The question asks to identify the individual who presented India's first Union Budget after independence in 1947. This is a factual question related to Indian political history and finance.
Correct Option: C) R. K. Shanmukham Chetty presented the first Union Budget of independent India on November 26, 1947. This budget covered a period of seven and a half months from August 15, 1947, to March 31, 1948.
On which network was the first SMS sent?
The question asks to identify the network on which the first Short Message Service (SMS) was sent. This is a historical fact related to telecommunications.
Correct Option: B) Vodafone
The first SMS was successfully sent over the Vodafone GSM network in the United Kingdom in 1992. This marked a significant milestone in mobile communication history.
The question asks to identify the category to which McAfee belongs. This requires knowledge of common computer software and hardware terms.
A) Anti-virus software
McAfee is a prominent company that produces security software, most notably anti-virus programs, which are designed to protect computers from viruses, malware, and other online threats.
The question presents an Assertion (A) and a Reason (R) related to the Indian judiciary. We need to evaluate the truthfulness of both statements independently and then determine if R correctly explains A. This requires knowledge of the fundamental principles of the Indian Constitution regarding the judiciary.
The Indian Constitution establishes an independent judiciary. This independence is secured through various provisions, such as the appointment process of judges, security of tenure, fixed service conditions, and the prohibition on discussion of judges' conduct in the legislature. The judiciary's role is to interpret the Constitution and laws, and to act as a guardian of fundamental rights, which necessitates its independence from both the executive and the legislature. Therefore, Assertion (A) is true.
An independent judiciary, by its very definition, is not supposed to favor any branch of the government, including the executive. Its primary role is to uphold the Constitution and the rule of law, even if it means ruling against the government. If the judiciary were to favor the government and help implement its plans, it would compromise its impartiality and independence, which are cornerstones of a democratic system. Therefore, Reason (R) is false.
Since A is true and R is false, there is no question of R being a correct explanation for A.
Correct Option: A) A is true but R is false.
This problem involves setting up and solving a system of two equations based on the given information about the ages of Swati and Aparna. We will use variables to represent their ages, form equations, and then solve for the age of Swati.
Let Swati's age be \(S\) years and Aparna's age be \(A\) years.
From the first statement, "The product of the ages of Swati and Aparna is 120", we can write the equation:
\[ S \times A = 120 \quad \text{(Equation 1)} \]From the second statement, "If Swati's age is more than thrice the age of Aparna by 2 years", we can write the equation:
\[ S = 3A + 2 \quad \text{(Equation 2)} \]Now, substitute Equation 2 into Equation 1 to eliminate \(S\):
\[ (3A + 2) \times A = 120 \]Distribute \(A\) on the left side:
\[ 3A^2 + 2A = 120 \]Rearrange the equation into a standard quadratic form \(aA^2 + bA + c = 0\):
\[ 3A^2 + 2A - 120 = 0 \]Solve this quadratic equation for \(A\). We can use factorization or the quadratic formula. For factorization, we look for two numbers whose product is \(3 \times (-120) = -360\) and whose sum is \(2\). These numbers are \(20\) and \(-18\).
\[ 3A^2 + 20A - 18A - 120 = 0 \] \[ A(3A + 20) - 6(3A + 20) = 0 \] \[ (A - 6)(3A + 20) = 0 \]This gives two possible values for \(A\):
\[ A - 6 = 0 \implies A = 6 \] \[ 3A + 20 = 0 \implies A = -\frac{20}{3} \]Since age cannot be negative, we discard \(A = -\frac{20}{3}\). Therefore, Aparna's age is \(A = 6\) years.
Now, substitute \(A = 6\) back into Equation 2 to find Swati's age \(S\):
\[ S = 3A + 2 \] \[ S = 3(6) + 2 \] \[ S = 18 + 2 \] \[ S = 20 \]So, Swati's age is 20 years.
Correct Option: B) 20
We are given two scenarios involving the selling price and profit/loss percentage. We can set up equations based on these scenarios, relating the selling price, cost price, and profit/loss percentages. By finding the difference in selling prices and the corresponding difference in percentage of cost price, we can determine the cost price.
Let the Cost Price (CP) of the water purifier be \( \text{Rs. } x \).
