Anand's mother is the sister of Chanda's father's son.
What is Anand's relationship with Chanda's father?
This is a blood relation problem. We need to deduce the relationship between Anand and Chanda's father by breaking down the given statement step-by-step and identifying the connections between individuals.
Correct Option: D) Grandson. Anand's mother is the daughter of Chanda's father. Therefore, Anand is the son of Chanda's father's daughter, which means Anand is the grandson of Chanda's father.
The question asks to identify what CMOS is. CMOS stands for Complementary Metal-Oxide-Semiconductor. It is a type of semiconductor technology used in microprocessors, microcontrollers, static RAM, and other digital logic circuits. In the context of personal computers, CMOS often refers to the small amount of memory on the motherboard that stores BIOS settings and system time/date.
Correct Option: A) Battery-powered memory chip
CMOS (Complementary Metal-Oxide-Semiconductor) in the context of a computer system refers to a small memory chip on the motherboard that stores BIOS settings, system date, and time. This chip is powered by a small battery (often a coin cell) to retain its data even when the computer is turned off.
Borosilicate glassware is used in microwave oven because
It is not brittle
It is highly heat resistant
It cooks faster than any other vessel
It is energy efficient
The question asks why borosilicate glassware is used in microwave ovens. This requires understanding the properties of borosilicate glass and how microwave ovens function.
Correct Option: B) It is highly heat resistant
This problem involves the relationship between two numbers, their ratio, their Highest Common Factor (HCF), and their Least Common Multiple (LCM). A fundamental property states that for any two positive integers, the product of the numbers is equal to the product of their HCF and LCM. We will use this property along with the given ratio and HCF to find the LCM.
Let the two numbers be \(A\) and \(B\). Given that their ratio is 4:5, we can write them as:
\[ A = 4x \] \[ B = 5x \]where \(x\) is a common factor.
The HCF (Highest Common Factor) of \(A\) and \(B\) is the greatest common divisor of \(4x\) and \(5x\). Since 4 and 5 are coprime (their only common factor is 1), the HCF of \(4x\) and \(5x\) is \(x\).
We are given that the HCF is 13. Therefore,
\[ x = 13 \]Now we can find the two numbers:
\[ A = 4x = 4 \times 13 = 52 \] \[ B = 5x = 5 \times 13 = 65 \]We know the fundamental property that for any two positive integers, the product of the numbers is equal to the product of their HCF and LCM:
\[ A \times B = \text{HCF}(A, B) \times \text{LCM}(A, B) \]Substitute the values we have:
\[ 52 \times 65 = 13 \times \text{LCM} \]Solve for LCM:
\[ \text{LCM} = \frac{52 \times 65}{13} \] \[ \text{LCM} = \frac{3380}{13} \] \[ \text{LCM} = 260 \]If two numbers are in the ratio \(a:b\) and their HCF is \(H\), then the numbers are \(aH\) and \(bH\).
The LCM of these numbers is given by \(\text{LCM} = a \times b \times H\).
Given ratio \(a:b = 4:5\) and \(H = 13\).
Substitute the values:
\[ \text{LCM} = 4 \times 5 \times 13 \] \[ \text{LCM} = 20 \times 13 \] \[ \text{LCM} = 260 \]A) 260
This is a blood relation problem. We need to deduce the relationship between Anil and Aditya based on the given statements. We will break down the statement "Anil is the father of my daughter's only niece" step by step to identify the key relationships.
B) Son — As deduced, Anil is the father of Aditya's granddaughter, who is the daughter of Aditya's son. Therefore, Anil is Aditya's son.
Simplify: \( \frac{5}{28} \) ÷ \( \frac{28}{35} \) ÷ (\( \frac{20}{112} \))
\( \frac{4}{5} \)
\( \frac{5}{4} \)
\( \frac{4}{7} \)
\( \frac{7}{4} \)
To simplify the given expression involving division of fractions, we will convert each division operation into multiplication by taking the reciprocal of the divisor. Then, we will multiply the fractions and simplify the result by canceling common factors in the numerator and denominator.
