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Given:

Number = \(15 \dfrac{2}{3} \ \)= 47/3

Concept Used:

For 2 numbers a/b, c/d

If a × d > b × c, then

a/b > c/d

Calculations:

Checking option (1), we get

Numbers = 47/3, 43/5

Now, 47 × 5 = 235

3 × 43 = 129

235 > 129

⇒ 47/3 > 43/5

Similarly, Checking option (2), we get

Numbers = 47/3, 20/2

Now, 47 × 2 = 94

3 × 20 = 60

94 > 60

⇒ 47/3 > 20/2

Similarly, Checking option (3), we get

Numbers = 47/3, 49/4

Now, 47 × 4 = 188

3 × 49 = 147

188 > 147

⇒ 47/3 > 49/4

Similarly, Checking option (4), we get

Numbers = 47/3, 49/3

Now, 47 × 3 = 141

3 × 49 = 147

141 < 147

⇒ 47/3 < 49/3

∴ The number greater than 47/3 is 49/3.

Formula used :

HCF = Highest Common Factor 

HCF of fraction = (HCF of numerator/LCM of denominator)

Calculations :

For finding the HCF first convert mixed fraction to simple fraction 

⇒ \(3\frac{1}{2}\;=\;\frac{7}{2}\)  and \(8\frac{3}{4}\;=\;\frac{35}{4}\) 

Now HCF of 7/2 and 35/4 

For numerator,

HCF of 7 and 35 = 7 

For denominator, 

LCM of 2 and 4 = 4 

Fraction = 7/4 = \(1\dfrac{3}{4}\)

So, 

x = \(1\dfrac{3}{4}\)      (x is the greatest such length or HCF)

∴ The value of x will be \(1\dfrac{3}{4}\)m.

Correct option is: (c) 500

Given:  

cube root of x is equal to the square root of y

Calculation:

A/Q

∛(x) = √(y)

Take the power 6 on both the sides

x^(6/3) = y^(6/2) 

x² = y³

Concept used:-

Trick to find cube root of a number.

Method and Calculation:-

 • Find the unit digit of cube root by looking at unit digit of given number.

For cube root of 531441, unit digit must be 1 (1³ is 1)

 • Find other digit(s) by ignoring the last three digits of number and looking at remaining digits.

512 < 531 < 729 (512 and 729 are cubes of 8 and 9, so remaining part of cube root will be 8)

Hence, 81 is our answer.

Concept used:-

Trick to find cube root of a number.

Method and Calculation:-

 • Find the unit digit of cube root by looking at unit digit of given number.

For cube root of 5832, unit digit must be 8 (8³ is 512)

 • Find other digit(s) by ignoring the last three digits of number and looking at remaining digits.

1 < 5 < 8 (1 and 8 are cubes of 1 and 2, so remaining part of cube root will be 1)

Hence, 18 is our answer

Concept used:-

Trick to find cube root of a number.

Method and Calculation:-

 • Strike out last three zeros from number and put 1 zero at the end oc answer derived from remaining number

 • Find the unit digit of cube root by looking at unit digit of truncated number.

For cube root of 74088, unit digit must be 2 (2³ is 8)

 • Find other digit(s) by ignoring the last three digits of truncated number and looking at remaining digits.

64 < 74 < 125 (64 and 125 are cubes of 4 and 5, so remaining part of cube root will be 4)

Hence, 420 is our answer (zero is added to final answer)

Concept used:-

Trick to find cube root of a number.

Method and Calculation:-

 • Find the unit digit of cube root by looking at unit digit of given number.

For cube root of 85184, unit digit must be 4 (4³ is 64)

 • Find other digit(s) by ignoring the last three digits of number and looking at remaining digits.

