There are three categories of students in a class of 60 students:
A : Very hardworking ; B : Regular but not so hardworking; C : Careless and irregular 10 students are in category A, 30 in category B and the rest in category C. It is found that the probability of students of category A, unable to get good marks in the final year examination is 0.002, of category B it is 0.02 and of category C, this probability is 0.20. A student selected at random was found to be one who could not get good marks in the examination. Find the probability that this student is category C.
[13] Probability
Chapter: [13] Probability
Concept: undefined >> undefined
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\frac{y}{x}\cos\left( \frac{y}{x} \right) dx - \left\{ \frac{x}{y}\sin\left( \frac{y}{x} \right) + \cos\left( \frac{y}{x} \right) \right\} dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[xy \log\left( \frac{x}{y} \right) dx + \left\{ y^2 - x^2 \log\left( \frac{x}{y} \right) \right\} dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( 1 + e^{x/y} \right) dx + e^{x/y} \left( 1 - \frac{x}{y} \right) dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( x^2 + y^2 \right)\frac{dy}{dx} = 8 x^2 - 3xy + 2 y^2\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(x2 − 2xy) dy + (x2 − 3xy + 2y2) dx = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} = y - x \cos^2 \left( \frac{y}{x} \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y = 2\sqrt{y^2 - x^2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x \cos\left( \frac{y}{x} \right) \cdot \left( y dx + x dy \right) = y \sin\left( \frac{y}{x} \right) \cdot \left( x dy - y dx \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(x2 + 3xy + y2) dx − x2 dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(2x2 y + y3) dx + (xy2 − 3x3) dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y + x \sin\left( \frac{y}{x} \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[y dx + \left\{ x \log\left( \frac{y}{x} \right) \right\} dy - 2x dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Solve the following initial value problem:
(x2 + y2) dx = 2xy dy, y (1) = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Solve the following initial value problem:
\[x e^{y/x} - y + x\frac{dy}{dx} = 0, y\left( e \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Solve the following initial value problem:
\[\frac{dy}{dx} - \frac{y}{x} + cosec\frac{y}{x} = 0, y\left( 1 \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