The given expression is:
\[ \frac{5}{28} \div \frac{28}{35} \div \left( \frac{20}{112} \right) \]Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. So, \(a \div b = a \times \frac{1}{b}\).
Convert the first division into multiplication:
\[ \frac{5}{28} \times \frac{35}{28} \div \left( \frac{20}{112} \right) \]Convert the second division into multiplication:
\[ \frac{5}{28} \times \frac{35}{28} \times \frac{112}{20} \]Now, we can multiply the numerators and denominators. Before multiplying, it's often easier to simplify by canceling common factors.
Let's simplify each fraction and look for common factors across all terms:
Simplify \(\frac{35}{28}\): Both are divisible by 7. \[\frac{35 \div 7}{28 \div 7} = \frac{5}{4}\].
Simplify \(\frac{112}{20}\): Both are divisible by 4. \[\frac{112 \div 4}{20 \div 4} = \frac{28}{5}\].
Substitute the simplified fractions back into the expression:
\[ \frac{5}{28} \times \frac{5}{4} \times \frac{28}{5} \]Now, cancel out common factors in the numerator and denominator:
The '5' in the numerator of the first fraction cancels with the '5' in the denominator of the third fraction.
The '28' in the denominator of the first fraction cancels with the '28' in the numerator of the third fraction.
The expression becomes:
\[ \frac{\cancel{5}}{\cancel{28}} \times \frac{5}{4} \times \frac{\cancel{28}}{\cancel{5}} = \frac{5}{4} \]Alternatively, multiply all numerators and all denominators first, then simplify:
\[ \frac{5 \times 35 \times 112}{28 \times 28 \times 20} \]Numerator: \(5 \times 35 \times 112 = 175 \times 112 = 19600\)
Denominator: \(28 \times 28 \times 20 = 784 \times 20 = 15680\)
So, the fraction is \(\frac{19600}{15680}\).
Simplify \(\frac{19600}{15680}\):
Divide both by 10: \(\frac{1960}{1568}\)
Divide both by 4: \(\frac{490}{392}\)
Divide both by 2: \(\frac{245}{196}\)
Divide both by 49: \[\frac{245 \div 49}{196 \div 49} = \frac{5}{4}\]
B) \(\frac{5}{4}\) is the simplified value of the given expression.
A junior college inducts students based on the following criteria –
1. Students who scored at least 75% in Physics, 85% in Mathematics and 70% in Chemistry.
2. Students who scored at least 60% in English.
3. Students who are good in a sport or play a musical instrument or know a dance form.
Which student among the following will the college definitely take?
A. Shakti with 80% in Physics, 65% in Chemistry, 85% in Mathematics, 61% in English and plays veena.
B. Megha secured 80% in Physics, 87% in Mathematics, 70% in English, 75% in Chemistry and is a singer.
C. Sheela secured 78% in Physics, 70% in Chemistry, 85% in Mathematics, 75% in English knows Manipuri folk dance.
D. Mallika secured 70% in Chemistry, 70% in Mathematics, 85% in Physics, 65% in English and plays basketball.
To determine which student will definitely be inducted, we need to check each student against all three given criteria. A student must satisfy all three criteria to be selected.
Let's list the criteria:
Now, let's evaluate each student:
The question asks which student the college will definitely take. This implies there might be only one student who meets all criteria, or we need to be careful if there's an ambiguity. In this case, both Megha and Sheela meet all criteria. However, competitive exams often have a single best answer. Let's re-read the question carefully. "Which student among the following will the college definitely take?". If multiple students meet the criteria, then all of them would be taken. There might be a subtle point missed or a typical competitive exam scenario where only one option is provided as correct. Let's re-check the options and criteria.
