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The solution of (dy / dx) = [y (x log y – y) / [x (y log x – x]) is

1) xy = cyx 2) xy = c 3) (xy)x = c 4) None of these Solution: (1) xy = cyx... View Article

The solution of the differential equation (dy / dx) + (2y / x) = 0 with y (1) = 1 is given by

1) y = 1 / x2 2) y = 1 / y2 3) x = 1 / y 4) x = y Solution: (1) y = 1 / x2... View Article

The differential equation representing the family of curves y² = 2c (x + √c), where c is a positive number, is of

1) order 1, degree 3 2) order 2, degree 2 3) degree 3, order 3 4) degree 4, order 4 Solution: (1) order 1, degree 3... View Article

A solution of the differential equation (dy / dx)² – x (dy / dx) + y = 0 is

1) y = 2 2) y = 2x 3) y = 2x - 4 4) y = 2x2 - 4 Solution: (3) y = 2x - 4... View Article

The solution of the differential equation [y (1 + x^-1) + sin y] dx + [x + log x + x cos y] dy = 0 is

1) xy + y log x = c 2) xy + x sin y = c 3) xy + y log x + x sin y = c 4) None of these Solution: (3) xy + y log x + x sin y = c... View Article

The solution of the differential equation y dx – x dy + (log x) dx = 0 is

1) y = log x + cx 2) y + 1 + log x = cx 3) y + cx = log (1 / x) 4) None of these Solution: (2) y + 1 + log x = cx... View Article

Solution of x sin (y / x) dy = (y sin (y / x) – x) dx is

1) cos (y / x) = c 2) log (y / x) + log x = c 3) log (y / x) - log x 4) None of these Solution: (4) None of these x sin (y / x)dy... View Article

The solution of differential equation x (dy / dx) = y – x cos² (y / x) is

1) tan (y / x) + log x = c 2) log (x / y) + log x = c 3) log (x / y) + tan x = c 4) tan (x / y) + tan x = c Solution: (1) tan (y / x) + log... View Article

The solution of the differential equation dy / dx = xy + x + y + 1 is

1) y = (1 / 2) x2 + x + c 2) log (y + 1) = (1 / 2) x2 + x + c 3) c (y + 1) = ex^2+(2x/2) 4) None of these Solution: (2) log (y + 1) = (1 / 2)... View Article

Solution of (1 + xy) y dx + (1 – xy) x dy = 0 is

1) log (x / y) + (1 / xy) = c 2) log (x / y) = c 3) log (x / y) - (1 / xy) = c 4) None of these Solution: (3) log (x / y) - (1 / xy) = c... View Article

The solution of (x + 1) (dy / dx) + 1 = e^x-y is

1) ey (x + 1) = c 2) ey (x + 1) = ex + c 3) ey (x + 1) = cex 4) None of these Solution: (2) ey (x + 1) = ex + c... View Article

22 June 2021: UPSC Exam Comprehensive News Analysis

CNA 22nd June 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND GOVERNANCE 1. Centre moots ban on ‘flash... View Article

Two sets A and B are as under…

Two sets A and B are as under : A = {(a,b) ∈R×R:|a-5| < 1 and |b-5| < 1}B = {(a,b) ∈R×R: 4(a-6)2+9(b-5)2 ≤ 36}. Then:a) A⋂B = phi(an empty... View Article

Let f(x) = x²+(1/x²) and g(x) = x-(1/x), x∈ R-{-1,0,1}. If h(x) = f(x)/g(x), then the local minimum value of h(x) is:

a) -2√2b) 2√2c) 3d) -3Solution:f(x) = x2+(1/x2)= (x-(1/x))2+2g(x) = x-(1/x)Put x-(1/x) = th(x) = f(x)/g(x)Let h(x) = k(t)= (t2+2)/t=... View Article

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

a) 1/5b) 3/4c) 3/10d) 2/5Solution:From total Probability TheoremP (R) = (4/10)×(1/2)+(6/10) × (4/12)= (1/5)+(1/5)= 2/5Answer: (d)... View Article

If sum of all the solutions of the equation 8cos x(cos ((π/6)+x). cos ((π/6)-(x))-(1/2)) = 1 in [0, π] is kπ, then k is equal to

a) 8/9b) 20/9c) 2/3d) 13/9Solution:8cos x(cos ((π/6)+x). cos ((π/6)-(1/2))-(1/2)) = 18.cos x[(cos (π/3)+ cos 2x-2)/2] = 14 cosx(cos... View Article

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