\(\frac{182}{130}\) when written in the simplest form is:
\(\frac{28}{20}\)
\(\frac{91}{65}\)
\(\frac{14}{10}\)
\(\frac{7}{5}\)
To write a fraction in its simplest form, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). This process is also known as reducing the fraction to its lowest terms.
The given fraction is \(\frac{182}{130}\).
Numerator \(= 182\)
Denominator \(= 130\)
We can find the GCD by listing factors or by prime factorization.
Let's use prime factorization:
The common prime factors are \(2\) and \(13\).
So, GCD \(= 2 \times 13 = 26\).
\[ \frac{182 \div 26}{130 \div 26} = \frac{7}{5} \]
The numbers \(7\) and \(5\) are prime numbers, and they do not have any common factors other than \(1\). Therefore, the fraction \(\frac{7}{5}\) is in its simplest form.
D) \(\frac{7}{5}\) is the simplest form of \(\frac{182}{130}\).
The reactivity of metals with water depends on their position in the reactivity series. Metals higher in the reactivity series react more vigorously with water, especially cold water, producing hydrogen gas and a metal hydroxide.
Correct Option: A) Potassium reacts vigorously with cold water. This is due to its high position in the reactivity series, indicating its strong tendency to lose electrons and form positive ions.
To find the age of the mother, we need to determine if the given statements provide enough information to calculate her age uniquely. We will set up equations based on the statements and check if we can solve for the mother's age.
Let \(M\) be the mother's age and \(S\) be the son's age.
From Statement I, we have:
\[ M = S + 10 \quad \text{(Equation 1)} \]Let \(D\) be the daughter's age.
From Statement II, we have:
\[ S = D + 24 \quad \text{(Equation 2)} \]Substitute Equation 2 into Equation 1:
\[ M = (D + 24) + 10 \]\[ M = D + 34 \]After combining both statements, we get an equation for the mother's age in terms of the daughter's age. However, the daughter's age (\(D\)) is unknown. We have one equation with two unknown variables (\(M\) and \(D\)). Therefore, we cannot find a unique numerical value for the mother's age.
Neither statement alone provides enough information, and even when combined, they are insufficient to determine the mother's exact age.
B) Neither I nor II is sufficient
The question asks to identify the part of the human reproductive system responsible for providing nutrition to the embryo from the mother's blood. This involves understanding the functions of various organs in the female reproductive system during pregnancy.
Correct Option: A) Placenta — The placenta is a temporary organ that develops in the uterus during pregnancy. It provides oxygen and nutrients to the growing baby and removes waste products from the baby's blood. It achieves this by facilitating the exchange of substances between the mother's blood and the fetal blood without direct mixing.
Which of the following statements is sufficient to answer the question?
Find the value of x.
Statements:
I: Sum of squares of positive consecutive even numbers is 52
II: Difference of the number is 2
Both I and II are sufficient
Only II is sufficient while I is not
Only I is sufficient while II is not
Neither I nor II is sufficient
We need to determine if statement I, statement II, or both are sufficient to find the value of 'x'. We will analyze each statement independently and then together if necessary.
Let the two positive consecutive even numbers be \(x\) and \(x+2\).
Analyze Statement I: Sum of squares of positive consecutive even numbers is 52.
Analyze Statement II: Difference of the number is 2.
Conclusion: Statement I alone is sufficient, while Statement II alone is not sufficient.
C) Only I is sufficient while II is not
The question asks to identify the person who does not belong to a specific group. We need to analyze the common profession or field of work for each individual listed in the options.
Correct Option: A) Mahendra Singh Dhoni
The problem asks us to calculate the work done in raising an object against gravity. When an object is lifted, the work done against gravity is equal to the change in its gravitational potential energy. The formula for gravitational potential energy (and thus work done in this context) is given by the product of mass, acceleration due to gravity, and height.
The work done (\(W\)) in raising an object to a certain height is equal to the gravitational potential energy gained by the object. The formula is:
\[ W = mgh \]Substitute the given mass, acceleration due to gravity, and height into the formula:
\[ W = (5.0 \text{ kg}) \times (9.8 \text{ m/s}^2) \times (2.0 \text{ m}) \]Perform the multiplication:
\[ W = 5.0 \times 9.8 \times 2.0 \]\[ W = 49.0 \times 2.0 \]\[ W = 98.0 \text{ J} \]The unit of work done is Joules (J).
Correct Option: D) 98 J
We need to find the Cost Price (CP) first. We are given two scenarios for selling the item: one at a loss and another where a profit would have been made if sold for ₹ 57 more. The difference in these selling prices corresponds to the difference in percentage loss/profit. Once the CP is found, we can calculate the selling price for a 30% profit.
Let the Cost Price (CP) of the item be \( \text{₹ } x \).
First scenario: Yaman sold the item at a loss of 10%.
Selling Price (SP1) \( = \text{CP} - 10\% \text{ of CP} = x - 0.10x = 0.90x \).
Second scenario: If he had sold it for ₹ 57 more, he would have made a profit of 20%.
This means the new selling price (SP2) would be \( \text{SP1} + 57 \).
Also, SP2 would be \( \text{CP} + 20\% \text{ of CP} = x + 0.20x = 1.20x \).
From the above, we can set up an equation:
\[ \text{SP1} + 57 = \text{SP2} \] \[ 0.90x + 57 = 1.20x \]Now, solve for \( x \):
\[ 57 = 1.20x - 0.90x \] \[ 57 = 0.30x \] \[ x = \frac{57}{0.30} \] \[ x = \frac{570}{3} \] \[ x = 190 \]So, the Cost Price (CP) of the item is ₹ 190.
Calculate the selling price for a profit of 30%:
Required Selling Price (SP3) \( = \text{CP} + 30\% \text{ of CP} \)
\[ \text{SP3} = 190 + (0.30 \times 190) \] \[ \text{SP3} = 190 + 57 \] \[ \text{SP3} = 247 \]The selling price to make a profit of 30% should be ₹ 247.
Correct Option: A) ₹ 247
This problem requires us to substitute the given symbol transformations into the mathematical expression and then evaluate the new expression following the order of operations (BODMAS/PEMDAS).
The original expression is \(125 – 50 \div 10 + 20 \times 4\).
Applying the transformations:
So, the new expression is \(125 \times 50 + 10 \div 20 – 4\).
The order of operations is Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
The expression is \(125 \times 50 + 10 \div 20 – 4\).
Multiplication: \(125 \times 50 = 6250\)
Division: \(10 \div 20 = 0.5\)
Substitute these values back into the expression:
\[ 6250 + 0.5 – 4 \]Addition: \(6250 + 0.5 = 6250.5\)
Subtraction: \(6250.5 – 4 = 6246.5\)
C) \(6246.5\) is the correct result after applying the symbol transformations and following the order of operations.
This is a blood relation question. We need to trace the relationships backward from P to Q to determine their connection. We will break down the statement "P is the brother of the son of Q's Son" into smaller, manageable parts.
Correct Option: C) P is the grandson of Q.