All Questions page - 56

Which was the first Internet service in India?

1) Advanced Research Projects Agency Network

2) Education and Research Network

3) INDNET

4) HINDNET

The inventor of printing press was -

1) Marshall McLuhan

2) Ts' ai Lun

3) Johann Guttenberg

4) Frederic Barbier

What is the difference between Bluetooth and Wi-Fi devices?

1) Bluetooth uses 2.4 GHz radio frequency band, whereas-Wi-Fi can use 2.4 GHz or 5 GHz frequency band.

2) Bluetooth is used for Wireless Local Area Networks (WLAN) only, whereas Wi-Fi is used for Wireless Wide Area Networks (WWAN) only.

3) When information is transmitted between two devices using Blue-tooth technology, the devices have to be in the line of sight of each other, but when Wi-Fi technology is used the devices need not be in the line of sight of each other

4) The statements (A) and (B) given above are correct in this context

What is the difference between a CFL and an LED lamp? (2011)

1. To produce light, a CFL uses mercury vapour and phosphor while an LED lamp uses semiconductor material.

2. The average life span of a CFL is much longer than that of an LED lamp.

3. A CFL is less energy-efficient as compared to an LED lamp.

Which of the statements given above is/ are correct?

1) 1 only

2) 2 and 3 only

3) 1 and 3 only

4) 1, 2 and 3

What is Aditya-L1 that is often mentioned in news?

1) Rover sent to Mars by Indian Space Research Organisation (ISRO)

2) Half-humanoid developed by ISRO for mission Gaganyaan.

3) ISRO's first scientific expedition to study the Sun.

4) ISRO's first telescope to study the outer atmosphere of Sun.

What is Aditya-L1 that is often mentioned in news?

1) Rover sent to Mars by Indian Space Research Organisation (ISRO)

2) Half-humanoid developed by ISRO for mission Gaganyaan.

3) ISRO's first scientific expedition to study the Sun.

4) ISRO's first telescope to study the outer atmosphere of Sun.

You buy a bottle of packed water on a street and end up emptying the bottle. What will you do?

1) Will keep the bottle and dispose in a garbage bin

2) Will throw it as you go along

3) Will throw it in a drain

4) Will find a dirty place and throw it there

Energy conservation is very important today because -

1) Sources of conventional energy are fast debleting

2) Electrical energy has become more expensive

3) Electrical energy consumption is increasing

4) None of the above

To sum the numbers 1.53, .006, .1223; which are correct as they are given. Find absolute and relative error.

Computing x1x2 and x1/x2 for x1=2.48, x2=3.4415, evaluate the relative and absolute error. Further comment on the accuracy of the result.

Why the calculations through calculator are approximate?

Using Power method, obtain the largest eigen value and corresponding eigen vector correct upto 2d of the following matrices:

1. \(\left[\begin{array}{ccc} 1&2&-1 \\ 2&1&2 \\ -1&2&1\end{array}\right]\)   
2. \(\left[\begin{array}{ccc} 4&1&1&1 \\ 3&-1&1&1\\ -1&1&2&0\\1&1&0&2\end{array}\right]\)

       3. \(\left[\begin{array}{ccc} 0&11&-5\\ -2&17&-7 \\ -4&26&-10\end{array}\right]\)

Find the smallest eigen value and corresponding eigen vector of the following matrices using Power method:

1. \(\left[\begin{array}{ccc} 3&2&1 \\ 2&3&2 \\ 1&2&2\end{array}\right]\)
2. \(\left[\begin{array}{ccc} 2&2&-1 \\ -5&9&-3 \\ -4&4&1\end{array}\right]\)
3. \(\left[\begin{array}{ccc} 2&-1&0 \\ -1&2&-1 \\ 0&-1&2\end{array}\right]\)

Find all the eigen values and corresponding eigen vectors using Power method:

1. \(\left[\begin{array}{ccc} 1&2&3 \\ 3&1&0 \\ -2&0&1\end{array}\right]\)
2. \(\left[\begin{array}{ccc} 4&1&0\\ 1&20&1 \\ 0&1&4\end{array}\right]\)
3. \(\left[\begin{array}{ccc} 2&1&1&0 \\ 1&1&0&1 \\ 1&0&0&1\\1&1&1&2\end{array}\right]\)

If the largest eigen value of the matrix\(\left[\begin{array}{ccc} 5&-2&0 \\ 1&2&-3 \\ 1&-2&4\end{array}\right]\)is 6 and corresponding eigen vector is\(\left[\begin{array}{ccc} 1 \\ -1/2 \\ 1\end{array}\right]\),then find the subdominant eigen value.

Find the eigen values of following matrix:

\(\left[\begin{array}{ccc} 1&-1&0&0&0&0 \\ 1&1&-1&0&0&0 \\ 0&1&1&-1&0&0\\0&0&1&1&-1&0\\0&0&0&1&1&-1\\0&0&0&0&1&1\end{array}\right]\)

Let y(x) be a continuous solution of the initial value problem

y' + 2y = f(x), y(0) = 0, where \( f(x) = \begin{cases} 1, & \quad \text{if } 0 \le x\le1,\\ 0, & \quad \text{if } x>1 \end{cases} \)

Then y\(( \frac{3}{2})\) is equal to

(a)  \(( \frac{sinh(1)}{e^3})\)  (b)   \(( \frac{cosh(1)}{e^3})\)   (c)  \(( \frac{sinh(1)}{e^2})\)  (d)   \(( \frac{cosh(1)}{e^2})\)