two numbers. We can use the relationship between HCF, LCM, and the two numbers, along with the properties of factors.
Let's verify the LCM: \(L = Hxy = 4 \times 5 \times 7 = 140\). The factors of LCM are \(4, 5, 7\). The "two other factors" refer to \(x\) and \(y\).
Also, \(A \times B = \text{HCF} \times \text{LCM}\) \(20 \times 28 = 4 \times 140\) \(560 = 560\). This confirms our numbers are correct.
C) 20
The question asks for the capital city of the Indian state of Nagaland. This is a factual question related to Indian geography and general knowledge. To answer this, one needs to recall the administrative capitals of Indian states.
Nagaland is one of the northeastern states of India. Its capital city is Kohima.
B) Kohima is the capital city of Nagaland.
This problem involves work and time. We can solve it by calculating the individual work rates of E and F and then using the combined work rate formula.
If E and F together complete the work in 10 days, their combined work rate (amount of work done per day) is:
\[ \text{Work rate of (E + F)} = \frac{1}{10} \text{ work/day} \]If E alone completes the work in 30 days, E's individual work rate is:
\[ \text{Work rate of E} = \frac{1}{30} \text{ work/day} \]The combined work rate is the sum of individual work rates. So, we can find F's work rate by subtracting E's work rate from the combined work rate:
\[ \text{Work rate of F} = \text{Work rate of (E + F)} - \text{Work rate of E} \]\[ \text{Work rate of F} = \frac{1}{10} - \frac{1}{30} \]To subtract the fractions, find a common denominator, which is 30.
\[ \text{Work rate of F} = \frac{3}{30} - \frac{1}{30} \]\[ \text{Work rate of F} = \frac{3 - 1}{30} \]\[ \text{Work rate of F} = \frac{2}{30} \]\[ \text{Work rate of F} = \frac{1}{15} \text{ work/day} \]If F's work rate is \(\frac{1}{15}\) work per day, it means F can complete the entire work in 15 days.
\[ \text{Days for F alone} = \frac{1}{\text{Work rate of F}} = \frac{1}{\frac{1}{15}} = 15 \text{ days} \]A) 15 days is the time F alone takes to complete the work.
The question asks to identify the founder of the Swaraj Party. This requires knowledge of key figures in the Indian independence movement and their associated political organizations.
Correct Option: B) Motilal Nehru was a co-founder of the Swaraj Party along with C.R. Das in 1923. They formed the party to contest elections to the legislative councils and carry on the struggle from within the system, differing from the 'No-Changers' within the Congress who advocated for constructive work outside the councils.
To simplify the given trigonometric expression, we will use fundamental trigonometric identities for angle transformations, specifically those involving \(\frac{\pi}{2}\) (or 90 degrees). We will convert terms like \(\cos(\theta - \frac{\pi}{2})\) and \(\sin(\theta + \frac{\pi}{2})\) into simpler forms involving \(\sin\theta\) or \(\cos\theta\) and then combine like terms.
Correct Option: A) \(\cos\theta - \sin\theta\)
The question asks to identify the founder of Banaras Hindu University (BHU), which completed 100 years in February 2016. This is a factual question related to Indian history and education.
Correct Option: B) Madan Mohan Malaviya is widely recognized as the founder of Banaras Hindu University (BHU). He established the university in 1916 with the support of many Indian princes and philanthropists.
The question asks to identify which of the given options is NOT a good conductor of electricity. This requires knowledge of common materials and their electrical conductivity properties. Good conductors allow electricity to pass through easily, while poor conductors (insulators) resist the flow of electricity.
Correct Option: A) Porcelain is a ceramic material and an excellent electrical insulator, meaning it does not conduct electricity well. It is often used in applications where electrical isolation is required, such as in high-voltage insulators.