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The value of cot \(\frac{9\pi}4\) is 1.

∴ The question becomes cot^–1(1).

Let cot^–1(1) = y

⇒ cot y = 1

= cot\((\frac{\pi}4)\) = 1

The range of principal value of cot^–1is (0, π)

and cot \((\frac{\pi}4)\)= 1

∴ The value of cot^–1(cot\(\frac{9\pi}4\)) is \(\frac{\pi}4.\)

(D) 2

π^c = \((\pi\times\frac{180}{\pi})°\) 

= 180° = 2 x 90°

The value of cot \(\frac{19\pi}6\) is √3.

∴ The question becomes cot^–1(√3).

Let cot^–1(√3) = y

⇒ cot y = √3

= cot\(\frac{\pi}6\) = √3

The range of principal value of cot^–1is (0, π)

and cot\(\frac{\pi}6\)= √3

∴ The principal value of cot^–1(cot\(\frac{19\pi}6\) ) is \(\frac{\pi}6\).

(b) 11^o

When the sum of the measures of two angles is 90°, the angles are called complementary angles. Each of them is called complement of the other.

The given complement of an angle is 79^o

Let the measure of its angle be x^o.

Then,

x + 79^o = 90^o

x = 90^o – 79^o

x = 11^o

Hence, the measure of its angle is 11^o.

(C) 57.3°

1^c = \((1\times\frac{180}{\pi})°\) = 57.3°

Angles: 

∠POQ, ∠POR, ∠POS, ∠OOS, ∠ROS, ∠QOR.

Angles :

(i) Acute angle 

(ii) Right angle 

(iii) Obtuse angle 

(iv) Straight angle 

(v) Reflex angle.

(C) 480°, 420°

Let the measures of two angles be x and y 

x + y = 5π^c

⇒ x + y = \((5\pi\times\frac{180}{\pi})°\)

∴ x + y = 900° ….(i) 

and x - y = 60° ….(ii) 

Adding (i) and (ii), we get 

x = 480° 

Putting x = 480° in (i), we get 

y = 420°

∴ the two angles are 480° and 420°.

One right angle is equal to 90 degrees.

B) Any pair of adjacent angles form a supplementary angle.

Correct option is D) ⌊f,⌊a

D) If the sum of two angles is supplementary then each of them is an obtuse angle.

Yes, sum of any two acute angles is 90°,

then they are complementary angles. If they are not acute means they may . be right angle (90°) or obtuse angle (> 90°) or etc.

So, its impossible. Therefore, each angle in any pair of complementary angles is always acute.

False

Measure of right angle is 90°. So, the sum of two right angles = 90° + 90° = 180°. Complementary angles are those whose sum is equal to 90°.

Hence, two right angles are never be complementary.

90°

Two angles are said to be complementary angles, if their sum is 90°. Hence, if two angles are complementary, then each angle cannot be more than 90°.

45°

Let x be the required angle.

Then, x + 45° = 90°

 ⇒  x = 90° – 45° = 45°

F(U,V)=(U’+V).(U+V’)

F=A’.B’+B’C’

(A' + B').(A + B) = A'B + A.B'

L.H.S

(A' + B'). (A + B)

A'A + A'B + B'.A + B'B

0 + A'.B + B'.A + 0

A'.B + A.B' = R.H.S (Hence, verified)

π (0,1,4,7)

∑ (2, 3, 5, 6)

   010, 011, 101, 110

  = U'VW' + U'VW + UV'W + UVW'

F (a,b,c,d) = 

(a + b + c + d).(a + b + c + d). (a + b' + c + d).(a + b' + c' + d). (a' + b + c + d) . (a' + b + c + d') . (a' + b' + c + d). (a' + b' + c + d'). (a' + b' + c' + d)

G(A,B,C)=(A+B+C).(A+B’+C’).(A’+B+C).(A’+B+C’)

H (x, y, z) = (x + y + z’). (x’ + y + z’) . (x’ + y’ + z)

F(U, V, W) = (U + V + W’) . (U + V’ + W’) . (U’ + V + W’)

F(X,Y,Z)=X’.Y’Z’+X’.Y’.Z’+X.Y’.Z’+X.Y.Z

G(U. V W) = (U + V + W). (U’ + V + W’). (U’ + V’ + W)

G (R Q, R) = P’QR’ + P’QR + PQ’R’ + PQR’ + PQR

G (P, Q, R) = P’QR’ + PQ’R’ + PQR’ + PQR

SOP form is given by

X’Y’Z’ + X’Y’Z + X’YZ + XY’Z’ + XYZ

F=(0,3,6,7)

So, SOP form of F is

F = (U’.V’W’) + (U’.VW) + (U.VW’) + (U.VW)

Sweating is important for thermal regulation.Sweat works as a defense against microbes to which our hands and feet are mostly exposed than the other parts of our body

The doctor advises to drink more water as:

• Water helps to maximize physical performance.
• Hydration has a major effect on energy levels and brain function.
• Drinking water may help to prevent and treat headaches.
• Drinking more water may help relieve constipation.

Urine is excreted from the human body which constitutes of mote than 95% water and other constituents like urea, chloride, sodium, potassium, creatinine and other dissolved ions, and inorganic and organic compounds. When there is an illness or disease, the constituents and its levels in urine also changes.

Therefore urinalysis is also an important diagnostic tool which may be used to screen for and/or help diagnose conditions such as a urinary tract infections, kidney disorders, liver problems, diabetes or other metabolic conditions.

