The question asks for the specific year in which Bakshi Jagabandhu led the Paika Rebellion against the British land revenue policy. To answer this, one needs to recall the historical timeline of significant rebellions in India, particularly those related to land revenue policies and led by prominent figures like Bakshi Jagabandhu.
D) 1817. The Paika Rebellion, led by Bakshi Jagabandhu, occurred in 1817 as a protest against the British land revenue policy and their overall oppressive rule in Odisha.
What was the overall unemployment rate in India as reported in the 6th Annual Employment-Unemployment Survey conducted by the Labour Bureau?
The question asks for a specific statistical figure: the overall unemployment rate in India as reported by the 6th Annual Employment-Unemployment Survey (EUS) conducted by the Labour Bureau. To answer this, one needs to recall or know the findings of this particular survey.
Correct Option: A) 5.4%
This problem requires us to substitute the given new meanings for mathematical operators into the given equation and then solve it using the BODMAS/PEMDAS rule.
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. We perform operations in this order from left to right.
First, perform Multiplication and Division from left to right.
Equation: \(32 + 14 - 16 \times 8 \div 4\)
Multiplication: \(16 \times 8 = 128\)
The equation becomes: \(32 + 14 - 128 \div 4\)
Division: \(128 \div 4 = 32\)
The equation becomes: \(32 + 14 - 32\)
Next, perform Addition and Subtraction from left to right.
Addition: \(32 + 14 = 46\)
The equation becomes: \(46 - 32\)
Subtraction: \(46 - 32 = 14\)
Thus, the value of the expression is 14.
Correct Option: A) 14
The question asks to identify the individual who assumed the charge of the Comptroller and Auditor General (CAG) of India in November 2024. This is a factual question related to recent appointments in a key constitutional office in India. Candidates need to be aware of current affairs, especially concerning high-profile government appointments.
A) K Sanjay Murthy assumed charge as the Comptroller and Auditor General of India in November 2024. He is a 1989-batch IAS officer and previously served as the Secretary of the Ministry of Corporate Affairs.
The question asks to identify an operating system from the given options. An operating system (OS) is system software that manages computer hardware and software resources and provides common services for computer programs. We need to distinguish between operating systems and application software.
Based on these evaluations, Windows 10 is clearly an operating system.
Correct Option: C) Windows 10 is an operating system commonly used on desktop computers. It provides the essential functions for the computer to operate and for other software applications to run.
The problem asks us to identify numbers in a given series that are immediately preceded by a symbol and immediately followed by a symbol. We need to scan the series from left to right and apply this condition to each number.
# * £ 3 9 € # % £ 1 % £ 8 8 1 4 9 % 5 8 & 7C) 1 is the correct answer because only one number (the first '1') in the series is immediately preceded by a symbol ('£') and immediately followed by a symbol ('%').
To answer this question, one needs to know the approximate latitudinal positions of the capital cities of the Indian states mentioned in the options. The question asks which capital city is closest to 24° N latitude.
B) Bhopal is located at approximately 23.25° N latitude, which is the closest to 24° N among the given options.
The question asks to identify the urban local self-government body responsible for managing small towns with limited municipal functions. This requires knowledge of the different types of urban local bodies in India and their respective roles and jurisdictions.
Correct Option: C) Town Area Committee manages small towns and performs limited municipal functions like street lighting and drainage. They are semi-municipal bodies with a restricted range of civic duties.
Find the value of K if the quadratic equations \( 2x^{2} + Kx + 8 = 0 \) and \( 3x^{2} + 4x + 12 = 0 \) have both roots common.
\( \frac{8}{3} \)
\( \frac{3}{2} \)
\( \frac{5}{3} \)
\( \frac{7}{2} \)
When two quadratic equations have both roots in common, their corresponding coefficients must be in proportion. We will use this property to set up a ratio of coefficients and solve for the unknown variable \(K\).
Identify the given quadratic equations:
Equation 1: \( 2x^{2} + Kx + 8 = 0 \)
Equation 2: \( 3x^{2} + 4x + 12 = 0 \)
Recall the condition for two quadratic equations to have both roots common. If two quadratic equations \( a_1x^2 + b_1x + c_1 = 0 \) and \( a_2x^2 + b_2x + c_2 = 0 \) have both roots common, then their corresponding coefficients must be proportional:
\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \]Apply this condition to the given equations:
Comparing Equation 1 with \( a_1x^2 + b_1x + c_1 = 0 \), we have \( a_1 = 2 \), \( b_1 = K \), \( c_1 = 8 \).
Comparing Equation 2 with \( a_2x^2 + b_2x + c_2 = 0 \), we have \( a_2 = 3 \), \( b_2 = 4 \), \( c_2 = 12 \).
So, we can write the proportionality relation as:
\[ \frac{2}{3} = \frac{K}{4} = \frac{8}{12} \]Simplify the ratio of the constant terms:
\[ \frac{8}{12} = \frac{2 \times 4}{3 \times 4} = \frac{2}{3} \]This confirms that the ratio of the constant terms is consistent with the ratio of the coefficients of \(x^2\).
Equate the ratio involving \(K\) with the known ratio:
\[ \frac{K}{4} = \frac{2}{3} \]Solve for \(K\):
Multiply both sides by 4:
\[ K = \frac{2}{3} \times 4 \] \[ K = \frac{8}{3} \]A) \( \frac{8}{3} \) is the correct value of \(K\) for which both quadratic equations have common roots.
The problem requires us to evaluate a mathematical expression after interchanging specific operators. We need to replace '+' with '−' and '−' with '+', and similarly '×' with '÷' and '÷' with '×'. After performing these substitutions, we will evaluate the new expression following the order of operations (BODMAS/PEMDAS).
B) 762 is the correct answer, as derived from the step-by-step evaluation of the modified expression.