The order of the differential equation of all tangent lines to the parabola y = x2 is
1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 The parametric form of the given equation is x... View Article
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The family of curves y = ea sin x, where a is an arbitrary constant, is represented by the differential equation
1) log y = tan x (dy / dx) 2) y log y = tan x (dy / dx) 3)... View Article
The degree and order of the differential equation y = px + x3 √a2p2 + b2, where p = dy / dx are respectively
1) 3, 1 2) 1, 3 3) 1, 1 4) 3, 3 Solution: (1) 3, 1 \(\begin{array}{l}y =x \frac{d y}{d... View Article
If y = (A / x) + Bx2, then x2 (d2y / dx2) =
1) 2y 2) y2 3) y3 4) y4 Solution: (1) 2y \(\begin{array}{l}\begin{array}{l} y=\frac{A}{x}+B x^{2} \\ \frac{d y}{d x}=-\frac{A}{x^{2}}+2 B x... View Article
If y = (sin-1 x)2, then (1 – x2) (d2y / dx2) – x (dy / dx) =
1) 0 2) -1 3) -2 4) 1 5) 2 Solution: (5) 2 \(\begin{array}{l}\begin{array}{l} \frac{d y}{d x}=\frac{2 \sin ^{-1} x}{\sqrt{1-x^{2}}}... View Article
The degree of the differential equation satisfying √1 – x2 + √1 – y2 = a (x – y) is
1) 1 2) 3 3) 2 4) None of these Solution: (1) 1 \(\begin{array}{l}\text \ Differentiating \ both \ the... View Article
Order of the equation [1 + 5 (dy / dx)]3/2 = 10 (d3y / dx3) is
1) 2 2) 3 3) 1 4) 0 Solution: (2) 3 \(\begin{array}{l}\begin{array}{l} \left(1+5 \frac{d y}{d x}\right)^{\frac{3}{2}}=10 \frac{d^{3} y}{d x^{3}}\\ \left(1+5... View Article
The differential equation of the system of circles touching the y-axis at origin is
1) (dy / dx) = [x2 + y2] / 2xy 2) dy / dx = [y2 – x2] / xy... View Article
The order and degree of differential equation (d3y / dx3)⅘ – 2 (dy / dx) (d2y / dx2)2 = 0 are
1) 2, 10 2) 3, 10 3) 3, 5 4) 3, 4 Solution: (4) 3, 4 \(\begin{array}{l}\left(\frac{d^{3} y}{d x^{3}}\right)^{\frac{4}{5}}-2 \frac{d... View Article
The differential equation of the family of parabolas with vertex at (0, -1) and having axis along Y – axis is
1) yy’ + 2xy + 1 = 0 2) xy’ + y + 1 = 0 3) xy’ – 2y... View Article
The order and degree of the differential equation y = x (dy / dx) + 2 / (dy / dx), are
1) 1, 2 2) 1, 3 3) 2, 1 4) 1, 1 Solution: (1) 1, 2 y = x (dy... View Article
The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is
1) y (dy / dx) = x 2) x (dy / dx) = – y 3) x (dy / dx)... View Article
The form of the differential equation of the central conics ax2 + by2 = 1 is
1) x = y (dy / dx) 2) x (dy / dx)2 + xy (d2y / dx2) – y (dy... View Article
22 Jun 2021: The Hindu Analysis
UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 22nd Jun 2021. Important news and... View Article
Zero-Day
A zero-day (also spelt as 0-day) is a software weakness not known to those who are vendors of the target... View Article
Let C be the circle with centre at (1, 1) and radius 1. If T is the circle centred at (0, k) passing through the origin and touching the circle C externally, then the radius of T is equal to
1) √3/√2 2) √3/2 3) 1/2 4) 1/4 Solution: (4) ¼ Distance between their centre \(\begin{array}{l}k+1=\sqrt{1+(k-1)^{2}}\\ \Rightarrow k+1=\sqrt{1+k^{2}+1-2 k}\\ \Rightarrow... View Article
Which of the following is a point on the common chord of the circle x2 + y2 + 2x – 3y + 6 = 0 and x2 + y2 + x – 8y – 13 = 0 ?
1) (1, – 2) 2) (1, 4) 3) (1, 2) 4) (1, – 4) Solution: (4) (1, – 4) The... View Article
The locus of the mid – point of the chord of the circle x2 + y2 – 2x – 2y – 2 = 0 which makes an angle of 120 at the centre, is
1) x2 + y2 – 2x – 2y – 1 = 0 2) x2 + y2 + x + y... View Article
The inverse of the point (1, 2) with respect to the circle x2 + y2 – 4x – 6y + 9 = 0, is
1) (1, 1/2) 2) (2, 1) 3) (0, 1) 4) (1, 0) Solution: (3) (0, 1) \(\begin{array}{l}\text \ Equation \... View Article
A line is drawn through the point P(3, 11) to cut the circle x2 + y2 = 9 at A and B. Then PA . PB is equal to
1) 9 2) 121 3) 205 4) 139 Solution: (2) 121 From geometry, we know PA . PB = (PT)2... View Article
