Explore topic-wise InterviewSolutions in Current Affairs.

(b+c+a)(b+c-a)

=(b+c)² - a² = 3bc

b² + c² - a² = bc

(b² + c² - a²)/2bc  =  1/2

So,  Cos A = 1/2.        (Cosine rule)

So, A = 60

Correct option is: (B) 45°

Correct answer is (D) ±2√6

Correct option is: (B) 0

Calculation:

From statement I

The only difference between the ages of Suresh and Mahesh is given. We cannot determine the sum of ages of Suresh and Mahesh.

So, the Statement I alone is not sufficient to answer the question.

From statement II

Let the age of Suresh and Mahesh 6 years before is 4x and 5x respectively.

Then, 5x – 4x = 7

⇒ x = 7

Present age of Mahesh = (5 × 7) + 6

⇒ 35 + 6

⇒ 41 years

Present age of Suresh = (4 × 7) + 6

⇒ 28 + 6

⇒ 34 years

Sum of the present ages of Suresh and Mahesh = 41 + 34

⇒ 75 years

So the statement I and II together is sufficient to answer the question.

From statement III

No relation between their present age is given. We cannot determine the sum of the ages of Suresh and Mahesh.

So, statement III alone is not sufficient to answer the question.

From statement I and statement III together

Let after 10 years Mahesh’s will be 3x and half of the present age of Suresh is x. Then the present age of Mahesh is (3x – 10) and the present age of Suresh is 2x.

Then, (3x – 10) – 2x = 7

⇒ 3x – 10 – 2x = 7

⇒ 3x – 2x = 10 + 7

⇒ x = 17

The present age of Mahesh = (3 × 17) – 10

⇒ 51 – 10

⇒ 41 years

The present age of Suresh = 2 × 17

⇒ 34 years

Sum of present ages of Suresh and Mahesh = 41 + 34

⇒ 75 years

So, the statement I and III together are sufficient to answer the question.

∴ If data in either statement I and II together or data in statements I and III together are sufficient to answer the question.

Correct option is: (A) 1

Given:

(a + b + c) ∶ d = 3 ∶ 1

(b + c + d) ∶ a = 5

(c + d + a) ∶ b = 2 ∶ 1

Calculations:

Let a + b + c + d be x

(a + b + c) ∶ d = 3 ∶ 1

Now, d = (x/4) × 1 = x/4

(b + c + d) ∶ a = 5 ∶ 1

Now, a = (x/6) × 1 = x/6

(c + d + a) ∶ b = 2 ∶ 1

Now, b = (x/3) × 1 = x/3

c = (a + b + c + d) – (a + b + d)

⇒ x – ((x/4) + (x/6) + (x/3))

⇒ x – (6x + 4x + 8x)/24

⇒ (24x – 18x)/24

⇒ x/4

So a ∶ b ∶ c ∶ d = x/6 ∶ x/3 ∶ x/4 ∶ x/4

⇒ a ∶ b ∶ c ∶ d = 2 ∶ 4 ∶ 3 ∶ 3

∴ a ∶ b ∶ c ∶ d is 2 ∶ 4 ∶ 3 ∶ 3

Correct option is B) anyone 

Correct option is B) constantly

Correct option is  B) Anyone

Correct option is A) encourages

Rush hour

Accidents on this road are frequent during the evening rush hour, especially during the winter.

Dish

My mom's pasta dish is really one of the best in the entire state.

Promotion

The promotion to VP of the company comes with a hefty salary hike and many more perks: you can achieve your dream if you get this!

Pamper

Rich parents often pamper their children by giving them lavish gifts and zero responsibilities.

Absolute value of -5/7 = 5/7

Absolute value of 4/3 = 4/3

5/7 < 4/3.

(1) (i)The unit digit in 77 is 7

And 7² = 49 whose unit digit is 9.

\(\because\) The ones digit (or unit digit) in the square of 77 is 9.

(ii) \(\because\) Number of non-square numbers between squares of two conscutive integers (or between n² & (n + 1)²) is 2n.

\(\therefore\) Number of non-square numbers between 24² and 25² is 2 x 24 = 48

(iii) \(\because\) 17² = 289 < 300 and 22² = 484 < 500 & 23² = 529 > 500

(iv) If a number has n digits the number of digits in its square root is (i) n/2 if n is even (ii) \(\frac{n+2}2\) if n is odd.

