Fill in the blank:
0, 2, 6, _____ , 20, 30, 42
To find the missing number in the given series, we need to identify the pattern or rule that governs the sequence of numbers. We will look for differences between consecutive terms, squares, cubes, or other mathematical relationships.
Alternatively, we can observe that each term can be represented as \(n(n+1)\) for \(n = 0, 1, 2, 3, \dots\):
Both methods confirm that the missing term is 12.
Correct Option: A) 12
Which of the following States hosted the 35th National Games in 2015?
The question asks to identify the state that hosted the 35th National Games of India in 2015. This is a factual question related to sports events in India, requiring knowledge of the host cities/states for major national competitions.
Correct Option: C) The 35th National Games were indeed hosted by the state of Kerala in 2015. The event took place across seven districts of Kerala: Thiruvananthapuram, Kollam, Alappuzha, Kochi, Thrissur, Kozhikode, and Kannur.
The question asks about the characteristics of a car moving with constant acceleration on a straight road. We need to understand the definitions of velocity and acceleration to determine the correct statement.
D) Velocity of the car is constantly changing. If a car has a constant non-zero acceleration, its velocity must be changing continuously. For example, if acceleration is \(2 \text{ m/s}^2\), the velocity increases by \(2 \text{ m/s}\) every second.
The question asks for the full form of the acronym UNHCR. This is a common acronym for an international organization, and knowing such full forms is important for competitive exams.
Correct Option: C) United Nations High Commissioner for Refugees
UNHCR is the United Nations High Commissioner for Refugees. It is a UN agency mandated to protect and support refugees at the request of a government or the UN itself and assists in their voluntary repatriation, local integration, or resettlement to a third country.
The question asks to identify the CEO of the Food Safety and Standards Authority of India (FSSAI) appointed in December 2015. This is a factual question related to appointments in statutory bodies, which is common in competitive exams.
In December 2015, Pawan Kumar Agarwal was appointed as the Chief Executive Officer (CEO) of the Food Safety and Standards Authority of India (FSSAI).
D) Pawan Kumar Agarwal was appointed as the new CEO of FSSAI in December 2015. He succeeded Yudhvir Singh Malik.
To find the gain percentage, we first need to calculate the gain (profit) by subtracting the cost price from the selling price. Then, we use the formula for gain percentage, which is \[\frac{\text{Gain}}{\text{Cost Price}} \times 100\%\].
Gain is the difference between the Selling Price and the Cost Price.
\[ \text{Gain} = \text{SP} - \text{CP} \]\[ \text{Gain} = \text{Rs. } 30 - \text{Rs. } 25 \]\[ \text{Gain} = \text{Rs. } 5 \]The formula for gain percentage is:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100\% \]\[ \text{Gain Percentage} = \left( \frac{5}{25} \right) \times 100\% \]\[ \text{Gain Percentage} = \left( \frac{1}{5} \right) \times 100\% \]\[ \text{Gain Percentage} = 0.2 \times 100\% \]\[ \text{Gain Percentage} = 20\% \]Correct Option: A) 20%
The question asks to identify the largest volcano on Earth in terms of mass and footprint as of 2017. This requires knowledge of major volcanic structures and their classifications.
Correct Option: C) Tamu Massif
The Tamu Massif, located in the Pacific Ocean, was identified in 2013 as a single, massive shield volcano. Its footprint covers an area of approximately \(310,000\) square kilometers (\(120,000\) square miles), making it comparable in size to the state of New Mexico in the USA or the British Isles. Its immense size, both in terms of area and estimated mass, led scientists to declare it the largest single volcano on Earth. While it is now considered an extinct submarine volcano, its discovery significantly changed the understanding of Earth's largest volcanic structures.
To divide a total amount in a given ratio, first find the sum of the ratio parts. Then, determine the value of one ratio unit by dividing the total amount by the sum of the ratio parts. Finally, multiply this unit value by each part of the ratio to find the individual shares.
Total amount to be divided = Rs. 169
Ratio = 2:5:6
Sum of ratio parts \( = 2 + 5 + 6 = 13 \)
One ratio unit \[= \frac{\text{Total amount}}{\text{Sum of ratio parts}}\]
\( = \frac{169}{13} \)
\( = 13 \)
So, one unit of the ratio is equal to Rs. 13.
Thus, the amounts are Rs. 26, Rs. 65, and Rs. 78.
\( 26 + 65 + 78 = 169 \)
This matches the total amount, confirming the calculations are correct.
B) 26, 65 & 78
The problem uses a direct letter-to-digit coding scheme. We need to identify the code for each letter present in the given words and then apply this scheme to the target word "PEARL".
Correct Option: C) 53269
The question asks to identify the category of numbers that includes all irrational numbers. We need to understand the definitions of different number systems and their relationships.
Correct Option: D) real. All irrational numbers are a part of the set of real numbers. The set of real numbers is composed of the union of rational numbers and irrational numbers.