Select the incorrect statement/s.
A. The value of 'g' depends on the mass and radius of the earth.
B. The ratio of the gravitational force exerted by the earth on the moon to that exerted by the moon on the earth is 1 : 6.
C. The SI unit of G is N m2/kg2.
The question asks to identify the incorrect statement among the given options related to gravity. We need to evaluate each statement based on the principles of gravitation.
The question asks to identify the 41st Prime Minister of Nepal from the given options. This requires knowledge of recent political history and leadership changes in Nepal.
Correct Option: B) K.P. Sharma Oli was sworn in as the 41st Prime Minister of Nepal on February 15, 2018, after his party, the CPN-UML, emerged as the largest party in the 2017 general elections.
The question asks for the maximum optimal value of the Least Common Multiple (LCM) of any three given numbers. To find the maximum possible LCM, we need to consider the conditions under which the LCM of numbers is maximized.
B) Product of all three numbers
This is correct because the LCM of three numbers is maximized when the numbers are pairwise coprime. In this case, their LCM is equal to their product. If they share common factors, their LCM will be less than their product.
Mendel's Law of Purity of Gametes, also known as the Law of Segregation, states that during gamete formation, the two alleles for a heritable character separate or segregate from each other such that each gamete receives only one allele. This law was formulated based on observations from specific genetic crosses.
D) Monohybrid Cross — Mendel's Law of Purity of Gametes (Law of Segregation) was formulated based on the results of his monohybrid crosses, which demonstrated that alleles for a trait separate during gamete formation.
Complete the series by choosing the missing term from the given alternatives:
AZZ, BBYYY, CCCXXXX, ________
The problem asks us to complete a letter series by identifying the pattern in the given terms. We need to analyze the changes in the letters and their repetitions from one term to the next.
Based on the analysis, the missing term should be 'DDDDWWWWW'.
Correct Option: C) DDDDWWWWW
The question asks to identify which of the given metals can be easily cut with a knife. This property is related to the softness and malleability of the metal. We need to recall the general properties of the listed metals.
D) Sodium — Sodium is an alkali metal, which is known for its extreme softness. It can be easily cut with a knife, revealing a silvery luster that quickly dulls due to oxidation.
What will be the value of \( \sqrt{183184} \)?
To find the square root of a large number like \(183184\), we can use the long division method for square roots or estimation combined with checking the last digit. The long division method is precise, while estimation helps narrow down the options quickly.
We group the digits as \(18 \ 31 \ 84\).
Step 1: Find the largest number whose square is less than or equal to \(18\). This is \(4\) (\(4^2 = 16\)). Write \(4\) as the first digit of the square root. Subtract \(16\) from \(18\), leaving \(2\).
\[ \begin{array}{r} 4 \\ \sqrt{18 \ 31 \ 84}\\ -16 \\ \hline 2 \end{array} \]Step 2: Bring down the next pair of digits, \(31\), to make the new dividend \(231\). Double the current quotient (\(4 \times 2 = 8\)). Now, find a digit \(x\) such that \(8x \times x \le 231\).
Step 3: Bring down the next pair of digits, \(84\), to make the new dividend \(6784\). Double the current quotient (\(42 \times 2 = 84\)). Now, find a digit \(y\) such that \(84y \times y \le 6784\). We know the last digit of the original number is \(4\), so the last digit of the square root must be \(2\) or \(8\). Since \(84y\) is in the \(840\)s, let's try \(y=8\). \[ 848 \times 8 = 6784 \] This matches perfectly. Write \(8\) as the third digit of the square root. Subtract \(6784\) from \(6784\), leaving \(0\).
\[ \begin{array}{r} 428 \\ \sqrt{18 \ 31 \ 84}\\ -16 \\ \hline 2 \ 31 \\ -1 \ 64 \\ \hline 67 \ 84 \\ -67 \ 84 \\ \hline 0 \end{array} \]Thus, the square root of \(183184\) is \(428\).
Correct Option: C) 428
The cost of 28\( \frac{1}{2} \) metres of cloth is Rs. 1,254. What will be the cost of 8\( \frac{3}{4} \) metres of cloth?
The problem can be solved by first finding the cost per meter of cloth and then multiplying it by the desired length of cloth. This involves converting mixed fractions to improper fractions, performing division to find the unit cost, and then multiplication to find the final cost.
Correct Option: D) Rs. 385
The missing number in the sequence will be:
16, 32, 64, 128, 256, ________, 1024, 2048
The problem presents a sequence of numbers and asks to find the missing number. We need to identify the pattern or rule governing the sequence to determine the missing term.
Therefore, the missing number is 512.
Correct Option: D) 512
The least fractional value of 4.025 will be equal to which of the following?
\( \frac{161}{40} \)
\( \frac{116}{20} \)
\( \frac{161}{20} \)
\( \frac{116}{40} \)
To find the least fractional value of a decimal number, we need to convert the decimal into a fraction and then simplify it to its lowest terms. This involves expressing the decimal as a fraction with a power of 10 in the denominator and then finding the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction.
A) \( \frac{161}{40} \) is the simplified fraction obtained by converting \(4.025\) to a fraction and reducing it to its lowest terms.