Q28. Of the four vectors A, B, C, D find out which pair forms an orthogonal set
A = 5i-3j, B = -7i+j, C = 3i+5j, D = i+j

(a)AC (b) AD (c) AB (d) BD (e) BC

Q29. Evaluate the expression
M (373,9) + R (3.4) + T (7.7) – R (5.8) where
M stands for Modulo arithmetic, R stands for Round-off operation and T stands for Truncation Operation

(a)7 (b)6 (c) 8 (d)9 (e)4

Q30. Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 20% and 25% savings. Assuming that they operate independently, what is the net saving achieved?

(a)45%  (b) 64% (c) 58% (d) 56% (e) 54%

Q31. The log values of two numbers to the base 10 are given as below:
X   log10X
3.141   0.4970612341
3.142   0.4972061807
Find log103.143.

(a) 0. 49734 (b) 0.59720 (c) 0.49110 (d) 0.49420 (e) 0.49440

Q32. What equation best describes the curve shown below:

(a)y = tan x (b) y + 3 = x (c)y + x = 0 (d) y = Cos x (e) y = ex 

Q33. The temperature at Kochi is given by the function: -t2/6+4t+12 where t is the elapsed time since noon. What is the percentage rise (or fall) in temperature between 6.00 PM and 9.00 PM?

(a) 25%  (b) 32% (c) 12%  (d) 15% (e) 18%

Q34. An aircraft takes off from A (72o N Lat, 45o E Long) at 2.00 AM local time to B (32o N Lat, 45o W Long). If the flying time is 10 hours what is the local time of landing at B?

(a) 5.40 AM (b) 4.00 AM (c) 6.00 AM (d) 7.00AM (e) 8.00AM

Q35. Fill in the last row of the following Truth Table:

 Interpret the resulting bit pattern as an integer in an 8-bit computer and write the decimal value.

(a)3 (b)4 (c)5 (d)1 (e)2

Q36. A file is transferred from one location to another in ‘buckets’. The size of the bucket is 10 kilobytes. The bucket gets filled at the rate of 0.0001 kilobytes per millisecond. The transmission time from sender to receiver is 10 milliseconds per bucket. After the receipt of the bucket the receiver sends an acknowledgement that reaches sender in 100 milliseconds. Assuming no error during transmission, write a formula to calculate the time taken in seconds to successfully complete the transfer of a file of size N kilobytes.

(a) 10.11 N (b) 10.011 N (c) 11.01 N (d) 11.011 N (e) 10.101 N

Q37. The electricity used in a device is given by the function P(N) = 4000 √N, where N is the time for which device is used. Find the percentage change in electricity usage if the time used by the device is increased by 1%.

(a) 0.5%  (b) 0.25% (c) 0.75% (d) 1%  (e) 2%

Q38. A power cable is to be run from a power plant on the bank of a river 900 meters wide to a factory that is located 3000 meters downstream on the opposite bank. If the cost of laying cable under water is Rs. 5 per meter and that of laying overhead on land is Rs. 4 per meter, find the point downstream where the cable is to cut across the river.

(a) 450  (b) 3900 (c) 2100 (d) 1800 (e) 2700