64 < 85 < 125 (64 and 125 are cubes of 4 and 5, so remaining part of cube root will be 4)

Hence, 44 is our answer

Given:

Sum of 3 numbers is 264

The first number is twice 2nd & 3 times the 3rd

Calculations:

Ratio of number = 1 : ½ : ⅓ = 6 : 3 : 2

So,

Let the numbers be 6x, 3x & 2x

According to the question

6x + 3x + 2x = 264

⇒ 11x = 264

⇒ x = 24

Second number = 3x = 3 × 24 = 72

∴ The correct choice is option 2.

Correct option (d) (Maximm-Minimum)

Explanation:

Since the minimum is in A and the maximum is in B, the value of x cannot be less than Maximum − Minimum.

Correct option (a) A continues to be in ascending order.

Explanation:

If elements of A are in ascending order a₁₂₄ would be the largest value in A. Also a₁₂₅ would be the largest value in B. On interchanging a₁₂₄ and a₁₂₅, A continues to be in ascending order, but B would lose its descending order arrangement since a₁₂₄ would be the least value in B. 

Correct option (b) 2^2/3

Explanation:

The expression can be written as 2^1/3+1/6+1/12+.… = 2^{INFINTE SUM OF THE GP} = 2^2/3. 

Correct option (d) None of these

Explanation:

All members of A are smaller than all members of B. In order to visualise the effect of the change in sign in k assume that A is {1, 2, 3...124} and B is {126, 12.7...250}. It can be seen that for this assumption of values neither options (a), (b) or (c) is correct.  

Correct option (a) 2

Explanation:

If you look for a few more terms in the series, the series is: 1, 1/3, 1/6, 1/10, 1/15, 1/21, 1/28, 1/36, 1/45, 1/55, 1/66, 1/78, 1/91, 1/105, 1/120, 1/136. 1/153 and so on. If you estimate the values of the individual terms it can be seen that the sum would tend to 2 and would not be good enough to reach even 2.25. 

Correct option (a) n(4n² +18n +23)/3

Explanation:

Solve this using trial and error. For 1 term the sum should be 15 and we get 15 only from the first option when we put is n = 1. 

Correct option (b) 1

Explanation:

The sum to infinite terms would tend to 1 because we would get (infinity)/(infinity + 2). 

Correct option (c) 8/3

Explanation:

Trying to plug in values we can see that the infinite sum of the GP 24, 8, 8/3... is 36. 

Hence the third term is 8/3.

Given:

X and Y invest Rs 21,000 and Rs 17,500 respectively.

Total loss is Rs 26,400.

Formula Used:

L₁ : L₂ = I₁ × T₁ : I₂ × T₂

Here, L = Loss, I = Investment, T = Time

Calculation:

X and Y invest Rs. 21,000 and Rs. 17,500 respectively

At the end of the year the ratio of loss = 21000 × 1 : 17500 × 1 = 6 : 5

The ratio of loss = 6 : 5

Total loss = 26400

The share loss of X = 6/11 × 26400 = Rs. 14400

The share loss of Y = 5/11 × 26400 = Rs. 12000

∴ The share loss of X and Y is Rs. 14400 and Rs. 12000.

Given:

The seller expects 32% return on his purchase price.

The seller sell in one day was 528.

Concept Used:

Purchase price = 100/(100 + Return%) × Selling price

Calculation:

The seller expects 32% return on his purchase price.

The seller sell in one day was 528.

The purchase price = 100/(100 + 32) × 528 = 100/132 × 528 = 400

The profit amount = 528 - 400 = Rs.128

∴ The profit amount is Rs.128.

Given:

Gain percent = 25% on cost price

Selling Price = Rs. 45,500

Formula used:

Profit = SP - CP

Calculation:

Let the cost price be 100 unit

According to the question

Expected Selling price = 100 + 25 = 125 unit

125 unit → Rs. 45,500

1 unit → 45500/125

1 unit → 364

100 unit → 364 × 100

CP = 100 unit = Rs. 36,400

Now, Profit = SP - CP

Profit = 45,500 - 36,400

Profit = Rs. 9100

∴ Required profit is Rs. 9100.

