Page 115 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

2
2
x
(c) cos2 , sin x and cos x number doubles in 2 hours then it will
be triple in
(d) cos 2x, sin x and cos x
log3 log2
(a) 2 (b) 2
[GATE-2013 (ME)] log2 log3

190. Consider the following statements log3 log2
about the linear dependence of the (c) (d)
real valued functions y = 1, y = log2 log3
x
1
2
and y = x , over the field of real 192. A radium decomposes at a rate
2
3
numbers. proportional to the amount of radius
present at that time. If 5% grams of
(I) , y y and y are linearly original amount disappears after 50
1
3
2
independent on 1 x  0 years then the amount will be remain
− 
after 100 years is
(II) , y y and y are linearly
3
2
1

dependent on 0 x  1 (a) 95.95% of the original amount
(b) 95% of the original amount
(III) , y y and y are linearly
1
3
2
dependent on 0 x  1 (c) 90% of the original amount

(IV) , y y and y are linearly (d) 90.25% of the original amount
3
1
2
independent on 1 x  1 193. The orthogonal trajectory of family of
− 
R
Which on among the following is straight lines y = ( k x − ) 1 , k 
correct? are given by
(a) Both I and IV are true (a) (x − ) 1 + ( y − ) 1 = c
2
2
2
(b) Both I and III are true
(b) x + 2 y = 2 c
2
(c) Both II and IV are true
2
2
2
(c) x + ( y − ) 1 = c
(d) Both III and IV are true
2
2
2
[GATE-2017 EC SESSION-1] (d) (x − ) 1 + y = c [GATE]
FORMATION OF DIFFERENTIAL 194. The differential equations of the
EQUATION
family of circles of radius ‘r’ and

191. The rate of which bacteria multiply is whose centre lies on ‘x’ axis.
proportional to the instantaneous
number present, if the original

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