Compute 69696 × 9999 = ?
To compute the product \(69696 \times 9999\), we can use a simplification technique. Instead of direct multiplication, we can express \(9999\) as \((10000 - 1)\). This allows us to use the distributive property of multiplication, which often simplifies calculations, especially in competitive exams.
First part:
\[ 69696 \times 10000 = 696960000 \]Second part:
\[ 69696 \times 1 = 69696 \]Let's perform the subtraction:
696960000 - 69696 ------------- 696890304
D) \(696890304\) is the correct result obtained by performing the calculation \(69696 \times (10000 - 1) = 696960000 - 69696 = 696890304\).
In a certain code, RIPPLE is written as 613382, PREACH is coded as 362457. How is PILLER written in that code?
This is a coding-decoding problem where each letter is assigned a specific digit. We need to identify the code for each common letter from the given examples and then apply it to the target word.
Correct Option: A) 318826 is the correct code for PILLER based on the established letter-digit mapping.
A flask has two holes. The 1st hole alone makes the flask empty in 9 minutes and 2nd hole alone makes the flask empty in 16 minutes. If water leaks out at a constant rate, how long in minutes does it take if both the holes together empty the flask?
\( \frac{19}{25} \)
4\( \frac{19}{25} \)
5\( \frac{20}{25} \)
5\( \frac{19}{25} \)
This problem can be solved using the concept of work and time, specifically by calculating the rate of emptying for each hole and then summing their rates to find the combined rate. The total time taken will be the reciprocal of the combined rate.
Calculate the rate of the 1st hole: If the 1st hole alone empties the flask in 9 minutes, its rate of emptying is \( \frac{1}{9} \) of the flask per minute.
Calculate the rate of the 2nd hole: If the 2nd hole alone empties the flask in 16 minutes, its rate of emptying is \( \frac{1}{16} \) of the flask per minute.
Calculate the combined rate of both holes: When both holes work together, their rates add up. Let \( R_{\text{combined}} \) be the combined rate.
\[ R_{\text{combined}} = R_1 + R_2 = \frac{1}{9} + \frac{1}{16} \]To add these fractions, find a common denominator, which is \( 9 \times 16 = 144 \).
\[ R_{\text{combined}} = \frac{16}{144} + \frac{9}{144} = \frac{16 + 9}{144} = \frac{25}{144} \]So, the combined rate is \( \frac{25}{144} \) of the flask per minute.
Calculate the total time taken: If the combined rate is \( \frac{25}{144} \) of the flask per minute, then the time taken to empty the entire flask (which is 1 unit of work) is the reciprocal of this rate.
\[ \text{Time} = \frac{1}{R_{\text{combined}}} = \frac{1}{\frac{25}{144}} = \frac{144}{25} \text{ minutes} \]Convert the improper fraction to a mixed number: Divide 144 by 25:
\[ 144 \div 25 = 5 \text{ with a remainder of } 19 \]So, \( \frac{144}{25} \) minutes can be written as \( 5 \frac{19}{25} \) minutes.
Correct Option: D) \( 5\frac{19}{25} \)
The question asks to identify the head of the Jury for the International Film Festival of India (IFFI) in November 2015. This is a factual question related to current affairs or general knowledge about film festivals.
Correct Option: B) Shekhar Kapoor was appointed as the head of the Jury of the International Film Festival of India in November 2015. He is a renowned Indian film director, screenwriter, and producer, best known for his works in Hindi cinema and international films like "Elizabeth" and "Bandit Queen".
The question asks to identify a tsunami warning sign from the given options. We need to recall the natural indicators that precede a tsunami.
Correct Option: C) Water falling back quickly from the beach. This is a classic and often observed natural warning sign of an approaching tsunami. The sea recedes unusually far, exposing the seabed, before the massive waves hit the shore.
This problem involves applying a set of given symbol substitutions to a mathematical expression and then evaluating the new expression using the standard order of operations (BODMAS/PEMDAS).
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Operations are performed from left to right for division/multiplication and for addition/subtraction.
First, perform multiplication and division from left to right:
\[ 6 \times 7 \div 3 + 8 - 20 \] \[ 42 \div 3 + 8 - 20 \] \[ 14 + 8 - 20 \]Next, perform addition and subtraction from left to right:
\[ 14 + 8 - 20 \] \[ 22 - 20 \] \[ 2 \]Correct Option: C) 2
The question asks to identify the most abundant rare gas. Rare gases are also known as noble gases. We need to recall the relative abundance of these gases in the Earth's atmosphere.
B) Argon is the most abundant rare gas in the Earth's atmosphere, constituting approximately 0.93% by volume.
Read the statements and select a conclusion from the given alternatives:
Statement:
Sukhvinder emphasized the need to replace the present training programme by other methods which will bring out the real merit of the candidates.
Conclusions:
I. It is not important to bring out the real merit of the candidates.
II. The present training programme does not bring out the real merit of the candidates.
Only conclusion I follows.
Only conclusion II follows.
Both I and II follow.
Neither I nor II follows.
This is a statement and conclusion type of question. We need to analyze the given statement and determine which of the conclusions logically follows directly from it, without making any external assumptions.
B) Only conclusion II follows.
The problem asks us to find the standard deviation given the variance of a set of data. We need to recall the fundamental relationship between variance and standard deviation.
B) 14. The standard deviation is the positive square root of the variance. Given the variance is 196, its positive square root is 14.
The Indian National Army reclaimed the Andaman and Nicobar Islands from British rule and named them?
Swaraj Islands
Shaheed and Swaraj Islands
Free Islands
Swatantra and Swaraj Islands
The question asks about the names given to the Andaman and Nicobar Islands by the Indian National Army (INA) after reclaiming them from British rule. This is a historical fact related to India's freedom struggle.
Correct Option: B) Shaheed and Swaraj Islands. Netaji Subhas Chandra Bose renamed Andaman Island as 'Shaheed Dweep' and Nicobar Island as 'Swaraj Dweep'.