A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact ? Do you think that statement of B is always true ?
Prove that if E and F are independent events, then the events E and F' are also independent.
If P(A) = 0.4, P(B) = p, P(A U B) = 0.6 and A and B are given to the independent events, find the value of ‘p’.
If E and F are independent events, then show that
(i) E and F' are independent events.
(ii) E' and F are also independent events.
If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
Find the particular solution of the following differential equation.
cosydx+(1+2e−x)sinydy=0;y(0)=π4
If the function f : R → R be defined by f(x) = 2x – 3 and g : R → R by g(x) = x³ + 5, then find fog and show that fog is invertible. Also, find (fog)⁻¹, hence find (fog)⁻¹(9).
Find the equations of the normal to the curve y = x³+ 2x + 6, which are parallel to line x + 14y + 4 = 0.
Using properties of determinants, prove that following :
|a+xyzxa+yzxya+z| = a2(a+x+y+z).
Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x² – 3xy²) dx = (y³ – 3x²y) dy, where C is a parameter.
Using properties of determinants, prove that :
|x²+1xyxzxyy²+1yzxzyzz²+1|
