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Question : If $m+n=1$, then the value of $m^{3}+n^{3}+3mn$ is equal to:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
Correct Answer: 1
Solution : Given: $m+n=1$ Cubing both sides, we get $(m+n)^3=1^3$ ⇒ $m^3+n^3+3mn(m+n)=1$ Putting the value of $(m+n)$ ⇒ $m^3+n^3+3mn(1)=1$ Thus, $m^3+n^3+3mn=1$ Hence, the correct answer is 1.
Question : If $x+ \sqrt{5} = 5+\sqrt{y}$ are positive integers, then the value of $\frac{\sqrt{x}+y}{x+ \sqrt{y}}$ is:
Option 1: 1
Option 2: 2
Option 3: $\sqrt{5}$
Option 4: 5
Solution : Given: $x+ \sqrt{5} = 5+\sqrt{y}$ By comparing rational and irrational numbers, we get ⇒ $x = 5$ and $\sqrt{y} = \sqrt{5}$ ⇒ $y = 5$ By putting the values of $x$ and $y$ in the given expression, $ \frac{\sqrt{x}+y}{x+ \sqrt{y}}$ $=\frac{\sqrt{5}+5}{5+ \sqrt{5}}$ $= 1$ Hence,
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.
I arrived in Delhi in 2009 from a very small town. I had (1)______ lived in a big city before. It was a (2)______ experience for me. I walked around, learning (3)______ names of the streets and taking notes (4)______ the shops. After months of wandering, I (5)______ that I had slowly become familiar with Delhi and (6)______ at home. On weekends, I packed some chapatis that (7)______ as my mid-day meal. Then I left for a (8)______ park where I spent hours (9)______ the people of my new city (10)______ feeding the birds with bits of chapatis.
Question:
Select the most appropriate option to fill in the blank No. 1.
Option 1: totally
Option 2: never
Option 3: ever
Option 4: almost
Correct Answer: never
Solution : The second option is correct.
As per the 1st sentence of the cloze test, the subject had not lived in a big city in the past.
Thus, the adverb never, will be the correct choice in the first blank.
Question : Who was the Prime Minister when the Right to Property was scrapped as a Fundamental Right?
Option 1: Charan Singh
Option 2: Indira Gandhi
Option 3: Morarji Desai
Option 4: Jawaharlal Nehru
Correct Answer: Morarji Desai
Solution : The correct answer is Morarji Desai.
The Indian Constitution initially recognised the right to property as a fundamental right but faced challenges, particularly with the First Amendment of 1951 and subsequent laws concealed in the Ninth Schedule. Further erosion occurred during legal battles
Question : A sold a watch at a gain of 5% to B and B sold it to C at a gain of 4%. If C paid Rs. 91 for it, the price paid by A is:
Option 1: Rs. 83.33
Option 2: Rs. 84.33
Option 3: Rs. 83
Option 4: Rs. 82.81
Correct Answer: Rs. 83.33
Solution : Let the cost price (CP) of the watch for A be $x$. Selling price (SP) of A = CP of B = $\frac{105}{100}\times x$ SP of B = CP of C = $\frac{104}{100}\times\frac{105}{100}\times x$ Given: CP of C = Rs. 91 So, $\frac{104}{100}\times\frac{105}{100}\times x$
Question : Comprehension: Read the given passage and answer the questions that follow.
Key factors influencing subway air pollution will include station depth, date of construction, type of ventilation (natural or air conditioning), types of brakes (electromagnetic or conventional brake pads) and wheels (rubber or steel) used on the trains, train frequency, and more recently, the presence or absence of platform screen-door systems.
In particular, much subway particulate matter is sourced from moving train parts such as wheels and brake pads, as well as from the steel rails and power supply materials, making the particles predominantly iron-containing.
To date, there is no clear epidemiological indication of abnormal health effects on underground workers and commuters. New York subway workers have been exposed to such air without significant observed impacts on their health, and no increased risk of lung cancer was found among subway train drivers in the Stockholm subway system.
But a note of caution is struck by the observations of scholars who found that employees working on the platforms of Stockholm underground, where PM concentrations were greatest, tended to have higher levels of risk markers for cardiovascular disease than ticket sellers and train drivers.
The dominantly ferrous particles are mixed with particles from a range of other sources, including rock ballast from the track, biological aerosols such as bacteria and viruses, and air from the outdoors, and driven through the tunnel system on turbulent air currents generated by the trains themselves and ventilation systems.
Question: Which of the following diseases is found commonly among workers in underground subways?
Option 1: Abdominal
Option 2: Renal
Option 3: Cardiovascular
Option 4: Pulmonary
Correct Answer: Cardiovascular
Solution : The correct choice is the third option.
As stated in the second last passage, employees working on the platforms of Stockholm underground, where PM concentrations were highest, tended to have higher levels of risk markers for cardiovascular disease than ticket sellers and train drivers.
Question : Directions: After arranging the given words according to dictionary order, which word will come in the Fourth position? 1. Agenda 2. Agentry 3. Ageism 4. Ageist 5. Agency
Option 1: Ageist
Option 2: Agenda
Option 3: Agentry
Option 4: Agency
Correct Answer: Agenda
Solution : Given: 1. Agenda 2. Agentry 3. Ageism 4. Ageist 5. Agency
Step 1: Compare the first, second, and third letters of each word. Since all the words start with the same letter A and are followed by g and e, then move on to
Question : A sum of money at simple interest amounts to INR 610 in 3 years and to INR 650 in 4 years. The sum is:
Option 1: INR 610
Option 2: INR 570
Option 3: INR 550
Option 4: INR 490
Correct Answer: INR 490
Solution : Amount for 3 years = INR 610 Amount for 4 years = INR 650 Simple interest = Amount – Principal Simple interest for third year = 650 – 610 = INR 40 Total simple interest for 3 years = 40 × 3 = INR
Question : The Barabati Sports Stadium is located in the state of:
Option 1: Assam
Option 2: Goa
Option 3: Odisha
Option 4: Himachal Pradesh
Correct Answer: Odisha
Solution : The correct option is Odisha
The state of Odisha is home to the Barabati Stadium. It is located in Cuttack, one of the most well-known cities in the state. Over the years, the stadium—a multipurpose location—has played host to several domestic and international cricket matches.
Question : Directions: If A denotes addition, B denotes multiplication, C denotes subtraction, and D denotes division, then what will be the value of the following equation? 8 B 4 A 7 C 21 = ?
Option 1: 18
Option 2: 26
Option 3: 21
Option 4: 16
Correct Answer: 18
Solution : Given: A denotes addition, B denotes multiplication, C denotes subtraction, and D denotes division. 8 B 4 A 7 C 21 = ?
The equation after replacing the letters will be – = 8 × 4 + 7 – 21 = 32 + 7 –
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