The question asks about the country that assisted India in launching its first artificial satellite in 1975. This is a factual question related to India's space program history.
Correct Option: A) Soviet Union
The question asks for the specific field of study dedicated to the universe. We need to identify the correct term among the given options by understanding the definition of each term.
Correct Option: C) Cosmology is the scientific study of the origin, evolution, and eventual fate of the universe. It encompasses the study of celestial bodies, space, time, and the fundamental laws governing the cosmos.
The question asks to identify the leader of India's first expedition to Antarctica in 1982. This requires knowledge of significant historical scientific expeditions undertaken by India.
Correct Option: D) Dr. SZ Qasim was a distinguished Indian marine biologist who led India's first scientific expedition to Antarctica in 1981-82. This expedition successfully reached Antarctica on January 9, 1982, marking a significant milestone in India's scientific endeavors and establishing its presence in polar research.
The question asks to identify the pair that is NOT correctly matched between an instrument and a famous artist associated with it. This requires knowledge of prominent Indian classical musicians and the instruments they play.
Correct Option: A) Pakhawaj - Shiv Kumar Sharma. This pair is incorrectly matched because Shiv Kumar Sharma is famous for playing the Santoor, not the Pakhawaj.
To find the sum of even numbers between 1 and 111, we first need to identify the series of even numbers. Then, we can use the formula for the sum of an arithmetic progression or the specific formula for the sum of the first 'n' even numbers.
Substituting the values:
\[ 110 = 2 + (n-1)2 \]\[ 108 = (n-1)2 \]\[ \frac{108}{2} = n-1 \]\[ 54 = n-1 \]\[ n = 54 + 1 \]\[ n = 55 \]So, there are 55 even numbers between 1 and 111.Substituting the values:
\[ S_{55} = \frac{55}{2}(2 + 110) \]\[ S_{55} = \frac{55}{2}(112) \]\[ S_{55} = 55 \times 56 \]To calculate \(55 \times 56\):\(55 \times 56 = 55 \times (50 + 6) = 55 \times 50 + 55 \times 6 = 2750 + 330 = 3080\).
Alternatively, we can use the formula for the sum of the first 'n' even numbers, which is \(n(n+1)\). Since the series starts from 2 and goes up to 110, it represents the first 55 even numbers. Therefore, \(S_n = n(n+1)\).
\[ S_{55} = 55(55+1) \]\[ S_{55} = 55 \times 56 \]\[ S_{55} = 3080 \]C) 3080. The sum of the even numbers between 1 and 111 is 3080.
To find the ratio \((3a + 7b) : (6a - 3b)\) given the ratio \(a : b = 2 : 3\), we can express \(a\) and \(b\) in terms of a common constant \(k\). Then substitute these expressions into the given ratio and simplify.
Express \(a\) and \(b\) in terms of a constant:
Given that \(a : b = 2 : 3\), we can write this as a fraction:
\[ \frac{a}{b} = \frac{2}{3} \]This implies that \(a\) and \(b\) are in the proportion of 2 and 3. So, we can let:
\[ a = 2k \]\[ b = 3k \]where \(k\) is a non-zero constant.
Substitute these values into the expression \((3a + 7b) : (6a - 3b)\):
The expression we need to evaluate is \((3a + 7b) : (6a - 3b)\), which can also be written as a fraction:
\[ \frac{3a + 7b}{6a - 3b} \]Substitute \(a = 2k\) and \(b = 3k\) into this fraction:
\[ \frac{3(2k) + 7(3k)}{6(2k) - 3(3k)} \]Simplify the expression:
Perform the multiplications in the numerator and denominator:
\[ \frac{6k + 21k}{12k - 9k} \]Combine the terms in the numerator and denominator:
\[ \frac{27k}{3k} \]Cancel out the common term \(k\):
Since \(k\) is a non-zero constant, we can cancel it from the numerator and denominator:
\[ \frac{27}{3} \]Calculate the final ratio:
Divide 27 by 3:
\[ 9 \]So, the ratio is \(9 : 1\).
A) 9 : 1 — By substituting \(a=2k\) and \(b=3k\) into the given expression and simplifying, we arrive at the ratio \(9:1\).
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This stands for Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
First, evaluate the expression inside the parentheses:
\[ (3 \times 4 + 15 \div 3) \]Inside the parentheses, perform multiplication and division from left to right:
Multiplication: \(3 \times 4 = 12\)
Division: \(15 \div 3 = 5\)
So, the expression inside the parentheses becomes:
\[ (12 + 5) = 17 \]Substitute this value back into the original expression:
\[ 30 - 17 + 8 \times 3 \div 6 \]Next, perform multiplication and division from left to right in the remaining expression:
Multiplication: \(8 \times 3 = 24\)
Division: \(24 \div 6 = 4\)
The expression now is:
\[ 30 - 17 + 4 \]Finally, perform addition and subtraction from left to right:
Subtraction: \(30 - 17 = 13\)
Addition: \(13 + 4 = 17\)
D) 17 is the correct value obtained by following the order of operations.
This problem involves calculating the simple interest rate required for a sum of money to become four times its original value over a given period. We will use the formula for simple interest to solve this.
The Simple Interest is the difference between the Amount and the Principal.
\[ \text{SI} = A - P \]\[ \text{SI} = 4P - P \]\[ \text{SI} = 3P \]The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]We have \(\text{SI} = 3P\), \(T = 20\) years, and we need to find \(R\).
\[ 3P = \frac{P \times R \times 20}{100} \]We can cancel \(P\) from both sides of the equation (assuming \(P \neq 0\)).
\[ 3 = \frac{R \times 20}{100} \]\[ 3 = \frac{R}{5} \]\[ R = 3 \times 5 \]\[ R = 15\% \]Thus, the simple interest rate per annum is 15%.
D) 15% is the correct answer. The calculation shows that a 15% simple interest rate is required for the principal to quadruple in 20 years.
Find the value of (?)
61.2 × 36? × 302.4 × 251.3 = 305
The problem requires us to find the value of '?' in an equation involving exponents. The key to solving this is to express all numbers as powers of a common base, which in this case is 6 or 30, and then equate the exponents.
B) 0.7 is the correct value for '?'.
The question asks for the location of the National War Memorial, which was inaugurated by Prime Minister Narendra Modi. This is a factual question related to current affairs and national monuments in India.
Correct Option: B) The National War Memorial is located in New Delhi, the capital of India. It stands as a tribute to the soldiers who have served the nation.