The equation of circle with centre (- a, – b) and radius √a2 – b2 is Circles and System of Circles 1) x2 + y2 + 2ax + 2by + 2b2 = 0 2) x2 + y2 - 2ax - 2by - 2b2 = 0 3) x2 + y2 - 2ax - 2by + 2b2 = 0 4) x2 + y2... View Article
The general solution of the differential equation dy / dx = cot x cot y is 1) cos x = c cosec y 2) sin x = c sec y 3) sin x = c cos y 4) cos x = c sin y Solution: (2) sin x = c sec y... View Article
The solution of the dy / dx = 1 / x is 1) y + log x + c = 0 2) y = log x + c 3) ylogx + c = 0 4) None of these Solution: (2) y = log x + c dy / dx = 1 / x y = log x + c... View Article
The solution of the differential equation (dy / dx) + sin2 y = 0 is 1) y + 2 cos y = c 2) y - 2 sin y = c 3) x = cot y + c 4) y = cot x + c Solution: (3) x = cot y + c... View Article
The differential equation for the line y = mx + c is (where c is arbitrary constant) 1) (dy / dx) = m 2) (dy / dx) + m = 0 3) dy / dx = 0 4) None of these Solution: (1) (dy / dx) = m y = mx + c dy / dx = m... View Article
The differential equation of all conics whose centre lie at the origin is of order 1) 2 2) 3 3) 4 4) None of these Solution: (2) 3 Equation of all conics: ax2 + 2hxy + by2 = 1, --- a, h, b are arbitrary constants.... View Article
The order of differential equations of all parabolas having directrix parallel to the x-axis is 1) 3 2) 1 3) 4 4) 2 Solution: (1) 3 The equation of all parabolas having directrices parallel to the x-axis is (x - h)2 = ± 4a (y... View Article
The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively 1) 2, 1 2) 1, 2 3) 3, 2 4) 2, 3 Solution: (2) 1, 2... View Article
A first-order and first-degree differential equation in variables x and y is characterized by 1) First order of differentiation of y with respect to x and first degree of dy /dx 2) Order of differentiation of y with respect to x and... View Article
The order of the differential equation of the family of all concentric circles centred at (h, k) is 1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 (x - h)2 + (y - k)2 = r2. Order of the differential equation = 1.... View Article
Family y = Ax + A3 of curves represented by the differential equation of degree 1) Three 2) Two 3) One 4) None of these Solution: (1) Three... View Article
The differential equation of all circles in the first quadrant which touches the coordinate axes is of order 1) 1 2) 2 3) 3 4) None of these Solution: (1) 1 The equation of the family of a circle that touch both the axes is (x - a)2 + (y -... View Article
The differential equation of all circles of radius a is of order 1) 2 2) 3 3) 4 4) None of these Solution: (1) 2 The equation of the family of circles of radius a is (x - h)2 + (y - k)2 = a2... View Article
The order of the differential equation whose solution is y = a cos x + b sin x + ce-x is 1) 3 2) 2 3) 1 4) None of these Solution: (1) 3 y = a cos x + b sin x + ce-x is a three-parmeter family of curves, so its... View Article
The order of the differential equation of all circles of radius r, having a centre on the y-axis and passing through the origin is 1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 The equation of a family of circles of radius $r$ passing through the origin and having a... View Article
The order of the differential equation whose solution is x2 + y2 + 2gx + 2fy + c = 0 is 1) 1 2) 2 3) 3 4) 4 Solution: (3) 3 Since this equation has 3 arbitrary constants i. e. g, f, and c therefore order of this... View Article
The order and degree of the differential equation (√dy / dx) – 4 (dy / dx) – 7x = 0 are 1) 1 and 1/2 2) 2 and 1 3) 1 and 1 4) 1 and 2 Solution: (4) 1 and 2... View Article
The order and degree of the differential equation √sinx (dx + dy) = √cosx (dx – dy) is 1) (1, 2) 2) (2, 2) 3) (1, 1) 4) (2, 1) Solution: (3) (1, 1)... View Article
The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants, will be 1) 2 2) 4 3) 6 4) None of these Solution: (2) 4 It is a fundamental concept.... View Article
The relation y = A sin x + B cos x can be represented by the differential equation 1) dy / dx = y 2) d2y / dx2 = y 3) (d2y / dx2) + y = 0 4) None of these Solution: (3) (d2y / dx2) + y = 0... View Article
