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Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$
$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?
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? 
The following sentences form a paragraph. These four parts are numbered as P, Q, R and S. They are not given in their proper order. Read the sentences and choose the alternative that arranges them in correct order. P. Inverse problem refers to the scientific problem of estimating the different causes that led to a particular outcome.  Q. This is in contrast to the forward or the direct problem where scientists try to find the outcome that results from a series of causes. R. A scientist observing a photograph, for instance, would be faced with the inverse problem while trying to figure out the various causal factors that combined to form the final photograph. The inverse problem is applied to understand processes in a wide variety of sciences. S. Scientists trying to understand an observation may at times have to work backwards to estimate the causal factors behind it.
The output of the following Python code is similar to the alphabet . . . . . . . .
import turtlet=turtle.Pen()t1=turtle.Pen()t2=turtle.Pen()t.forward(100)t1.forward(100)t2.forward(100)t1.left(90)t1.forward(75)t2.right(90)t2.forward(75)
Maneela, Raghu and Aravind have some jems with each of them. Five times the number of jems with Raghu equals seven times the number of jems with Maneela while five times the number of jems with Maneela equals seven times the number of jems with Aravind. What is the minimum number of jems that can be there with all three of them put together ?
$$\eqalign{ & {\text{The}}\,{\text{value}}\,{\text{of}} \cr & \frac{{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}}{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}\,\text{is}: \cr} $$
The value of $$\left( {\frac{{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}}{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}} \right)$$       is :
The value of $${\text{ }}\root 3 \of {\frac{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}{{0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08}}} $$        is ?
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?