Upon re-evaluation, the question implies selecting one student from the given options. If multiple students qualify, there might be an issue with the question's premise or options provided. However, in such scenarios, we select the option that is presented as the correct answer if it indeed qualifies. Both Megha and Sheela qualify based on the stated criteria. If only one answer is to be chosen, and 'C' is marked correct, let's ensure there isn't any subtle distinction. There isn't. Both B and C fully satisfy all conditions.
Assuming this is a standard MCQ where only one option is correct, and given the provided correct answer is C, we proceed with Sheela. Both B and C are valid candidates based on the given rules.
Let's re-verify Megha's details:
Megha clearly passes all criteria.
Let's re-verify Sheela's details:
Sheela also clearly passes all criteria.
Since both Megha and Sheela satisfy all conditions, and typically only one option is correct in MCQs, there might be an error in the question or options provided, or an unstated preference. However, following the explicit rules, both B and C are valid. If forced to choose one and C is the designated correct answer, we select C.
Correct Option: C) Sheela meets all the criteria.
A telephone bill costs Rs.13 for 19 minutes. What is the cost in rupees for 15 minutes 50 seconds? (Rounded to one decimal).
To solve this problem, we need to first determine the cost per minute. Since the cost is given for 19 minutes, we can find the cost per minute. Then, we convert the required time (15 minutes 50 seconds) entirely into minutes. Finally, we multiply the cost per minute by the total time in minutes to find the total cost.
Given that the cost for 19 minutes is Rs. 13.
\[ \text{Cost per minute} = \frac{\text{Total cost}}{\text{Total minutes}} = \frac{13 \text{ Rs.}}{19 \text{ minutes}} \]The required time is 15 minutes 50 seconds.
Since 1 minute = 60 seconds, we can convert 50 seconds to minutes:
\[ 50 \text{ seconds} = \frac{50}{60} \text{ minutes} = \frac{5}{6} \text{ minutes} \]So, the total time in minutes is:
\[ \text{Total time} = 15 + \frac{5}{6} \text{ minutes} = \frac{15 \times 6 + 5}{6} \text{ minutes} = \frac{90 + 5}{6} \text{ minutes} = \frac{95}{6} \text{ minutes} \]Multiply the cost per minute by the total time in minutes:
\[ \text{Cost} = \text{Cost per minute} \times \text{Total time} \]\[ \text{Cost} = \frac{13}{19} \text{ Rs./minute} \times \frac{95}{6} \text{ minutes} \]\[ \text{Cost} = \frac{13 \times 95}{19 \times 6} \]We know that \(95 = 19 \times 5\), so we can simplify the expression:
\[ \text{Cost} = \frac{13 \times (19 \times 5)}{19 \times 6} = \frac{13 \times 5}{6} \]\[ \text{Cost} = \frac{65}{6} \text{ Rs.} \]Now, perform the division:
\[ \frac{65}{6} \approx 10.8333... \text{ Rs.} \]Rounding 10.8333... to one decimal place gives 10.8.
Correct Option: A) 10.8
The calculated cost for 15 minutes 50 seconds is approximately Rs. 10.83, which rounds to Rs. 10.8 when rounded to one decimal place.
The problem presents a coding-decoding scenario where a word is coded into another. We need to identify the pattern or rule used for coding "BLACK" into "AMZDJ" and then apply the same rule to decode "BEAUTIFUL".
Let's write down the letters of the original word and its coded form, along with their alphabetical positions.
Observe the change in alphabetical position for each letter:
The pattern is alternating: \(-1, +1, -1, +1, -1\).
Now, apply this alternating \(-1, +1\) pattern to each letter of "BEAUTIFUL".
Combining the coded letters, we get AFZVSJEVK.
Correct Option: B) AFZVSJEVK
The question asks about the duration of the Mahabharata war. This is a factual question related to ancient Indian history and mythology, specifically the epic Mahabharata. The duration of the war is a well-known detail from the epic.
B) 18. The Kurukshetra War, as described in the Mahabharata, lasted for 18 days.