To calculate the compound interest when compounded half-yearly, we need to adjust the annual interest rate and the time period. The annual rate is halved, and the number of compounding periods is doubled for the given time. Then, we use the compound interest formula or calculate it step-by-step for each half-year.
Since the interest is compounded half-yearly, the annual rate is divided by 2, and the number of periods is multiplied by 2.
The formula for the amount (\(A\)) with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]Compound Interest is the difference between the Amount and the Principal.
\[ CI = A - P \]\[ CI = 1210 - 1000 \]\[ CI = \text{₹}210 \]C) ₹210 is the correct compound interest calculated for ₹1,000 at 20% per annum for 1 year compounded half-yearly.
Find the value of \(\frac{1+\sqrt{3}}{1-\sqrt{3}}+\frac{1-\sqrt{3}}{1+\sqrt{3}}\).
To find the value of the given expression, we will first rationalize each fraction by multiplying the numerator and denominator by the conjugate of the denominator. Then, we will add the two simplified fractions.
Correct Option: A) -4
The question asks to identify the two places connected by National Waterway-2 (NW-2). This requires knowledge of the major National Waterways in India and the specific stretches of rivers they cover.
National Waterway-2 (NW-2) is located on the Brahmaputra River. It connects Sadiya in the eastern part of Assam to Dhubri in the western part of Assam. This waterway is crucial for transportation in the North-Eastern region of India.
Correct Option: D) Sadiya and Dhubri are the two places connected by National Waterway-2, which is on the Brahmaputra River.
This problem involves the relationship between the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers. A fundamental property states that the product of two numbers is equal to the product of their LCM and HCF. We will use this property to find the unknown second number.
Identify the given values:
Recall the fundamental property:
The product of two numbers is equal to the product of their LCM and HCF.
Substitute the given values into the formula:
\[ 12 \times \text{Second Number} = 60 \times 3 \]Calculate the product of LCM and HCF:
\[ 60 \times 3 = 180 \]Set up the equation to find the Second Number:
\[ 12 \times \text{Second Number} = 180 \]Solve for the Second Number:
\[ \text{Second Number} = \frac{180}{12} \]Perform the division:
\[ \text{Second Number} = 15 \]Correct Option: C) 15
A alone can finish a task in 10 days and B alone can finish the same task in 20 days. In how many days can A and B working together finish this task?
6 \( \frac{2}{3} \) days
6 \( \frac{1}{3} \) days
6 \( \frac{1}{2} \)days
6 days
To solve this problem, we will calculate the individual work rates of A and B. The work rate is the reciprocal of the time taken to complete the task. Then, we will add their individual work rates to find their combined work rate. Finally, the reciprocal of the combined work rate will give us the total time taken for A and B to complete the task together.
Correct Option: A) 6 \( \frac{2}{3} \) days
The question asks to identify the 'father of modern science'. This requires knowledge of key figures in the history of science and their contributions to the scientific method and understanding of the universe.
Correct Option: A) Galileo Galilei is widely regarded as the 'father of modern science' due to his significant contributions to physics, astronomy, and the development of the scientific method, emphasizing observation, experimentation, and mathematical analysis.
The question asks for the definition of a Visual Display Unit (VDU). We need to identify which of the given options correctly represents a VDU in the context of computer hardware.
Correct Option: B) Monitor — A Visual Display Unit (VDU) is another term for a computer monitor. It is the most common output device used to display visual information to the user.
Select the Venn diagram that best represents the relationship between the following classes. Mammals, Amphibians, Blue Whale.
To determine the correct Venn diagram representing the relationship between the classes "Mammals," "Amphibians," and "Blue Whale," we need to understand the classification of these categories.
Correct Option: D) The diagram shows two circles: one circle (Mammals) contains a smaller circle (Blue Whale), and a separate circle represents Amphibians.
Pradhan Mantri Jan Dhan Yojana was launched on:
28th Aug 2015
15th Aug 2014
15th Aug 2015
28th Aug 2014
The question asks for the launch date of the Pradhan Mantri Jan Dhan Yojana (PMJDY). This requires knowledge of important government schemes and their inception dates, which is a common topic in competitive exams.
Correct Option: D) 28 th Aug 2014
The Pradhan Mantri Jan Dhan Yojana (PMJDY) was officially launched on August 28, 2014. It aims to provide universal access to banking facilities with at least one basic banking account for every household, financial literacy, access to credit, insurance, and pension facilities.
The problem asks us to identify which of the given four codes for the word JUNCTION is used to code CUSTOMER as XFHGLNVI. We need to analyze the pattern in each of the four codes provided for JUNCTION and then apply the same pattern to CUSTOMER to see which one matches XFHGLNVI.
C) Code 1 uses the pattern where each letter is replaced by its opposite letter in the alphabet (sum of alphabetical positions is 27). Applying this rule to CUSTOMER yields XFHGLNVI, which matches the given coded word.