\(\because\) 6/2 = 3 and \(\frac{5+1}2=3\)

Hence, if a number has 5 or 6 digits in it then number of digits in its square root will be 3.

(v) \(\because\) 169 < 180 < 196 i.e., 13² < 180 < 14²

⇒ 13 < \(\sqrt{180}\) < 14

Hence, the value of \(\sqrt{180}\) lies between integers 13 and 14.

(2) (i) \(\because\) 16 is a square of 4 and ends in 6

Also square root of 16 is 4 which does not have 6 in unit's place.

Hence, the statement is false.

(ii) A square number(or perfect square) always have even number of zeros at the end.

Hence, given statement is true.

\(\because\) If a number has n number of zeros then its square will have 2n number of zeros.

(iii) The number of zeroes in the square of 91000 is 2 x 3 = 6

Hence, given statement is false.

(iv) 75² = (70 + 5)² = 70² + 2 x 70 x 5 + 5²

 = 4900 + 700 + 25 = 5625

Hence, given statement is false

(v) \(\sqrt{225}=\sqrt{3\times3\times5\times5}=\sqrt{3^2\times5^2}\) 

\(=\sqrt{(3\times5)^2}\) = 3 x 5 = 15

Hence, given statement is true.

\(1.3\bar 2+0.\bar{35}\) 

= 1.322222...+ 0.353535...

= 1.675757

= \(1.6\bar{75}\)

Let x = \(1.6\bar{75}\)

\(\therefore\) 10x = \(16.\bar{75}\)

1000 x = 1675.\(\bar{75}\)

\(\therefore\) 1000 x - 10 x = 1675. \(\bar{75}\) - 16. \(\bar{75}\)

⇒ 990 x = 1659

⇒ x = \(\frac{1659}{990}\) = \(\frac{553}{330}\) 

Hence, required p/q form is \(\frac{553}{330}\)

To find the cumulative frequency of this value, we just need to add its absolute frequency to the running total. In other words, take the last cumulative frequency you found, then add this value's absolute frequency. Example: 3 | F = 2 | CF = 2.

• Make Proper Use of The Available Resources.
• Ensure Business Development and Growth.
• Quality Products And Services.
• Availability of Goods and Services.
• Ensuring Discipline in the Workplace.
• Attracting the Best Candidates for the Job.
• Make Futuristic Plans.
• Reduce the Element of Risks.

\(\sqrt{\frac{1-cosA}{1+cosA}}+\sqrt{\frac{1+cosA}{1-cosA}}\)

 = \(\sqrt{\cfrac{1-(1-2sin^2\frac A2)}{1+(2cos^2 \frac A2-1)}}\) + \(\sqrt{\cfrac{1+(2cos^2 \frac A2-1)}{1-(1-2sin^2\frac A2)}}\) 

 = \(\sqrt{\cfrac{2sin^2\frac A2}{2cos^2\frac A2}}\) + \(\sqrt{\cfrac{2cos^2\frac A2}{2sin^2\frac A2}}\)

 = tan A/2 + cot A/2

sec A + tan A = \(\frac{a+1}{a-1}\)----(1)

\(\because\) sec²A - tan²A = 1

⇒ (sec A + tan A) (sec A - tan A) = 1

⇒ sec A - tan A = \(\frac1{sec A + tan A}\) = \(\cfrac{1}{\frac{a+1}{a-1}}\) = \(\frac{a-1}{a+1}\)

⇒ sec A - tan A = \(\frac{a-1}{a+1}\)----(2)

By adding equations (1) & (2), we get

2 sec A = \(\frac{a+1}{a-1}\) + \(\frac{a-1}{a+1}\)  = \(\frac{(a+1)^2+(a-1)^2}{(a-1)(a+1)}\)

⇒ 2sec A = \(\frac{2(a^2+1)}{a^2-1}\)

⇒ sec A = \(\frac{a^2+1}{a^2-1}\)

\(\therefore\) cos A = \(\frac1{sec A}=\frac{a^2-1}{a^2+1}\)

It allows a peripheral device to connect to a computer, and to send/receive data to

Elle was the unit of measurement that was used to measure cloth.

