The circle passing through (1, – 2) and touching the X-axis at (3, 0), also passes through the point
1) (-5, 2) 2) (2, -5) 3) (5, – 2) 4) (-2, 5) Solution: (3) (5, – 2) \(\begin{array}{l}\text \... View Article
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The centre of the circle passing through the point (0, 1) and touching the curve y = x2 at (2, 4) is
1) [- 16 / 5, 27 / 10] 2) [- 16 / 7, 53 / 10] 3) [- 16 /... View Article
Compute the shortest distance between the circle x2 + y2 – 10x – 14y – 151 = 0 and the point (-7, 2).
1) 0 2) 1 3) 2 4) 4 Solution: (3) 2 \(\begin{array}{l}x^{2}+y^{2}-10 x-14 y-151=0\\ \text \ General \ equation \... View Article
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 +... 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... 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... 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... 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... 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... 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... 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 \(\begin{array}{l}\begin{array}{l} y^{2}=\pm 4 a(x-h)... 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... 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.... 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 \(\begin{array}{l}\begin{array}{l} \text { Differentiating the given equation,... 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... 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... 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... 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... 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.... 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... View Article
