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Question : If $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$, then find the value of $\cot A$.
Option 1: $1$
Option 2: $\frac{1}{2}$
Option 3: $\frac{1}{3}$
Option 4: $2$
Correct Answer: $\frac{1}{2}$
Solution : Given, $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$ Taking $\sin A$ as common ⇒ $\frac{\sin A(2-\frac{\cos A}{\sin A})}{\sin A(1+\frac{\cos A}{\sin A})}=1$ ⇒ $2-\cot A=1+\cot A$ ⇒ $2\cot A = 1$ ⇒ $\cot A = \frac12$ Hence, the correct answer is $\frac12$.
Question : If $\theta$ is a positive acute angle and $4\cos ^{2}\theta -4\cos \theta +1=0$, then the value of $\tan (\theta -15^{\circ})$is equal to:
Option 1: $0$
Option 2: $1$
Option 3: $\sqrt{3}$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $1$
Solution : Given: $4\cos ^{2}\theta -4\cos \theta +1=0$ The above equation is written as $⇒(2\cos \theta - 1)^2 = 0$ $⇒2\cos \theta-1 = 0$ $⇒\cos \theta = \frac{1}{2}$ $⇒\cos \theta = \cos60^{\circ}$ $⇒\theta = 60^{\circ}$ Now, putting the value of $\theta$ in $\tan (\theta -15^{\circ})$, we get,
Question : Directions: In the given question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
My father is very _______ to me; we play football every evening.
Option 1: friendly
Option 2: friends
Option 3: friend-like
Option 4: friendship
Correct Answer: friendly
Solution : The correct choice is the first option.
The adjective friendly is the correct choice in this context because it describes the nature of the relationship between the speaker and their father. "Friendly" means having a kind, pleasant, or amicable disposition towards someone, and it indicates
Question : What can be the maximum interval between two Sessions of Parliament?
Option 1: Three months
Option 2: Four months
Option 3: Six months
Option 4: Nine months
Correct Answer: Six months
Solution : The correct option is Six months
A maximum of six months cannot elapse between two legislative sessions. In other words, there should be at least two annual meetings of the Parliament. Typically, there are three sessions per year. The Constitution's Article 85 addresses the
Question : Select the most appropriate ANTONYM of the word ‘polite’ in the given sentence.
The rude and insensitive murderer pleaded for mercy in the court.
Option 1: Pleaded
Option 2: Mercy
Option 3: Insensitive
Option 4: Rude
Correct Answer: Rude
Solution : The correct choice is the fourth option.
In the given sentence, the context describes a murderer exhibiting behaviour that is contradictory to being polite.
The murderer is portrayed as rude and insensitive, which stands in direct contrast to the concept of being
Question : Select the INCORRECTLY spelt word.
Option 1: Acknowledgement
Option 2: Accomodate
Option 3: Address
Option 4: Acquire
Correct Answer: Accomodate
Solution : The second option is the correct answer.
The incorrectly spelled word is "accommodate". The correct spelling is "accommodate", meaning to provide lodging or make adjustments.
The meanings of the other options are as follows:
Acknowledgement means recognition or acceptance of something.
Address refers to
Question : Directions: Find out the number of triangles in the given figure.
Option 1: 13
Option 2: 15
Option 3: 16
Option 4: 17
Correct Answer: 16
Solution : The given figure can be labelled as shown below –
Now, in the above figure, there are a total of 16 triangles. They are ABK, KBN, KLJ, HIM, HNF, FHG, NLM, NKH, BCN, NEF, CNE, DCE, BDF, KEG, ACH, ADG.
Hence, the third option is
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: ggijkk
Option 2: aacdff
Option 3: mmopqq
Option 4: qqstuu
Correct Answer: aacdff
Solution : Let's check the options –
First option: ggijkk; g + 0 = g; g + 2 = i; i + 1 = j; j + 1 = k; k + 0 = k Second option: aacdff; a + 0 = a; a + 2 =
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".
Kindly confirm by letter and telephone (1) / that you will be able (2) / to attend the interview. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The error lies in the second part of the sentence.
That should be replaced with whether. The conjunction that is used to introduce the reported clause and whether is used in case of two or more alternatives.
Therefore, the correct sentence is: Kindly confirm
Question : The threshold limit for total income eligible for rebate under Section 87A has been increased from 5,00,000 to INR_____for assesses opting for the new tax regime as per the Finance Bill 2023.
Option 1: 7,00,000
Option 2: 11,00,000
Option 3: 8,00,000
Option 4: 10,00,000
Correct Answer: 7,00,000
Solution : The correct answer is 7,00,000.
A financial document outlining the Indian government's tax proposals and budgetary allocations for the fiscal year 2023-2024 is the Finance Act 2023. The tax rebate under Section 87A has been increased to Rs. 5,00,000 for taxable income up to
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