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Question : If $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ then the value of $\left(\sin ^4 \theta+\cos ^4 \theta\right)$ is:
Option 1: $1$
Option 2: $\frac{5}{3}$
Option 3: $\frac{2}{3}$
Option 4: $\frac{1}{3}$
Correct Answer: $\frac{1}{3}$
Solution : Given: $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ We know that $\sin^2 \theta + \cos^2 \theta = 1$ Squaring both sides, $⇒\sin^4 \theta + \cos^4 \theta + 2\sin^2\theta\cos^2\theta= 1$ $⇒\sin^4 \theta + \cos^4 \theta + 2(\sin\theta\cos\theta)^2 = 1$ $⇒\sin^4 \theta + \cos^4 \theta + 2\times (\frac{1}{\sqrt{3}})^2 = 1$
Question : Directions: Select the set in which the numbers are related in the same way as those of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 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.) (264, 462); (132, 330)
Option 1: (211, 340)
Option 2: (188, 378)
Option 3: (386, 584)
Option 4: (282, 496)
Correct Answer: (386, 584)
Solution : Given: (264, 462); (132, 330)
Like, (264, 462)→264 + 198 = 462 (132, 330)→132 + 198 = 330
Let's check the options – First option: (211, 340)→211 + 198 = 409 ≠ 340 Second option: (188, 378)→188 + 198 = 386 ≠ 378 Third
Question : Directions: Some equations have been solved using the same pattern of a certain system. Find out the correct answer for the unsolved equation using the same pattern. If 4 × 5 × 2 = 524, 3 × 7 × 2 = 723, 6 × 8 × 7 = 876, then, 9 × 4 × 5 = ?
Option 1: 495
Option 2: 459
Option 3: 549
Option 4: 954
Correct Answer: 459
Solution : Given: 4 × 5 × 2 = 524, 3 × 7 × 2 = 723, 6 × 8 × 7 = 876
The first number moves to the third position, the second number moves to the first position, and the third number moves to the
Question : Study the given graph and answer the question that follows.
In how many years was the revenue of the company more than 1.2 times the average expenditure over the given five years?
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 3
Correct Answer: 2
Solution : According to the question Total expenditure in 2014 to 2018 = 150 + 210 + 350 + 275 + 325 = 1310 ⇒ Average from 2014 to 2018 = $\frac{\text{1310 }}{5}$ = 262 ⇒ 1.2 times of expenditure = 262 × 1.2 = 314.4 In
Question : Two numbers are 90% and 75% less than a third number. By what percentage should the first number be increased so that it becomes equal to the second number?
Option 1: 250
Option 2: 200
Option 3: 150
Option 4: 100
Correct Answer: 150
Solution : Given: Two numbers are 90% and 75% less than a third number. Let the third number be 100. Now, the first and second numbers are 90% and 75% less than the third number. So, the first number = (100 – 100 × $\frac{90}{100}$) = 10
Question : The surface area of a sphere is 221.76 cm2. Its volume (in cm3) is (correct to one decimal place): (Take $\pi=\frac{22}{7}$)
Option 1: 315.6
Option 2: 289.8
Option 3: 280.4
Option 4: 310.5
Correct Answer: 310.5
Solution : The total surface area of the sphere = $4\pi r^2$ Where, $r$ = radius of the sphere According to the question, we have $4\pi r^2 = 221.76$ $⇒4 \times (\frac{22}{7}) \times r^2 = 221.76$ $⇒ r^2 = 17.64$ $\therefore r = 4.2\ \text{cm}$ Now, The
Question : Reverse transcription was discovered by:
Option 1: Beadle & Tatum
Option 2: Waston & Crick
Option 3: Temin & Baltimore
Option 4: har Govind Khorana
Correct Answer: Temin & Baltimore
Solution : The correct option is - Temin & Baltimore.
David Baltimore and Howard Temin independently and concurrently discovered reverse transcriptase in retroviruses (at the time, RNA tumor viruses), which revolutionized molecular biology and laid the groundwork for retrovirology and cancer biology in 1970.
Question : Directions: If it was Tuesday, the 21st of February 2017, then what would be the day of the week on the 5th of February 2025? (2020 and 2024 are leap years.)
Option 1: Thursday
Option 2: Tuesday
Option 3: Monday
Option 4: Wednesday
Correct Answer: Wednesday
Solution : Given: The 21st of February 2017 is Tuesday.
First, find the total number of days – 2017→7 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 = 313
Question : Select the most appropriate word for the given group of words.
A calculated move to gain an advantage.
Option 1: Grunt
Option 2: Bonsai
Option 3: Gambit
Option 4: Profit
Correct Answer: Gambit
Solution : The correct choice is the third option.
Explanation: In this context, the phrase "calculated move to gain an advantage" suggests a strategic and intentional action. Gambit is a term commonly used to describe a calculated opening move in chess or any other deliberate strategy
Question : If the length of a certain rectangle is decreased by 4 cm and breadth is increased by 2 cm, it would result in a square of the same area. What is the perimeter of the original rectangle?
Option 1: 15 cm
Option 2: 24 cm
Option 3: 20 cm
Option 4: 10 cm
Correct Answer: 20 cm
Solution : Let length be L and breadth be B, Since the sides of the square are equal, ⇒ L − 4 = B + 2 ...........(1) ⇒ L = B + 6 The area of the rectangle is equal to the area of the square,
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