Let →a = ∧i+∧j+∧k, →b = 4∧i−2∧j+3∧k , and →c = ∧i−2∧j+∧k Find a vector of magnitude 6 units,which is parallel to the vector 2→a−→b+3→c.
Find the equations of the normal to the curve y = x³+ 2x + 6, which are parallel to line x + 14y + 4 = 0.
A speaks truth in 60% of the cases, while B in 90% of cases. In what percent of cases are they likely to contradict each other in stating the same fact ? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A ?
Find the general solution of the differential equation (1 + tan y)(dx – dy) + 2xdy = 0.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 9 and B wins if he gets a total of 7. If A starts the game, find the probability of winning the game by B.
In a school, there are 1,000 students, out of which 380 are girls. Out of 380 girls, 10% of the girls scored highest in GS. What is the probability that a student chosen randomly scored highest in GS given that the chosen student is a girl ?
Using properties of determinants, prove that
|x+λ2x2x2xx+λ2x2x2xx+λ| = (5x+λ)(λ−x)2.
