The question asks to identify the scheme that focuses on establishing a lab for sustainable technologies in rural areas. We need to evaluate each option based on its stated objectives and scope.
Correct Option: C) Cross-Cutting and Futuristic Initiatives. This category typically includes programs aimed at developing innovative and sustainable solutions for various societal needs, including those in rural areas. Such initiatives often involve establishing research and development facilities (labs) to address specific challenges like sustainable technology adoption in rural settings.
This problem involves setting up and solving a system of linear equations based on the given information about the cost of pens and pencils. We will define variables for the original costs, form two equations, solve them to find the individual costs, and then calculate the required value.
Let the original cost of one pen be \(P\) (in Rs) and the original cost of one pencil be \(C\) (in Rs).
From the first statement, "The cost of 12 pens and 7 pencils is Rs 233", we can form the first equation:
\[ 12P + 7C = 233 \quad \text{(Equation 1)} \]From the second statement, "If the cost of a pen decreases by Rs 1.50 and the cost of a pencil increases by Rs 1, then the cost of 2 pens and 3 pencils is ₹48".
The new cost of a pen is \(P - 1.50\).
The new cost of a pencil is \(C + 1\).
So, we can form the second equation:
\[ 2(P - 1.50) + 3(C + 1) = 48 \]Simplify Equation 2:
\[ 2P - 3 + 3C + 3 = 48 \]\[ 2P + 3C = 48 \quad \text{(Equation 2)} \]Now we have a system of two linear equations:
Equation 1: \(12P + 7C = 233\)
Equation 2: \(2P + 3C = 48\)
To solve this system, we can use the elimination method. Multiply Equation 2 by 6 to make the coefficient of \(P\) the same as in Equation 1:
\[ 6 \times (2P + 3C) = 6 \times 48 \]\[ 12P + 18C = 288 \quad \text{(Equation 3)} \]Subtract Equation 1 from Equation 3:
\[ (12P + 18C) - (12P + 7C) = 288 - 233 \]\[ 11C = 55 \]\[ C = \frac{55}{11} \]\[ C = 5 \]Substitute the value of \(C = 5\) into Equation 2 to find \(P\):
\[ 2P + 3(5) = 48 \]\[ 2P + 15 = 48 \]\[ 2P = 48 - 15 \]\[ 2P = 33 \]\[ P = \frac{33}{2} \]\[ P = 16.50 \]So, the original cost of one pen is Rs 16.50 and the original cost of one pencil is Rs 5.
The question asks for the original cost of 4 pens and 1 pencil:
\[ 4P + 1C = 4(16.50) + 1(5) \]\[ = 66 + 5 \]\[ = 71 \]The original cost of 4 pens and 1 pencil is Rs 71.
D) 71
The question asks to identify the social and religious reform movement established by Atmaram Pandurang in Bombay (Mumbai) in 1867. This requires knowledge of key reform movements in 19th-century India and their founders and founding years.
Correct Option: B) Prarthana Samaj was established by Atmaram Pandurang in Bombay (Mumbai) in 1867. It was a significant movement for religious and social reform, promoting monotheism, social equality, and condemning idolatry and the caste system. Its objectives included disapproval of the caste system, promotion of widow remarriage, improvement in the age of marriage for both males and females, and women's education.
To solve this problem, we need to understand the relationship between power, current, and potential difference. The formula for electrical power will be used, and then we will substitute the given changes in current and potential difference to find the new power and compare it with the initial power.
Recall the formula for electrical power:
The power \(P\) dissipated in a conductor is given by the product of the potential difference \(V\) across it and the current \(I\) flowing through it:
Define initial conditions:
Let the initial current be \(I_1\) and the initial potential difference be \(V_1\). The initial power \(P_1\) is then:
Define new conditions:
According to the problem statement:
Calculate the new power \(P_2\):
Substitute the new values of current and potential difference into the power formula:
Compare new power with initial power:
Since \(P_1 = V_1 \times I_1\), we can substitute \(P_1\) into the equation for \(P_2\):
This means the new power is three times the initial power.
Correct Option: C) three fold
The question asks to identify the festival where the 'Maru Sri' or 'Maru Shri' desert pageant is held. This requires knowledge of prominent Indian festivals and their associated events or locations.
B) Jaisalmer Desert Festival
The Jaisalmer Desert Festival is a famous annual event held in Jaisalmer, Rajasthan, India. It is celebrated in the Thar Desert and is known for showcasing the rich cultural heritage of Rajasthan. The "Maru Shri" (Mr. Desert) and "Miss Moomal" pageants are integral parts of this festival, featuring traditional attire and performances, making it the correct answer.
Identify the double displacement reaction from the following.
(i) 2AgCl(s) → 2Ag(s) + Cl₂(g)
(ii) Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)
(iii) 2KBr(aq) + BaI₂(aq) → 2KI(aq) + BaBr₂(s)
(iv) Pb(s) + CuCl₂(aq) → PbCl₂(aq) + Cu(s)
The question asks to identify a double displacement reaction from the given options. A double displacement reaction is a type of chemical reaction where two compounds react, and the positive ions (cations) and negative ions (anions) of the two reactants switch places, forming two new compounds. This often results in the formation of a precipitate, a gas, or water.
A) (iii) represents a double displacement reaction because the cations and anions of the two reactant compounds (KBr and BaI₂) exchange places to form two new compounds (KI and BaBr₂).
The effective nuclear charge (\(Z_{\text{eff}}\)) is the net positive charge experienced by an electron in a multi-electron atom. It is influenced by the actual nuclear charge (atomic number, \(Z\)) and the shielding effect of inner electrons. For elements within the same period, as the atomic number increases, the number of protons increases, leading to a stronger pull on the valence electrons and thus a higher effective nuclear charge, assuming the shielding effect doesn't increase proportionally.
B) Fluorine (F) has an atomic number of 9. Among the given options, it has the highest number of protons. Since all elements are in the same period, the shielding effect is relatively constant, and the increasing nuclear charge leads to the highest effective nuclear charge for Fluorine.
The positive square root of (34² − 16²) is:
The problem asks for the positive square root of the expression \(34^2 - 16^2\). We can solve this by first calculating the squares, then finding the difference, and finally taking the square root. Alternatively, we can use the algebraic identity \(a^2 - b^2 = (a-b)(a+b)\) to simplify the calculation.
So, \(34^2 - 16^2 = (34 - 16)(34 + 16)\).
Now, substitute these values back into the expression:
\[ 34^2 - 16^2 = 18 \times 50 \]Calculate the product:
\[ 18 \times 50 = 900 \]We need to find the positive square root of 900.
\[ X = \sqrt{900} \]Since \(30 \times 30 = 900\), the positive square root of 900 is 30.
\[ X = 30 \]C) 30
Refer to the following letter, number, symbol series and answer the question.
(Left) D 2 R X 5 8 T ^ & 9 3 H 8 C % K T A # 3 T 5 4 S % 9 & R % 5 (Right)
If all the letters are dropped from the series, which of the following will be the 10th element from the left in the series formed?
The problem asks us to identify the 10th element from the left in a modified series. The modification involves dropping all letters from the original series. We need to first filter out the letters and then count the elements from the left to find the 10th one.
D) # is the 10th element from the left after dropping all letters from the series.