(b) Digital India

(d) all of these

e-police system is based on the principle that providing the best possible communication and coordination will lead to the most effective policing. 

It involves two main tools: a mobile workstation installed in each patrol car, and a positioning system that shows headquarters each officers’ location and status.

Digital India projects to connect India digitally with a planned allocation. The plan is to establish a digital platform to digitally connect and deliver government programs and services to individuals across India, thereby harnessing the power of information technology.

The project also plans to connect all villages through high speed internet by 2019. The plan is ambitious to say the least, though it is not truly original. The plan is to create a digital platform to serve nine verticals; e-governance, eKranti, public internet access program, broadband highway, information access for all, mobile connectivity, early harvest programs, IT for jobs, and electronic manufacturing.

Digital India

E-Transport provides various facilities like- Registration of motor vehicle, Driving License, Tax and deposits etc.

(a) Digital India

E-Governance.

Digital India

Asynchronous, which means “not at the same time,” allows the participants to complete the WBT (Web-based training) at their own pace, without live interaction with the instructor. Basically, it is information that is accessible on a self-help basis, 24/7. The advantage is that this kind of e-Learning offers the learners the information they need whenever they need it. It also has interaction amongst participants through message boards, bulletin boards and discussion forums. These include computer based training,(CBTs) modules on CD-Rom’s, Web based training accessed through intranet (WBTs) or through well written articles and other,write ups.

E-Learning is learning utilizing electronic technologies to access educational curriculum outside of a traditional classroom. In most cases, it refers to a course, program or degree delivered completely online.

e-Learning is nothing but the use of technology to connect teachers and students who are physically miles apart. The training can be delivered by a number of means. In the past, these have included the use of mainframe computers, floppy diskettes, multimedia CD-ROMs, and interactive videodisks. Most recently, Web technology (both Internet and Intranet delivery) are being used.

(i) Advantages of E-leaming:

• The 4A of E-learning. – Anytime, Any Place, Any Pace, Any Subject: 
• e-learning materials can be accessed at the most convenient time for learning, if the course material is well constructed then learning can take place in short segments and can be customised to suit the learner’s needs.
• Empowerment: Students are in charge of their own learning.
• Flexibility: e-learning material can be accessed in a non-sequential way, enabling students to navigate content in different ways, or obtain a global view before tackling the details of individual units.
• Cost Effective: large numbers of students can have access to the same materials but can be supported by peer-to-peer or student-to-tutor support services thus, reducing the cost of delivery. 
• Up-to-date Content: Course content is located in one place so it can be easily updated and can provide direct links to supporting materials such as Internet and library resources.
• Tailored Learning: the time needed to learn a particular topic or skill is reduced or “compressed” as learning can be modified to suit the users needs and requirements. E-learning can provide a variety of learning experiences including interactive elements.
• Retainable: the smaller and more relevant the learning is the easier it is to capture and remember.
• Consistent: all students get the same standardised set of materials from elearning.
• Interactive: well constructed materials will have elements of interactivity through simulations etc. which will underpin and enforce the learning.
• Collaborative: The use of groups and teams working together in collaborative learning and learner-learner interaction enforces employability skills.
• Used To Track Student Performance: student usage of the materials can be monitored and early potential drop-out can be detected and given remedial support.
• Used for Self Assessment: students can be offered automatically-marked self¬assessment exercises to identify skill/knowledge levels and learning needs before engaging with course content.

(ii) Disadvantages of E-learning: 

• Technology dependent: learners will need access to a machine of minimum specification as dictated by the e-learning supplier or access to a service with a high bandwidth to transfer the course materials in a timely way.
• Material Incompatibility: some materials designed for one particular system will not function properly on another (for example, the Apple Macintosh and the Windows PC). Standards will help in the area. 
• Unsuitable for Certain Types of Training: any skill that relies heavily on inter-personal contact although these courses could be supplemented by Elearning.
• Unsuitable for Certain Types of Learners: E-learning, requires a high-level of self-discipline and personal time management. E-Learners need to be highly self-motivated to take full advantage of the medium as often the online learning experience can be impersonal. Working through ‘packaged’ programmes can be irritating.
• Expensive: start-up cost of an E-learning, service is expensive and the cost of production of online training materials is very high. Teachers must be confident that the extra costs are balance with the benefits of delivering a course online. Significant time needs to be invested in course set-up and in ongoing maintenance (checking links, updating course content etc.).
• Reliant on Human Support: E-learning is still dependent on help on either the course materials or the software.
• No Match for Face-to-Face Teaching: Electronic communication does not necessarily provide a good match for face-to-face communication and is more linear than face-to-face discussion.
• Too Reliant on IT Skills: learners may have limited IT skills, or be uncomfortable with electronic communication and need to learn how to use the medium effectively.

Books is not used in e-learning

E-Commerce to purchase anything through internet

E- Governance is Known as Single Point Delivery System which provides various facilities like-e-Citizen, e-Transport, e-medicine, e-education etc.

E-commerce (electronic commerce or EC) is the buying and selling of goods and services, or the transmitting of funds or data, over an electronic network, primarily the internet. These business transactions occur either as business-to-business, business-to-consumer, consumer-to-consumer or consumer-to-business. The terms e-commerce and e-business are often used interchangeably.

Global Packet Radio System.

OTP (One Time Password)