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Consider the following pattern of numbers: \(\dfrac{\begin{matrix} 8 \\\ 6 \ \\\ 4 \ \end{matrix}}{ \ 6} \ \ \dfrac{\begin{matrix} 10 \\\ 5 \ \\\ 6 \ \end{matrix}}{ \ 11} \ \ \dfrac{\begin{matrix} 15 \\\ 7 \ \\\ 8 \ \end{matrix}}{ \ 16} \ \ \dfrac{\begin{matrix} 13 \\\ 4 \ \\\ 8 \ \end{matrix}}{ \ ?}\) What is the number at ? in the above pattern?
Solution of the variables x1 and x2 for the following equations is to be obtained by employing the Newton-Raphson iterative method
equation (i) 10x2 sin x1 - 0.8 = 0
equation (ii) 10$${\text{x}}_2^2$$ - 10x2 cos x1 - 0.6 = 0
Assuming the initial values x1 = 0.0 and x2 = 1.0, the Jacobian matrix is
During a class experiment, a teacher took two objects and immersed them in water. She recorded the readings using a spring balance as shown below: Object Wt. of Stone in Air (Newton) Wt. of Stone in Water (Newton) Weight of Liquid Displaced (Newton) Buoyant Force acting on body (Newton)  A 92 X 16 Y B Q 70 Z 10 Which of the following is correct?
Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work?
Read the passage carefully and choose thebest answer to each question out of the four alternativesand click the button corresponding to it. To know language is to be able to speak it; even a childwho does not yet attend school can speak his or herlanguage. In order to speak a language it is important tolisten to it and to read a few pages in it everyday. A childpicks up language and learns to talk just as (s)he learnsto walk. Walking and talking comes naturally to a child asit grows. In our country, a child may grow up speakingmore than one language, if these languages are spoken inthe home and in the neighbourhood. we call this multilingualism. A child speaks a language or languagesmuch before (s)he starts going to school. To know alanguage then is first of all to be able to speak it as easilyand naturally as a tree year old child does. Later on thechild will learn to read and write in that language. In orderto read and write in a language, one has to speak it. But itis possible to speak a language but not able to read orwrite in it. A baby does not speak until it is nine monthsold but it understands a few words at six months of age.It has been listening ever since it was born, and even alittle before that. So the first strategy in speaking alanguage is to listen. It is necessary for one to __________ the language before(s)he writes in that language.
Consider the following statements regarding homogenous coordinate transformation matrix: 1. A homogenous transformation matrix can be considered to consist of four sub-matrices. 2. The upper left 3 × 3 sub-matrix represents the position vector. 3. The upper right 3 × 1 sub-matrix represents the rotation matrix. 4. The lower left 1 × 3 sub-matrix represents perspective transformation. Which of the above statements are correct? 
Read the passage carefully and choose thebest answer to each question out of the four alternativesand click the button corresponding to it. To know language is to be able to speak it; even a childwho does not yet attend school can speak his or herlanguage. In order to speak a language it is important tolisten to it and to read a few pages in it everyday. A childpicks up language and learns to talk just as (s)he learnsto walk. Walking and talking comes naturally to a child asit grows. In our country, a child may grow up speakingmore than one language, if these languages are spoken inthe home and in the neighbourhood. we call thismultilingualism. A child speaks a language or languagesmuch before (s)he starts going to school. To know alanguage then is first of all to be able to speak it as easilyand naturally as a tree year old child does. Later on thechild will learn to read and write in that language. In orderto read and write in a language, one has to speak it. But itis possible to speak a language but not able to read orwrite in it. A baby does not speak until it is nine monthsold but it understands a few words at six months of age.It has been listening ever since it was born, and even alittle before that. So the first strategy in speaking alanguage is to listen. To know a language one must be able to?
The following equation needs to be numerically solved using the Newton-Raphson method. x3 + 4x - 9 = 0. The iterative equation for this purpose is (k indicates the iteration level)
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are number alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘A’ can be represented by 10, 75 etc and ‘B’ can be represented by 44, 79 etc. Similarly, you have to identify the set for the word ‘FOLDER’.  Matrix I    Matrix II   0 1 2 3 4   5 6 7 8 9 0 H L F M I 5 E I C J G 1 A U W S E 6 P R U S K 2 R Y C Z O 7 A W O D B 3 K T X V J 8 O T V Q L 4 D Q G P B 9 H N D M F
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are number alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘T’ can be represented by 02, 98 etc and ‘E’ can be represented by 12, 59, 97 etc. Similarly, you have to identify the set for the word ‘FAMILY’.  Matrix I    Matrix II   0 1 2 3 4   5 6 7 8 9 0 I M T K G 5 O C M R E 1 O R E Z X 6 J S F W Y 2 A G W U N 7 P I V N G 3 Q S L A H 8 L U B K W 4 J F V P B 9 H Q E T D