The question asks to identify the Nuclear Power Plant located in Uttar Pradesh from the given options. This requires knowledge of the geographical locations of major nuclear power plants in India.
Correct Option: C) Narora — The Narora Atomic Power Station (NAPS) is indeed located in Narora, Bulandshahr district, Uttar Pradesh. It is operated by the Nuclear Power Corporation of India Limited (NPCIL).
This problem can be solved by using the fundamental property of triangles: the sum of all angles in a triangle is always 180 degrees. We are given a relationship between two angles and the third angle, which we can use to set up an equation.
Let the three angles of the triangle \(\Delta ABC\) be \(\angle A\), \(\angle B\), and \(\angle C\).
According to the angle sum property of a triangle, the sum of its interior angles is 180 degrees:
\[ \angle A + \angle B + \angle C = 180^\circ \]The problem states that the sum of two angles, \(\angle A\) and \(\angle B\), is equal to the third angle, \(\angle C\). So, we can write this as:
\[ \angle A + \angle B = \angle C \]Now, substitute this relationship into the angle sum property equation from step 2:
\[ (\angle A + \angle B) + \angle C = 180^\circ \]Replace \((\angle A + \angle B)\) with \(\angle C\):
\[ \angle C + \angle C = 180^\circ \]Combine the terms involving \(\angle C\):
\[ 2 \angle C = 180^\circ \]Solve for \(\angle C\):
\[ \angle C = \frac{180^\circ}{2} \] \[ \angle C = 90^\circ \]Thus, the measure of the third angle is 90 degrees.
Correct Option: C) 90°
The question asks to identify the Indian NGO that received the UN's Equator Prize in 2019. This is a factual question related to current affairs and environmental awards, requiring knowledge of specific organizations and their achievements.
Correct Option: C) Deccan Development Society
The Deccan Development Society (DDS), based in Telangana, India, was one of the 22 winners of the prestigious UN Equator Prize in 2019. They were recognized for their innovative work in promoting biodiversity conservation, food security, and women's empowerment through traditional agricultural practices and millet farming.
We need to find the amount of gold in alloy C, given the amount of copper in C and the ratios of gold to copper in alloys A and B. Since equal quantities of alloys A and B are melted to form C, we can calculate the total amount of gold and copper in C by summing their respective amounts from A and B.
Determine the proportion of gold and copper in Alloy A:
The ratio of gold to copper in alloy A is 7:2. The total parts are \(7 + 2 = 9\).
Determine the proportion of gold and copper in Alloy B:
The ratio of gold to copper in alloy B is 7:11. The total parts are \(7 + 11 = 18\).
Calculate the total proportion of gold and copper in Alloy C:
Since equal quantities of A and B are melted, let's assume we take \(18x\) kg of alloy A and \(18x\) kg of alloy B (we choose 18 as it's the LCM of 9 and 18, simplifying calculations). The total quantity of alloy C will be \(18x + 18x = 36x\) kg.
Total gold in C: \(14x + 7x = 21x\) kg
Total copper in C: \(4x + 11x = 15x\) kg
Formulate the ratio of gold to copper in Alloy C:
The ratio of gold to copper in alloy C is \(21x : 15x\), which simplifies to \(7 : 5\).
Use the given information to find the amount of gold:
We are given that the amount of copper in C is 10 kg.
From the ratio \(7:5\), if 5 parts represent copper, then 7 parts represent gold.
If 5 parts of copper = 10 kg,
then 1 part = \(\frac{10}{5} = 2\) kg.
Amount of gold in C = 7 parts \(= 7 \times 2 = 14\) kg.
D) 14 kg
Find the simple interest on ₹3,000 at 6 \( \frac{1}{4} \)% p.a. for the period from 5 Feb 2005 to 18 April 2005, both dates included.
To calculate the simple interest, we first need to determine the exact number of days for which the interest is to be calculated. Then, we convert this period into years and use the simple interest formula: \(SI = \frac{P \times R \times T}{100}\).
The simple interest is ₹37.50.
B) ₹37.50 is the correct simple interest calculated based on the given principal, rate, and period.
Pradhan Mantri Matru Vandana Yojana was launched on:
1st Jan 2016
1st Jan 2015
1st Jan 2017
1st Jan 2018
The question asks for the launch date of the Pradhan Mantri Matru Vandana Yojana (PMMVY). This requires knowledge of specific government scheme launch dates, which is a common type of question in competitive exams.
C) 1st Jan 2017 is the correct launch date for the Pradhan Mantri Matru Vandana Yojana (PMMVY).
The problem requires us to calculate a series of multiplications involving fractions and a whole number. We need to convert the verbal descriptions like "tenths", "hundredths", and "thousandths" into their fractional or decimal equivalents and then perform the multiplication in the correct order.
The phrase "3 times of 3 tenths of 3 hundredths of 3 thousandths of 30" can be written as a product:
\[ 3 \times \left(\frac{3}{10}\right) \times \left(\frac{3}{100}\right) \times \left(\frac{3}{1000}\right) \times 30 \]We can multiply the numerators and denominators separately, or convert to decimals and multiply.
Using fractions:
\[ \text{Value} = 3 \times \frac{3}{10} \times \frac{3}{100} \times \frac{3}{1000} \times 30 \]\[ \text{Value} = \frac{3 \times 3 \times 3 \times 3 \times 30}{10 \times 100 \times 1000} \]\[ \text{Value} = \frac{81 \times 30}{1000000} \]\[ \text{Value} = \frac{2430}{1000000} \]To convert the fraction to a decimal, we divide the numerator by the denominator. Since the denominator is \(10^6\), we move the decimal point 6 places to the left from the end of the numerator.
\[ \text{Value} = 0.002430 \]\[ \text{Value} = 0.00243 \]A) 0.00243 is the correct result obtained from the calculation.
The question asks to identify the 'Father of Modern Genetics'. This requires knowledge of key figures in the history of genetics and their primary contributions.
Correct Option: C) Gregor Mendel is widely recognized as the 'Father of Modern Genetics' due to his pioneering work on inheritance patterns in pea plants, which laid the foundation for the science of genetics.
The problem involves finding the value of an expression given the LCM of two prime numbers. The key property to use here is that the LCM of two distinct prime numbers is simply their product. We will first find the two prime numbers by factoring the given LCM and then substitute them into the expression.
Understand the property of LCM for prime numbers: If \(x\) and \(y\) are two distinct prime numbers, their Least Common Multiple (LCM) is their product, i.e., \(\text{LCM}(x, y) = x \times y\).
Use the given information: We are given that \(x\) and \(y\) are prime numbers, \(x > y\), and \(\text{LCM}(x, y) = 319\).
Formulate the equation: Based on the property, we have \(x \times y = 319\).
Find the prime factors of 319: We need to find two prime numbers whose product is 319. Let's try dividing 319 by small prime numbers:
Identify \(x\) and \(y\): Both 11 and 29 are prime numbers. Since it's given that \(x > y\), we have \(x = 29\) and \(y = 11\).
Calculate the value of the expression: We need to find the value of \(2x - 5y\).
\[ 2x - 5y = 2(29) - 5(11) \] \[ = 58 - 55 \] \[ = 3 \]Correct Option: D) 3
The question asks to identify the mountain pass that serves as a tri-junction point for India, China, and Myanmar. This requires knowledge of the geographical locations of various mountain passes in the Himalayas and their international borders.
Correct Option: A) Diphu Pass is a mountain pass located at the tri-junction of India (Arunachal Pradesh), China, and Myanmar. It is an important strategic pass in the eastern Himalayas.