Given: f(x) =cos^-1\(\cfrac{\text x}2\) + (2x + 7)^-1/2

\(\cfrac{d}{d\text x}\)f(x) = cos^-1\(\cfrac{\text x}2\) x \(\cfrac{d}{d\text x}\)(2x + 7)^-1/2+ \(\left(\cfrac{d}{d\text x}cos^{-1}\cfrac{\text x}2\right)\)(2x + 7)^-1/2

\(\left(\because \cfrac{d}{d\text x}u\text v=u\times\cfrac{d\text v}{du}+\cfrac{du}{d\text x}\text v\right)\)

= \(-\cfrac{2}2\)(2x + 7)^-3/2cos^-1\(\cfrac{\text x}2\) - \(\cfrac{1}{\sqrt{1-\left(\frac{\text x}2\right)^2}}\times\)\(\cfrac12\) (2x + 7)^-1/2

(By chain rule)

 = -(2x + 7)^-3/2 cos^-1\(\cfrac{\text x}2\) - \(\cfrac{1}{\sqrt{4-\text x^2}}\) (2x + 7)^-1/2

= -(2x + 7)^-1/2\(\left(\cfrac{cos^{-1}\cfrac{\text x}2}{2\text x+7}+\cfrac1{\sqrt{4-\text x^2}}\right)\) 

= \(-\cfrac{1}{\sqrt{2\text x+ 7}}\) \(\left(\cfrac{cos^{-1}\cfrac{\text x}2}{2\text x+7}+\cfrac1{\sqrt{4-\text x^2}}\right)\) 

a. Audio Integrated line-out, microphone, and line-in ports, that provide access to integrated audio, when there is no sound cards on the computer 

b. USB Connects up to 127 different devices, such as printer with single connector to computer 

c. HDMI Connects computer to a display device, using a digital cable

d. VGA Connects computer to a display device, using an analogue cable

e. LAN Connects computer to a local network, using a network cable

A point at which a peripheral device attaches to or communicates with a computer so that the peripheral device can send data to or receive information from the computer

Input

Processing

Output

Storage

We need d/dx (e^{1+In x})

First, rewrite the expression using a^b+c ≡ a^b.a^c

e^{1+In x} = e¹.e^{In x} = xe

d/dx (xe) = e

∴ d/dx (e^{1+In x}) = e

Manage, data and information

Diverse set of technology tools and resources used to communicate, create, disseminate, store and manage information 

Let length and breadth are 4x & 3x respectively.

\(\therefore\) Perimeter = 2(4x + 3x) = 14x

\(\therefore\) 14x = 308 m

⇒ \(x = \frac{308}{14}\,m = 22\,m\)

\(\therefore\) l = 88 m

b = 66 m

Consider,

p²- 5p - 6

Spiliting the middle term

= p²-6p + p - 6

=p(p-6)+1(p-6)

= (p+1)(p-6)

\(\Rightarrow p^2-5p-6=(p+1)(p-6)\)

\(\frac{3}{1 + i} - \frac{2}{2 - i} + \frac{2}{1 - i} \)

\(= \frac{3(1 + i)}{2} - \frac{2(2 + i)}{5} + \frac{2(1 + i)}{2} \)

\(= \frac{3}{2} - \frac{4}{5} + 1 + i (\frac{-3}{2} - \frac{2}{5} + 1)\)

\(= ​​\frac{17 - 9i}{10} \)

x dx + y dy \(=\frac{x\,dx+y\,dy}{x^2+y^2}\)

⇒ 2x dx + 2y dy \(=\frac{2x\,dx+2y\,dy}{x^2+y^2}\) (Multiply both sides by 2)

⇒ ∫2x dx + ∫2y dy \(=\int\frac{2x\,dx+2y\,dy}{x^2+y^2}\)

⇒ x² + y² = ln(x² + y²) + c (∵ d[ln(x²+y²)] \(=\frac{2x\,dx+2y\,dy}{x^2+y^2})\)

Hardware

Software

Data

people

procedures

Nitrogen Cycle is a biogeochemical process through which nitrogen is converted into many forms, consecutively passing from the atmosphere to the soil to organism and back into the atmosphere.

It involves several processes such as nitrogen fixation, nitrification, denitrification, decay and putrefaction.