Given:

The cost price of 35 kg of rice  = Rs. 9.50 per kg

the cost price of 30 kg of rice = Rs. 10.50 per kg

Formula Used:

Profit  = (Profit%/100 ) × CP

Calculation:

Total cost price of mixture of 35 kg and 30 kg of rice  = (35 × 9.50 + 30 × 10.50)

Total cost price of 65 kg mixture  = (332.5 + 315) ⇒ Rs. 647.5

⇒Rate per kg of mixture  = 647.5/65

profit of the mixture per kg  = (135/100) × (647.5/65) ⇒ Rs. 13.44

∴ The selling price of the mixture of rice per kg is Rs.13.50

Spot that the above series is a combination of two A.P.s.

The 1st A.P. is (1 + 6 + 11 +…) and the 2nd A.P. is (4 + 5 + 6 +…) 

Since the terms of the two series alternate, 

S = (1 + 6 + 11 +… to 100 terms) + (4 + 5 + 6 + … to 100 terms)

= 100[2 x 1 +99 x 5]/2+ 100[2 x 4+99 x 1]/2 

→ (Using the formula for the sum of an AP

= 50[497 + 107] = 50[604] = 30200

Alternatively, we can treat every two consecutive terms as one.

So we will have a total of 100 terms of the nature: 

(1 + 4) + (6 + 5) + (11 + 6) …→ 5, 11, 17…

Now, a = 5, d = 6 and n = 100

Hence the sum of the given series is

S = 100/2 x [ 2 x 5 +99 x 6]

= 50 [ 604] = 30200

Correct option (c) 7 days

Explanation:

The combined travel would be 28 on the first day, 29 on the second day, 30 on the third day, 31 on the fourth day, 32 on the fifth day and 33 on the sixth day, 34 on 7^th day. They meet after 7 days.

Correct option (b) Rs 21,578

Explanation:

This is an intensive calculation, problem and you are not supposed to know how to do the calculations in this question mentally. The problem has been put here to test your concepts about whether you recogsize how this is a question of GPs. If you feel like, you can use a calculator/computer spreadsheet to get the answer to this question.

The logic of the question would hinge on the fact that the value of the investment of the fifteenth year would be 1000. At the end of the 15^th year, the investment of the 14^th year would be equal to 1000 × 1.05, the 13^th year’s investment would amount to 1000 × 1.052 and so on till the first year’s investment which would amount to 1000 × 1.05¹⁴ after 15 years. Thus, you need to calculate the sum of the GP: 1000, 1000 × 1.05, 1000 × 1.05² , 1000 × 1.05³ for 15 terms.

Correct option (a) 112.5    

Explanation: 

The series of plank sizes would be: 0.75 × 0.5, 0.75 × 1, 0.75 × 1.5….0.75 × 12. The sum of this AP is 112.5.

Correct option (d) 2

Explanation:

Since, sum to n terms is given by (2n + 7), 

Sum to 1 terms = 9 

Sum to 2 terms = 11 

Thus, the 2nd term must be 2, 

Going through the trial and error = 2(20)² + 3 – 2(19)² – 3 = 78.

Given y = tan^–1 (2x/ 1 - x²)

Put x = tan θ 

⇒ θ = tan^–1x

y = tan^–1 (2 tan θ/ 1 - tan² θ)

= tan^–1 (tan 2θ) 

= 2θ 

= 2tan^–1x 

differentiating w.r.to 'x' on both sides, we have 

(dy/dx) = 2(d/dx) = tan⁻¹ x

= 2(1/1 + x²)

∴ (dy/dx) = (2/ 1 + x²)

Correct option (a) 44

Explanation:

The series will be 108, 117, 126,…. 495.

Hence, = 495 -108/9 +1 = 44

Correct option (b) −626

Explanation:

The first 100 terms of this (1 − 2 − 3) + (2 − 3 − 4) + … + (33 − 34 − 35) + 34

The first 33 terms of the above series (indicated inside the brackets) will give an AP.−4, −5, −6.... −36 = 33 × −20 = −660 (sum of this A.P.). 

