\(1\frac{1}{2}\div3\frac{1}{4}\) =
\( \frac{13}{6} \)
\( \frac{6}{13} \)
4 \( \frac{12}{11} \)
4 \( \frac{11}{12} \)
To solve this problem, we need to perform division with mixed fractions. The general approach involves converting mixed fractions into improper fractions, then performing the division by multiplying the first fraction by the reciprocal of the second fraction.
Convert the first mixed fraction to an improper fraction:
\[ 1\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]Convert the second mixed fraction to an improper fraction:
\[ 3\frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]Rewrite the division problem using the improper fractions:
\[ \frac{3}{2} \div \frac{13}{4} \]To divide by a fraction, multiply by its reciprocal:
The reciprocal of \( \frac{13}{4} \) is \( \frac{4}{13} \).
\[ \frac{3}{2} \times \frac{4}{13} \]Multiply the numerators and the denominators:
\[ \frac{3 \times 4}{2 \times 13} = \frac{12}{26} \]Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[ \frac{12 \div 2}{26 \div 2} = \frac{6}{13} \]Correct Option: B) \( \frac{6}{13} \)
The question asks to identify the author of the classical Sanskrit drama 'Mrichakatika'. This requires knowledge of prominent ancient Indian playwrights and their works.
Correct Option: B) Sudraka is widely credited as the author of 'Mrichakatika' (The Little Clay Cart), a significant work in Sanskrit drama. It is a prakarana (play of manners) that provides insights into urban life in ancient India.
The question asks for the specific term used to denote the mean distance from the Sun to the Earth. This is a fundamental unit in astronomy for measuring distances within our solar system.
C) Astronomical unit
An Astronomical Unit (AU) is defined as the mean distance from the center of the Earth to the center of the Sun. Its value is approximately \(1.496 \times 10^{11}\) meters or about 150 million kilometers. It is primarily used for measuring distances within our solar system.
The question asks for the chemical classification of fats and oils. We need to identify the correct organic compound class to which they belong.
Correct Option: A) Triglycerides are the primary chemical form of fats and oils. They are esters derived from glycerol and three fatty acids.
The question asks to identify the protein that is found abundantly in eggs. This requires knowledge of common proteins and their primary sources.
B) Albumin — Albumin is the most abundant protein in egg white, making up about 54% of the egg's total protein content. It is a high-quality protein, rich in essential amino acids, and is easily digestible.
[17.98 ÷ 6.2] + [10.8 ÷ 0.5] − [0.96 ÷ 0.8] =
To solve this problem, we need to perform the division operations first, following the order of operations (BODMAS/PEMDAS). After calculating the values of each bracketed term, we will then perform the addition and subtraction from left to right.
The first term is \(17.98 \div 6.2\).
\[ 17.98 \div 6.2 = \frac{17.98}{6.2} \]To simplify, we can multiply the numerator and denominator by 10 to remove the decimal from the denominator:
\[ \frac{17.98 \times 10}{6.2 \times 10} = \frac{179.8}{62} \]Now, perform the division:
\[ 179.8 \div 62 = 2.9 \]The second term is \(10.8 \div 0.5\).
\[ 10.8 \div 0.5 = \frac{10.8}{0.5} \]Multiply the numerator and denominator by 10:
\[ \frac{10.8 \times 10}{0.5 \times 10} = \frac{108}{5} \]Now, perform the division:
\[ 108 \div 5 = 21.6 \]The third term is \(0.96 \div 0.8\).
\[ 0.96 \div 0.8 = \frac{0.96}{0.8} \]Multiply the numerator and denominator by 10:
\[ \frac{0.96 \times 10}{0.8 \times 10} = \frac{9.6}{8} \]Now, perform the division:
\[ 9.6 \div 8 = 1.2 \]The original expression was \([17.98 \div 6.2] + [10.8 \div 0.5] - [0.96 \div 0.8]\).
Substituting the values:
\[ 2.9 + 21.6 - 1.2 \]First, add \(2.9\) and \(21.6\):
\[ 2.9 + 21.6 = 24.5 \]Next, subtract \(1.2\) from \(24.5\):
\[ 24.5 - 1.2 = 23.3 \]Thus, the final result is \(23.3\).
D) 23.3 is the correct answer, as calculated by performing the division operations first and then the addition and subtraction.
Full form of NIC is:
National Information Centre
National Informatics Counsel
National Informatics Centre
None of the above
The question asks for the full form of the acronym NIC. This is a factual recall question related to common organizations or terms in the context of Indian administration and technology.
Correct Option: C) National Informatics Centre is the correct full form of NIC, referring to a key organization in India responsible for providing e-governance solutions and IT infrastructure to government departments.
Doldrum is a Zone of:
Inter tropical convergence zone
Inter tropical divergence zone
Local winds
Frontolysis
The question asks to identify what the Doldrums represent. This requires knowledge of global atmospheric circulation patterns and associated pressure belts.
Correct Option: A) Inter tropical convergence zone
This question tests knowledge of the constitutional provisions related to Panchayati Raj Institutions, specifically regarding the timeline for holding elections in case of dissolution. The 73rd Constitutional Amendment Act of 1992 governs these provisions.
Correct Option: C) Six months — Article 243E(3)(b) of the Indian Constitution clearly states that if a Panchayat is dissolved, elections to constitute a new Panchayat must be completed within six months from the date of its dissolution.