The question asks to identify the sport in which Dipika Pallikal and Joshna Chinappa won a doubles title at the World Championships on April 9, 2022. This requires knowledge of recent sports achievements by prominent Indian athletes.
C) Squash — Dipika Pallikal and Joshna Chinappa are prominent Indian squash players. They won the women's doubles title at the WSF World Doubles Squash Championship on April 9, 2022, defeating England's Sarah-Jane Perry and Alison Waters in the final.
To simplify the given expression, we must follow the order of operations, commonly remembered by the acronym PEMDAS/BODMAS. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
The given expression is:
\[ 48 \div 8 \times 3 - 6 \]According to the order of operations, we first perform division and multiplication from left to right. The first operation from the left is division:
\[ 48 \div 8 = 6 \]Substitute this result back into the expression:
\[ 6 \times 3 - 6 \]Next, perform the multiplication:
\[ 6 \times 3 = 18 \]Substitute this result back into the expression:
\[ 18 - 6 \]Finally, perform the subtraction:
\[ 18 - 6 = 12 \]Correct Option: D) 12
The question asks about the number of priorities outlined in the Union Budget 2022-23 for growth during the 'Amrit Kaal'. To answer this, one needs to recall the key features and priorities highlighted in that specific budget speech.
C) Four. The Union Budget 2022-23 identified four key priorities for growth during the Amrit Kaal.
Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.
EXAMPLE:
13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
3 : 25 :: 8 : 100 :: 12 :?
The problem presents a series of number pairs and asks to find the missing number in the last pair based on the relationship observed in the previous pairs. We need to identify the mathematical operation or pattern connecting the first number to the second number in each given pair.
Analyze the first pair: 3 : 25
Let the first number be \(N_1 = 3\) and the second number be \(N_2 = 25\).
We observe that \(25\) is the square of \(5\). To get \(5\) from \(3\), we can add \(2\) to \(3\).
So, the relationship could be: \(N_2 = (N_1 + 2)^2\).
Let's check this: \((3 + 2)^2 = 5^2 = 25\). This matches the given pair.
Analyze the second pair: 8 : 100
Let the first number be \(N_3 = 8\) and the second number be \(N_4 = 100\).
Using the same proposed relationship: \(N_4 = (N_3 + 2)^2\).
Let's check this: \((8 + 2)^2 = 10^2 = 100\). This also matches the given pair.
Apply the pattern to the third pair: 12 : ?
Let the first number be \(N_5 = 12\) and the missing number be \(N_6\).
Using the established relationship: \(N_6 = (N_5 + 2)^2\).
Substitute \(N_5 = 12\): \(N_6 = (12 + 2)^2\).
Calculate: \(N_6 = (14)^2\).
\(N_6 = 196\).
Thus, the missing number is 196.
A) 196 is the correct answer because it follows the pattern \((N+2)^2\) established by the first two pairs.
The question asks for the conversion of 1 commercial unit of electrical energy into joules. A commercial unit of electrical energy is commonly known as 1 kilowatt-hour (kWh). We need to convert kilowatt-hours to joules using the definitions of kilowatt and hour.
Understand the commercial unit: The commercial unit of electrical energy is 1 kilowatt-hour (kWh).
Break down kilowatt-hour:
Relate to Joules: The unit of power is Watt, and 1 Watt is defined as 1 Joule per second (\(1 \text{ W} = 1 \text{ J/s}\)). Therefore, 1 Joule is equal to 1 Watt-second (\(1 \text{ J} = 1 \text{ W} \cdot \text{s}\)).
Perform the conversion: \[ 1 \text{ kWh} = 1 \text{ kW} \times 1 \text{ h} \] Substitute the values in terms of Watts and seconds: \[ 1 \text{ kWh} = (1000 \text{ W}) \times (3600 \text{ s}) \] \[ 1 \text{ kWh} = 3600000 \text{ W} \cdot \text{s} \] Since \(1 \text{ W} \cdot \text{s} = 1 \text{ J}\): \[ 1 \text{ kWh} = 3600000 \text{ J} \] Express this in scientific notation: \[ 1 \text{ kWh} = 3.6 \times 10^6 \text{ J} \]
Thus, 1 commercial unit of electrical energy is equal to \(3.6 \times 10^6\) joules.