The required answer would be –660 + 34 = –626.

Correct option (a) –250   

 Explanation:

The series (1 – 6 + 2 – 7 + 3 – 8 +… to 100 terms) can be rewritten as:

⇒ (1 + 2 + 3 + … to 50 terms) – (6 + 7 + 8 + … to 50 terms)

Both these are AP’s with values of a and d as →

a = 1, n = 50 and d = 1 and a = 6, n = 50 and d = 1, respectively.

Using the formula for sum of an A.P. we get:

→ 25(2 + 49) – 25(12 + 49)

→ 25(51 – 61) = –250

Alternatively, we can do this faster by considering (1 – 6), (2 – 7), and so on as one unit or one term. 1 – 6 = 2 – 7 = … = –5. Thus the above series is equivalent to a series of fi fty –5’s added to each other. 

So, (1 – 6) + (2 – 7) + (3 – 8) + … 50 terms = –5 x 50 = –250

Given straight line equation is 3x – 4y + 12 = 0 ––––– (1) 

⇒ 3x – 4y = –12 

⇒ (3x/-12) - (4y/-12) = 1

⇒ (x/-4) + (y/3) = 1 

X – intercept = – 4 

Y – intercept = 3 

Area of the triangle formed by the straight line (1) with the 

co-ordinate axes is (1/2) |(X – intercept) (Y – intercept)| 

= (1/2) |(–4) (3)| 

= 6 sq. units.

Let X – intercept = a

Y – intercept = b 

By hypothasis a + b = 0

⇒ b = – a 

Intercept form (x/a) + (y/b) = 1 

⇒ (x/a) + (y/-a) = 1

⇒ x – y = a 

But this straight line passing through (–2, 4). 

∴ – 2 – 4 = a 

⇒ a = – 6 

∴ Required straight line equation is 

x – y = – 6 

⇒ x – y + 6 = 0

The correct answer is Vector color value and resolution remains undisturbed under scaling or de-scaling.

Here are the most important advantages of vector graphics:

1. They have “infinite” resolution
2. They are scalable
3. They are lightweight (small file size)
4. They are intuitively created
5. They are easily manipulated
6. They are easily reusable
7. They are multipurpose
8. They can produce very realistic results
9. They can be animated
10. They can be edited with code
11. They can be interactive 

The correct answer is "option 4".

CONCEPT:

When a computer processor accesses any external memory or the device that is slow to respond then the delay experienced by the processor is called Wait State.

Since processor speed is faster than memory chips, the processor may sit idle for some cycles due to slow memory access.

So, the total number of wait states can be defined as the total number of cycles needed by the CPU.

CALCULATION:

Memory access time = 60 ns

Additional delay = 10 ns

Total memory access time = Memory access time + Additional delay

= 60 ns + 10 ns = 70 ns

CPU Frequency = 33MHz

Clock time = \(\frac{1}{33MHz}\) → \(\frac{1}{33*10^6}\)ns → \(\frac{1}{33}\) × 10^-6 ns

= 30.30 ns

No. of wait states = \(\left\lceil\frac{70\ ns}{30.30\ ns} \right\rceil\)= 3

Hence , the number of wait states required is 3.

1. Clock rate or clock frequency is one of the important factors to measure processor performance.

The correct answer is 8 bits.

• A byte is a unit of digital information that most commonly consists of eight bits.
• Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason, it is the smallest addressable unit of memory in many computer architectures.
• To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as The Internet Protocol (RFC 791)(1981) refer to an 8-bit byte as an octet.
• Furthermore, 1024 bytes make one kilobyte. 

• 1024 Bytes = 1 Kilobyte
• 1024 Kilobytes = 1 Megabyte
• 1024 Megabytes = 1 Gigabyte
• 1024 Gigabytes = 1 Terabyte

Concept:

A Computer driver, is a set of files that tells a piece of hardware how to function by communicating with a computer's operating system. All pieces of hardware require a driver, from your internal computer components, such as your graphics card, to your external peripherals, like a printer. Or we can say that it is a Drivers are small programs that enable the operating system to communicate with peripheral devices

Below is a list of hardware devices and peripherals that require drivers.