Scenario 1: Loss of 40%
If there is a loss of 40%, the Selling Price (SP1) is 100% - 40% = 60% of the Cost Price.
\[ \text{SP1} = (100\% - 40\%) \times x = 0.60x \]Scenario 2: Profit of 10%
If the selling price is increased by Rs. 125, the wholesaler gets a profit of 10%. This means the new Selling Price (SP2) is 100% + 10% = 110% of the Cost Price.
\[ \text{SP2} = (100\% + 10\%) \times x = 1.10x \]Relating SP1 and SP2
According to the problem, if the selling price (SP1) is increased by Rs. 125, it becomes SP2.
\[ \text{SP2} = \text{SP1} + 125 \]Substitute the expressions for SP1 and SP2 into the equation:
\[ 1.10x = 0.60x + 125 \]Solve for \(x\):
Subtract \(0.60x\) from both sides:
\[ 1.10x - 0.60x = 125 \] \[ 0.50x = 125 \]Divide by 0.50:
\[ x = \frac{125}{0.50} \] \[ x = \frac{125}{\frac{1}{2}} \] \[ x = 125 \times 2 \] \[ x = 250 \]So, the cost price of the purifier is Rs. 250.
Correct Option: A) Rs. 250
This is a coding-decoding question where a word is coded based on a specific pattern. We need to identify the pattern used to code "IRON" as "GOKI" and then apply the same pattern to decode "KNIFE".
Original word: I R O N
Coded word: G O K I
The pattern is a decreasing subtraction sequence: \(-2, -3, -4, -5\).
C) IKEAY is the correct option as it matches the letters derived from applying the \(-2, -3, -4, -5, -6\) pattern to KNIFE.
The question asks to identify the tennis player who received the Padma Bhushan award in 2016. This requires knowledge of prominent Indian sports personalities and their national awards.
Correct Option: A) Sania Mirza was awarded the Padma Bhushan in 2016. She is a highly accomplished Indian professional tennis player, known for her success in doubles and mixed doubles. She was ranked world No. 1 in women's doubles.
This question tests general knowledge about common acronyms, specifically one related to banking and finance. The task is to identify the full form of "ATM".
Correct Option: B) Automated Teller Machine
This problem involves calculating profit percentage based on a given condition where the gain is expressed in terms of the selling price of a certain number of items. We will use the fundamental formulas for profit and profit percentage.
Let \( \text{SP} \) be the selling price of one pen and \( \text{CP} \) be the cost price of one pen.
When Vijay sells 12 pens, the total selling price is \( 12 \times \text{SP} \).
The total cost price for 12 pens is \( 12 \times \text{CP} \).
The problem states that he gains the selling price of 2 pens. So, the total gain is \( 2 \times \text{SP} \).
The formula for gain is: \( \text{Gain} = \text{Total Selling Price} - \text{Total Cost Price} \).
Substitute the values into the gain formula:
\[ 2 \times \text{SP} = (12 \times \text{SP}) - (12 \times \text{CP}) \]Rearrange the equation to find the relationship between \(\text{SP}\) and \(\text{CP}\):
\[ 12 \times \text{CP} = (12 \times \text{SP}) - (2 \times \text{SP}) \] \[ 12 \times \text{CP} = 10 \times \text{SP} \]Now, we can express \(\text{SP}\) in terms of \(\text{CP}\) or vice versa. Let's find the gain per pen:
\[ \text{Gain per pen} = \text{SP} - \text{CP} \]From \( 12 \times \text{CP} = 10 \times \text{SP} \), we get \[\text{SP} = \frac{12}{10} \times \text{CP} = \frac{6}{5} \times \text{CP}\].
Calculate the gain per pen:
\[ \text{Gain per pen} = \frac{6}{5} \times \text{CP} - \text{CP} = \left(\frac{6}{5} - 1\right) \times \text{CP} = \frac{1}{5} \times \text{CP} \]The profit percentage is calculated as:
\[ \text{Profit Percentage} = \frac{\text{Gain}}{\text{Cost Price}} \times 100\% \]Using the gain per pen and cost price per pen:
\[ \text{Profit Percentage} = \frac{\frac{1}{5} \times \text{CP}}{\text{CP}} \times 100\% \] \[ \text{Profit Percentage} = \frac{1}{5} \times 100\% \] \[ \text{Profit Percentage} = 20\% \]B) 20%