D) \(3.6 \times 10^6\) is the correct value for 1 kilowatt-hour in joules.
The question asks us to evaluate two arguments in relation to the statement: "Education is the backbone of human society." We need to determine if each argument strengthens or weakens the given statement.
Analyze the Statement: The statement claims that education is fundamental and essential for human society, much like a backbone supports a body. This implies education is crucial for the proper functioning, stability, and progress of society.
Evaluate Argument I: "Schools are learning centres of societal norms and regulations."
Evaluate Argument II: "Any society with less concern about education cannot grow and develop in present times."
Conclusion: Both Argument I and Argument II provide reasons that support the central idea that education is vital for the structure, functioning, growth, and development of human society. Hence, both arguments strengthen the statement.
Correct Option: B) Both I and II strengthen the statement.
To determine the direction of the force acting on a charged particle moving in a magnetic field, we use Fleming's Left-Hand Rule or the vector cross product formula for magnetic force. Fleming's Left-Hand Rule is particularly useful for visualizing the directions of current (or velocity of positive charge), magnetic field, and force.
With the forefinger pointing down and the middle finger pointing east, your thumb will naturally point towards the north.
The magnetic force \(\vec{F}\) on a charged particle is given by the formula:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]where \(q\) is the charge (positive for a proton), \(\vec{v}\) is the velocity vector, and \(\vec{B}\) is the magnetic field vector. The direction of \(\vec{v} \times \vec{B}\) can be found using the right-hand rule for cross products.
Since the proton has a positive charge, the force direction is the same as the direction of \(\vec{v} \times \vec{B}\).
Correct Option: D) The force acting on the proton will be towards the north, as determined by Fleming's Left-Hand Rule or the right-hand rule for vector cross products.
The question asks to identify the elected president of the Constituent Assembly of India. This requires knowledge of the key figures involved in the framing of the Indian Constitution and their specific roles.
Correct Option: B) Dr. Rajendra Prasad was elected as the permanent President of the Constituent Assembly on December 11, 1946. His leadership was crucial in guiding the proceedings and ensuring the smooth functioning of the assembly.
This problem can be solved by setting up a system of two linear equations with two variables. We will assign variables to the cost of a toy car and a toy bike, form the equations based on the given information, and then solve the system using elimination or substitution methods.
Let \(C\) be the cost of one toy car and \(B\) be the cost of one toy bike.
From the first statement, "Seven toy cars and five toy bikes together cost Rs 600", we can form the first equation:
\[ 7C + 5B = 600 \quad \text{(Equation 1)} \]From the second statement, "Five toy cars and three toy bikes together cost Rs 400", we can form the second equation:
\[ 5C + 3B = 400 \quad \text{(Equation 2)} \]To solve this system of equations, we can use the elimination method. Multiply Equation 1 by 3 and Equation 2 by 5 to make the coefficients of \(B\) equal:
Multiply Equation 1 by 3:
\[ 3 \times (7C + 5B) = 3 \times 600 \]\[ 21C + 15B = 1800 \quad \text{(Equation 3)} \]Multiply Equation 2 by 5:
\[ 5 \times (5C + 3B) = 5 \times 400 \]\[ 25C + 15B = 2000 \quad \text{(Equation 4)} \]Now, subtract Equation 3 from Equation 4 to eliminate \(B\):
\[ (25C + 15B) - (21C + 15B) = 2000 - 1800 \]\[ 25C - 21C + 15B - 15B = 200 \]\[ 4C = 200 \]Solve for \(C\):
\[ C = \frac{200}{4} \]\[ C = 50 \]Thus, the cost of each toy car is Rs 50.
C) Rs 50 — By setting up and solving the system of linear equations, we found that the cost of each toy car (\(C\)) is Rs 50.
This problem involves arranging six friends based on their relative heights. We need to deduce the tallest person by systematically combining the given height comparisons and identifying the shortest person as a fixed reference point.
From the third point, we have Janak < Parth < Gagan.
From the second point, we know Janak > Manoj. So, Manoj < Janak < Parth < Gagan.
From the first point, we know Anant > Gagan. Combining this with the previous chain, we get: Manoj < Janak < Parth < Gagan < Anant.
D) Anant is the tallest among them, as derived from the combined height comparisons.