• Card reader
• Controller
• Modem
• Motherboard chipset
• Network card
• Printer
• Scanner
• Sound card

If the appropriate driver is not installed, the device may not function properly, if at all. With some devices, the device may work, but all of its features may not work.    

The correct answer is  sending the first email.

• The American programmer who invented email was Ray Tomilson.
• He year 1971 for the first time between the two computers 'ARPANET system' on a message .
• In 2012, he by the Internet Society, the Internet Hall of Fame " was included .
• Earlier, users could compose messages to others using the same computer.
• He first had looked for a user to separate from their host symbol rate (@) is used .

• Douglas Humperdinck was the "computer mouse" in 1960 was invented . Then he made it out of wood.
• Douglas gave the first demonstration of the mouse at the 1968 Computer Conference in San Francisco .

The correct answer is Storing data permanently​.

• The CPU is also called the 'brain of the computer'.
  • The full name of the CPU is "Central Processing Unit".
  • The computer cannot function without a CPU. It controls and manages the computer.
  • The user gives instructions to the computer which is processed by the CPU.
  • The speed of the computer depends on the CPU. 

• The main task of C.P.U. -
  • The main function of the CPU is to execute data. 
  • It performs all types of data processing tasks.
  • It manages and controls all the hardware of the computer. 
  • It Completes all hardware-related tasks.
  • The CPU decodes the input data by fetching it, after that executes that data.
  • This data appears on the monitor as output.
  • Fetch means to receive data. The CPU receives the data from the input.
  • Decode means to interpret the received data instructions.

The correct answer is Winword.

• We can launch the Microsoft Word application from the Run window by running the command Winword.
• Note that this command does not work from the command line as the winword.exe location is not added to the PATH environment variable.
• However, we can use the 'start winword' command to open the Word application from the command prompt. 

• To open the command prompt we use shortcut key window key + R.
• Command Prompt is a command-line interpreter application available in most Windows operating systems. It's used to execute entered commands. 

The correct answer is 2.

• Binary information is sometimes also referred to as machine language since it represents the most fundamental level of information stored in a computer system.
• At a physical level, the 0 and 1 are stored in the central processing unit of a computer system using transistors.
• All data in a computer system consists of binary information. 'Binary' means there are only 2 possible values: 0 and 1.

• Computer software translates between binary information and the information you actually work with on a computer such as decimal numbers, text, photos, sound, and video.
• Binary information is also transmitted using magnetic properties; the two different types of polarities are used to represent zeros and ones. An optical disk, such as a CD-ROM or DVD, also stores binary information in the form of pits and lands (the area between the pits).

(A) Would have

Ayesha asked Salma if she had seen the film ‘Takur’ Salma replied in the negative but added that she was planning to see the film on Sunday. Reference Skill

The correct answer is Super Computer.

• Super Computer is the largest, fastest, and costliest computer. 
• Super Computer term is commonly applied to the fastest high-performance systems available at any given time.
• Super Computer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2017, there are supercomputers that can perform over 1017 FLOPS (a hundred quadrillion FLOPS, 100 petaFLOPS, or 100 PFLOPS).
• Since November 2017, all of the world's fastest 500 supercomputers run Linux-based operating systems.

• A personal computer is a general-purpose computer whose size, capabilities and original sale price make it useful for individuals, and is intended to be operated directly by an end-user with no intervening computer operator. A personal computer may be a desktop computer or a laptop, netbook, tablet, or a handheld PC.
• The personal computer is a small computer with a microprocessor, designed for use by an individual.
• Common applications for supercomputers include testing mathematical models for complex physical phenomena or designs, such as climate and weather, the evolution of the cosmos, nuclear weapons and reactors, new chemical compounds (especially for pharmaceutical purposes), and cryptology.
• Laptop computers, also known as notebooks, are portable computers that you can take with you and use in different environments. They include a screen, keyboard, and a trackpad or trackball, which serves as the mouse.

