The question asks for the historical importance of Jantar Mantar in Delhi. This requires knowledge of the historical purpose and function of this specific monument.
Correct Option: D) Astronomical observatory. The Jantar Mantar in Delhi is one of five such observatories built by Maharaja Jai Singh II of Jaipur. It was constructed in 1724 and contains various instruments designed to measure the positions and movements of celestial bodies, predict eclipses, and determine local time.
The question asks about the meaning of "Bharat Stage Emission Standards". This is a well-known regulatory framework in India. The approach is to recall the primary focus of these standards.
Therefore, the standards are directly related to vehicular pollution.
Correct Option: A) Vehicular pollution. Bharat Stage Emission Standards (BSES) are emission standards instituted by the Government of India to regulate the output of air pollutants from motor vehicles. These standards are based on European regulations (Euro norms) and aim to control the release of harmful gases and particulate matter from vehicle exhausts, thereby addressing vehicular air pollution.
Statements followed by some conclusions are given below.
Statement:
M > L > N
N = R
Conclusions:
I. R > L
II. R < M
Find which of the given conclusions logically follows from the given statements.
Only conclusion I follows.
Only conclusion II follows.
Both I and II follow.
Neither I nor II follows.
This problem involves analyzing inequalities and equalities to determine the logical relationship between different variables. We need to combine the given statements and then check if the conclusions can be derived from the combined statement.
We are given two statements:
From Statement 1, we know that \(M\) is greater than \(L\), and \(L\) is greater than \(N\). So, \(M > L > N\).
From Statement 2, we know that \(N\) is equal to \(R\).
Substitute \(N = R\) into the first statement. This gives us the combined relationship:
\[ M > L > R \]From our combined statement \(M > L > R\), we can see that \(L > R\). This means \(R\) is less than \(L\).
Therefore, the conclusion \(R > L\) is false.
From our combined statement \(M > L > R\), we can infer that \(M > R\). This is equivalent to \(R < M\).
Therefore, the conclusion \(R < M\) is true.
Correct Option: B) Only conclusion II follows.
Find the odd statement: Two lines are perpendicular to each other if they are,
Adjacent sides of a rectangle.
Diagonals of a rhombus
Hypotenuse and one side of a right-angle triangle.
Adjacent sides of a square
The question asks to identify the statement that does NOT describe two lines perpendicular to each other. Perpendicular lines intersect at a 90-degree angle. We need to evaluate each option based on geometric properties.
Correct Option: C) Hypotenuse and one side of a right-angle triangle. This statement is odd because the hypotenuse and a side (leg) of a right-angle triangle are not perpendicular to each other. The two legs of a right-angle triangle are perpendicular.
A certain number of men agreed to do a work in 20 days. 5 men did not come for work. Others completed the work in 40 days. Find the number of men who had agreed to do the work originally.
This problem can be solved using the concept of "Men and Work". The total amount of work is constant. The work done is directly proportional to the number of men and the number of days they work. We can set up an equation based on the total work being the same in both scenarios.
Let \(M\) be the original number of men who agreed to do the work.
Let \(D_1\) be the number of days originally agreed upon, which is 20 days.
Let \(M_2\) be the number of men who actually worked, which is \(M - 5\).
Let \(D_2\) be the number of days they actually took to complete the work, which is 40 days.
The total work done is constant. We can express work as the product of the number of men and the number of days.
Work (original plan) = Work (actual completion)
\[ M_1 \times D_1 = M_2 \times D_2 \]
Substitute the given values into the equation:
\[ M \times 20 = (M - 5) \times 40 \]
\[ 20M = 40(M - 5) \]
Divide both sides by 20:
\[ M = 2(M - 5) \]
Distribute the 2 on the right side:
\[ M = 2M - 10 \]
Rearrange the terms to solve for \(M\):
\[ 10 = 2M - M \]
\[ M = 10 \]
So, the number of men who had agreed to do the work originally was 10.
Correct Option: B) 10
How many prime numbers are there between the positive integers 60 and 100?
To find the number of prime numbers between 60 and 100, we need to list all integers in this range and then identify which ones are prime. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Correct Option: D) 8
Below are given statements followed by some conclusions. You have to decide which conclusions logically follow from the given statements.
Statements:
In small towns, one out of every ten shops is a jewellery shop.
In some towns, the average income of one jewellery shop owner is greater than the average income of a doctor in that town.
Conclusions:
I. Small towns have more jewellery shops than any other type of shop.
II. Jewellery shop owners earn more than doctors in all towns.
Only conclusion I follows
Only conclusion II follows
Both conclusions I and II follow
Neither conclusion I nor II follows
This is a logical reasoning question based on statements and conclusions. We need to evaluate each conclusion independently based solely on the information provided in the statements and determine if it logically follows.
D) Neither conclusion I nor II follows. Both conclusions make claims that are not supported or are contradicted by the given statements.
Washing soda can be used for ________.
To purify drinking water from germs
For cooking
To soften hard water
For non-poisonous household cleaning items
The question asks about the primary use of washing soda. We need to recall the chemical properties and common applications of washing soda (sodium carbonate).
C) To soften hard water. Washing soda (sodium carbonate) reacts with calcium and magnesium ions present in hard water, forming insoluble carbonates that precipitate out, thus removing the hardness.
To find the value of the given algebraic expression, we will first simplify the expression by distributing \(y\) inside the parenthesis. Then, we will substitute the given value of \(y\) into the simplified expression and perform the arithmetic operations.
Simplify the expression:
The given expression is \( y(y^{4} - y^{2} - y) \).
Distribute \(y\) to each term inside the parenthesis:
\[ y \cdot y^{4} - y \cdot y^{2} - y \cdot y \]\[ y^{1+4} - y^{1+2} - y^{1+1} \]\[ y^{5} - y^{3} - y^{2} \]Substitute the value of \(y\):
We are given \( y = 5 \). Substitute this value into the simplified expression:
\[ (5)^{5} - (5)^{3} - (5)^{2} \]Calculate the powers:
Perform the subtraction:
Substitute the calculated power values back into the expression:
\[ 3125 - 125 - 25 \]\[ 3000 - 25 \]\[ 2975 \]Thus, the value of \( y(y^{4} - y^{2} - y) \) when \( y = 5 \) is 2975.
Correct Option: B) 2975
The problem involves finding the product of two positive integers given their sum and difference. We can set up a system of two linear equations with two variables and solve for the integers. Once the integers are found, their product can be calculated.
The sum of the two integers is 34:
\[ x + y = 34 \quad \text{(Equation 1)} \]Their difference is 8:
\[ x - y = 8 \quad \text{(Equation 2)} \]Add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 34 + 8 \]\[ 2x = 42 \]Divide by 2 to find \(x\):
\[ x = \frac{42}{2} \]\[ x = 21 \]Substitute the value of \(x\) into Equation 1 to find \(y\):
\[ 21 + y = 34 \]Subtract 21 from both sides:
\[ y = 34 - 21 \]\[ y = 13 \]So, the two positive integers are 21 and 13.
Product \(= x \times y = 21 \times 13\)
To multiply 21 by 13:
Thus, the product is 273.
Correct Option: B) 273