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Question : If $\cos 48^{\circ}=\frac{m}{n}$, then $\sec 48^{\circ}-\cot 42^{\circ}$ is equal to:
Option 1: $\frac{m-\sqrt{n^2-m^2}}{m}$
Option 2: $\frac{m-\sqrt{n^2-m^2}}{n}$
Option 3: $\frac{n-\sqrt{n^2-m^2}}{n}$
Option 4: $\frac{n-\sqrt{n^2-m^2}}{m}$
Correct Answer: $\frac{n-\sqrt{n^2-m^2}}{m}$
Solution : Given that $\cos 48^{\circ}=\frac{m}{n}$, We know that $\sec 48^{\circ}=\frac{n}{m}$, We know that $\tan \theta=\sqrt{\sec^2 \theta-1}$, Now, $\cot 42^{\circ}=\tan 48^{\circ}=\sqrt{\sec^2 48^{\circ}-1}=\sqrt{\left(\frac{n}{m}\right)^2-1}=\sqrt{\frac{n^2}{m^2}-1}=\frac{\sqrt{n^2-m^2}}{m}$ So, $\sec 48^{\circ}-\cot 42^{\circ}=\frac{n}{m}-\frac{\sqrt{n^2-m^2}}{m}=\frac{n-\sqrt{n^2-m^2}}{m}$. Hence, the correct answer is $\frac{n-\sqrt{n^2-m^2}}{m}$.
Question : Five different companies, A, B, C, D, and E, make robotic toys. The total number of robotic toys produced by these five companies is 8,00,000. The cost of production of each robotic toy is INR 5,000. The distribution of the total production is given in the following pie chart. What is the total cost of production of the given item by companies A and E together?
Option 1: INR 190 crores
Option 2: INR 85 crores
Option 3: INR 96 crores
Option 4: INR 140 crores
Correct Answer: INR 140 crores
Solution : Production by company A = 90° Production by company E = 36° Total production by A and E together = 90° + 36° = 126° So, Total cost required = $\frac{126°}{360°}$ × 8,00,000 × 5,000 = 1,400,000,000 or INR 140 crores Hence, the
Question : Directions: In a certain code language, DEEPAK is written as 3 and MEME is written as 2. How will PLAN be written in that language?
Option 1: 11
Option 2: 2
Option 3: 5
Option 4: 4
Correct Answer: 2
Solution : Given: DEEPAK is written as 3, and MEME is written as 2.
The number of letters of DEEPAK are divided by 2, to obtain the code – The number of letters in DEEPAK = 6→6 ÷ 2 = 3 Thus, DEEPAK is coded as 3.
Question : Given below are four sentences in jumbled order. Pick the option that gives their correct order.
A. However, Yusuf comforted himself by imagining the hotel food in store for him the next day. B. First, Yusuf's stomach was occupied by excitement. C. It was difficult to eat dinner that night. D. Secondly, mother was on one of her health trips and had prepared sprouted beans and yoghurt.
Option 1: BADC
Option 2: BCAD
Option 3: ACBD
Option 4: CBDA
Correct Answer: CBDA
Solution : The correct choice is the fourth option.
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence. If there is no need to substitute it, select ‘No substitution required’. The application of the medicine seemed to lesson his pain
Option 1: No substitution required
Option 2: lesion
Option 3: lessen
Option 4: lessoned
Correct Answer: lessen
Solution : The correct option is the third option.
Explanation: Lessen means to reduce or decrease something, which fits the context of the sentence where the medicine appeared to reduce the pain.
Therefore, the correct sentence should be, "The application of the medicine seemed to lessen his
Question : Directions: In the following question, identify the diagram that represents the best relationship among the classes given below. Government Servants, Lecturers, Doctors
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Government servants can either be lecturers or doctors or can be both. So, there will be a mutual intersection between the circles of government servants, lecturers, and doctors. Also, lecturers can be doctors too. So, there will be an overlap between lecturer's and doctor's circles.
The
Question : By selling 35 articles, a shopkeeper gains the selling price of 15 articles. Find his gain percentage.
Option 1: 88%
Option 2: 40%
Option 3: 75%
Option 4: 60%
Correct Answer: 75%
Solution : Given: Selling 35 articles, the shopkeeper gains the selling price of 15 articles. We know that, Selling price = Cost price + Profit Let the selling price of an article be denoted SP and the cost price as CP. ⇒ 35SP = 35CP + 15SP
Question : Select the most appropriate meaning of the underlined idiom in the given sentence. He does not have money to pay back the loan, he is in a tight corner.
Option 1: in a difficult situation
Option 2: hiding in the house
Option 3: in the prison
Option 4: being bankrupt
Correct Answer: in a difficult situation
Solution : The correct choice is the first option.
Explanation: The idiom "in a tight corner" is used to convey that someone is in a challenging situation where finding a solution or escape may be problematic. It implies being in a predicament or facing
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
This area suffers from ____.
Option 1: Drought
Option 2: Droaghts
Option 3: Draughts
Option 4: Drafts
Correct Answer: Drought
Solution : The correct choice is the first option "drought".
"Drought" means a prolonged period of abnormally low rainfall and the word fits perfectly in the sentence, conveying that the area is experiencing a period of insufficient rainfall.
The meanings of the other options are as follows:
Question : In which of the following cities of British India was Lata Mangeshkar born?
Option 1: Bombay
Option 2: Calcutta
Option 3: Lucknow
Option 4: Indore
Correct Answer: Indore
Solution : The correct answer is Indore
On September 28, 1929, Lata Mangeshkar was born into a Marathi family in Indore, the capital of the princely state of Indore, which was a part of the Central India Agency in British India. Indore is now a district
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