The correct answer is "option 1".

CONCEPT:

A supercomputer is a computer that gives a high level of performance as compared to any general-purpose computer.

The performance of a supercomputer is commonly measured in Floating-Point Operations Per Second (FLOPS).

As per the recently released semiannual Top 500 list of supercomputers, Sunway TaihuLight has been named as the world’s fastest supercomputer title.

​EXPLANATION:

option1: Sunway TaihuLight is the fastest Chinese supercomputer with a LINPACK speed of 105 Peta FLOPS available from 2016.

option2: Titan / OLCF-2 is a supercomputer used for science research available from 2013 & have LINPACK speed of 17.59 Peta FLOPS.

option3: Piz Daint is a supercomputer with a LINPACK speed of 25.3 Peta FLOPS.

option4: Sequoia is a supercomputer developed by IBM as a part of the Advanced Simulation & Computing Program with a speed of 20.13 Peta FLOPS.

1. Supercomputer Piz Daint is named after mountain Piz Daint in the Swiss Alps.
2. LINPACK Benchmark - A measure of the system's floating point computing power.
3. LINPACK Benchmark is used to build a list of Top 500 supercomputers.
4. 1 Peta FLOPS = 10¹⁵ Floating Point Operations Per Second.
5. FLOPS - Floating Point Operations Per Second.

The correct answer is Ctrl+E.

• Shortcut commands save time because it eliminates the need of using the mouse or tracker. 
• There are several command shortcut commands.
• For instance,
  • Ctrl + C = Copy,
  • Ctrl + V = Paste,
  • Ctrl + F to find any text.
  • Ctrl + E - Align selected text or line to the center
  • Ctrl + T - Open a new tab in an Internet browser
  • Ctrl + R - Refreshes (reloads) the open page
  • Ctrl + C - Copy the text

The correct answer is Pratyush.

• Pratyush is set up at the Indian Institute of Tropical Meteorology (IITM) in Pune and is used for weather and climate predictions.
• India’s most powerful supercomputer Pratyush, the first multi-petaflop device in the country which is being used to improve weather and climate predictions, has made it to the 39th spot on the Top 500 List of supercomputers in the world.
• The 4 petaflop supercomputer has improved India’s ranking in the list from high 300s to under 50 for the first time.
• One petaflop is a million billion floating-point operations per second and is a reflection of the computing capacity of a system
• Pratyush will be used to do more accurate weather and climate forecasting, including the all-important monsoon predictions.

• Mihir:
  • Mihir is a 2.9 petaflop supercomputer that is operational at the National Centre for Medium-Range Weather Forecast in Noida.
  • Its ranks 66th in the Top 500 List of supercomputers in June. 
• Summit:
  • Summit a supercomputer developed by IBM. It is capable of 200 petaflops, making it the second-fastest supercomputer in the world.
• Sierra:
  • Sierra is a supercomputer is used by the National Nuclear Security Administration.
  • It is primarily used for predictive applications in stockpile stewardship, helping to assure the safety, reliability, and effectiveness of the United States' nuclear weapons.

The correct answer is Binary digit.

• A bit is short for Binary digit.
• A binary digit is the smallest unit of information in a computer.
• It is used for storing information and has a value of true/false, or on/off. 
• When 8 bits are clustered together to make a byte.
• An individual bit has a value of either 0 or 1, which is generally used to store data and implement instructions in groups of bytes.
• A computer is often classified by the number of bits it can process at one time or by the number of bits in a memory address.
• In computer storage, bits are often grouped together in 4-bit clusters called a nibble.

• A binary tree is a tree-type non-linear data structure with a maximum of two children for each parent. 
• Every node in a binary tree has a left and right reference along with the data element.
• The node at the top of the hierarchy of a tree is called the root node. 

Kshama asked Deepthi whether she would help her cross the road.

Deepthi replied that she would surely help and that she did not mind.