Nitrogen gas exists in both organic and inorganic forms. Organic nitrogen exists in living organisms, and they get passed through the food chain by the consumption of other living organisms.

Inorganic forms of nitrogen are found in abundance in the atmosphere. This nitrogen is made available to plants by symbiotic bacteria which can convert the inert nitrogen into a usable form – such as nitrites and nitrates.

Nitrogen undergoes various types of transformation to maintain a balance in the ecosystem. Furthermore, this process extends to various biomes, with the marine nitrogen cycle being one of the most complicated biogeochemical cycles.

Given:

A man covers 1 / 4^th of the distances at the speed of 10 km / hr, 20 km / hr, 40 km / hr and 8 km / hr

Formula:

Average speed = Total distance / Total time

Calculation:

Let total distance be 160 km.

1 / 4 of 160 = 40 km

Time take to covers 40 km distance at the speed of 10 km / hr = 40 / 10 = 4 hrs

Time take to covers 40 km distance at the speed of 20 km / hr = 40 / 20 = 2 hrs

Time take to covers 40 km distance at the speed of 40 km / hr = 40 / 40 = 1 hr

Time take to covers 40 km distance at the speed of 8 km / hr = 40 / 8 = 5 hrs

Total time = 4 + 2 + 1 + 5 = 12 hrs

Given:

Ram covers first 45 km at the speed of 15 km/hr

He covers next 40 km at the speed of 20 km/hr.

He covers next 60 km at the speed of 30 km/hr

Formula used:

Average speed = Total distance/Total time

Calculation:

Total distance covered = 45 + 40 + 60 = 145 km

Total time = (45/15) + (40/20) + (60/30) = 7 hr

∴ Average speed = 145/7 kmph

As f(t) & u(t) is given, when we put the value of u(t) in function f then,

f(u(t)) = 3*t^4 i -4t^2 j + 5k; then  f(u(t))' = (12*t^3) i -(8*t) j.

when we write that function including time in that function then we will write it as,

(f(u)')(t) =  (12*t^3) i -(8*t) j.

Correct option is (d) 28

Explanation :

Since 2x − 3y − 5z + d = 0 passes through (−1, 2, 4), we have 

2(-1) - 3(2) - 5(4) + d = 0

d = 28

Aggression can serve a number of different purposes, including:  

• To express anger or hostility 
• To assert dominance 
• To intimidate or threaten 
• To achieve a goal 
• To express possession 
• A response to fear 
• A reaction to pain 
• To compete with others

Let the two consecutive multiples of 6 be x,

x + 6

x, x + 6

x(x + 6) + 9 = 729

x² + 6x + 9 = 729

x² + 6x = 720 

x² + 6x – 720 = O 

x + 6x = 720 

(x + 3)² = 720 + 9 

(x + 3)² = 729 

x + 3 = ± 27 

x = 24, – 30 

The numbers are 24, – 30

The correct answer is Fridays For Future.

• Fridays For Future or FFF is a global climate strike movement that started in August 2018, when 15-year-old Greta Thunberg began a school strike for climate.
  • In the three weeks leading up to the Swedish election, she sat outside Swedish Parliament every school day, demanding urgent action on the climate crisis.
  • She was tired of society’s unwillingness to see the climate crisis for what it is a crisis.
  • On the 8th of September, Greta and her fellow school strikers decided to continue their strike until the Swedish policies provided a safe pathway well under 2° C, i.e. in line with the Paris agreement.
  • They created the hashtag #FridaysForFuture and encouraged other young people all over the world to join them.
  • This marked the beginning of the global school strike for climate.
  • Their call for action sparked an international awakening, with students and activists uniting around the globe to protest outside their local parliaments and city halls.
  • Along with other groups across the world, Fridays for Future is part of a hopeful new wave of change, inspiring millions of people to take action on the climate crisis, and we want you to become one of us.

The Heckscher-Ohlin model is an economic theory that proposes that countries export what they can most efficiently and plentifully produce. Also referred to as the H-O model or 2x2x2 model, it's used to evaluate trade and, more specifically, the equilibrium of trade between two countries that have varying specialties and natural resources.

Let x be the number

x² = 25

x = √25 = ±5

numbers are –5, +5