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Question : If $2 \sin \theta+2 \sin ^2 \theta=2$, then the value of $2 \cos ^4 \theta+2 \cos ^2 \theta$ is:
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 0
Correct Answer: 2
Solution : Given: $2 \sin \theta+2 \sin ^2 \theta=2$ ⇒ $2\sin\theta + 2\sin^2\theta = 2(\sin^2\theta + \cos^2\theta)$ ⇒ $2\sin\theta + 2\sin^2\theta = 2\sin^2\theta + 2\cos^2\theta$ ⇒ $2\sin\theta = 2\cos^2\theta$ ⇒ $\sin\theta = \cos^2\theta$ Putting the value in the given equation, $2 \cos ^4 \theta+2 \cos ^2 \theta$
Question : What is meant by "Capital Gains"?
Option 1: Part of the profits added to the capital
Option 2: Appreciation in the money value of assets
Option 3: Additions to the capital invested in a business
Option 4: None of these
Correct Answer: Appreciation in the money value of assets
Solution : The correct answer is appreciation in the money value of assets.
The term " capital gain" refers to the profit or rise in the value of a capital asset when it is sold or transferred for more than
Question : Which is the smallest three-digit number which when increased by 5 becomes divisible by both 2 and 3?
Option 1: 102
Option 2: 105
Option 3: 103
Option 4: 108
Correct Answer: 103
Solution : Consider the numbers, 102, 103, 105, and 108 ⇒ For 102, When increased by 5, the number becomes 107 which is not divisible by 2. Now, The number = 103 When increased by 5, the number = 108 ⇒ $\frac{108}{2}=54$ and $\frac{108}{3}=36$ Number = 105,
Question : How many composite numbers are there from 53 to 97?
Option 1: 36
Option 2: 38
Option 3: 37
Option 4: 35
Correct Answer: 35
Solution : Given: The numbers are from 53 to 97. Numbers with more than two factors are called composite numbers. The composite number between 53 and 97 = 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77,
Question : Choose the correct spelling of the underlined word.
The school calander this year has turned out really nice.
Option 1: celender
Option 2: calendar
Option 3: calunder
Option 4: calender
Correct Answer: calendar
Solution : The correct choice is the second option.
Explanation:
We have to consider the correct spelling of the word "calendar". The standard and correct spelling of the word is "calendar". The error is in the usage of an "a" instead of an "e", making
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at MN as shown below.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on line MN). So, the left side of the reflected image will appear
Question : Directions: In a certain code language, P – Q means P is the wife of Q; P ÷ Q means P is the husband of Q; P × Q means P is the son of Q; P + Q means P is the daughter of Q. Based on the above, if H – I × J ÷ K + G, then how is I related to G?
Option 1: Daughter's son
Option 2: Mother's father
Option 3: Mother's mother
Option 4: Son
Correct Answer: Daughter's son
Solution : Given: P – Q ⇒ P is the wife of Q P ÷ Q ⇒ P is the husband of Q P × Q ⇒ P is the son of Q P + Q ⇒ P is the daughter of Q
As per the
Question : There is a number consisting of two digits. The digit in the unit's place is twice that of the ten's place and if 2 is subtracted from the sum of the digits, the difference is equal to $\frac{1}{6}$th of the number. The number is:
Option 1: 26
Option 2: 25
Option 3: 24
Option 4: 23
Correct Answer: 24
Solution : Let the digit at the tens's place and the digit at the unit's place be 'a' and 'b' respectively. Given that b = 2a, The number becomes 10a + b = 10a + 2a = 12a Now, the sum of digits = (a + b)
Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.
Malti had to wait long to see her son, Abhik. She had worked hard to (1)______ her husband’s last wish that Abhik should (2)______ his higher education at Cambridge. Abhik (3)______ to be meritorious and hardworking and had secured a seat. Making ends meet was (4)______ and a trip back home in the vacation, (5)______ for the mother and son.
Question:
Select the most appropriate option to fill in the blank no. 2.
Option 1: provide
Option 2: approach
Option 3: delete
Option 4: pursue
Correct Answer: pursue
Solution : The correct choice is the fourth option.
Pursue means to achieve something over a long time. It helps convey that the last wish of Malti's husband was that his son Abhik complete his higher education at Cambridge.
Therefore, the complete sentence is: "She had
Question : Microorganisms are classified into how many major groups?
Option 1: 1
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : The correct option is 4
There are four main categories of microorganisms:
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