HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`. What is the probability that he will win a prize at least once. 

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \[\frac{1}{100} .\]  What is the probability that he will win a prize exactly once.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`  What is the probability that he will win a prize at least twice.

 The equation of a line is 2x -2 = 3y +1 = 6z -2 find the direction ratios and also find the vector equation of the line. 

A person makes two types of gift items A and B requiring the services of a cutter and a finisher.  Gift item A requires 4 hours of the cutter's time and 2 hours of finisher's time. Fifth item B requires 2 hours of the cutter's time and 4 hours of finisher's time. The cutter and finisher have 208 hours and 152 hours available time respectively every month. The profit on one gift item of type A is ₹ 75 and on one gift item of type, B is ₹ 125. Assuming that the person can sell all the gift items produced, determine how many gift items of each type should he make every month to obtain the best returns?

Write the dual of the following.

p ∨ (q ∧ r)

Write the dual of the following.

p ∧ (q ∧ r)

Write the dual of the following.

(p ∨ q) ∧ (r ∨ s)

Write the dual of the following.

p ∧ ∼ q

Write the dual of the following.

(∼ p ∨ q) ∧ (∼ r ∧ s)

Write the dual of the following.

∼ p ∧ (∼ q ∧ (p ∨ q) ∧ ∼ r)

Write the dual of the following.

[∼ (p ∨ q)] ∧ [p ∨ ∼ (q ∧ ∼ s)]

Write the dual of the following.

c ∨ {p ∧ (q ∨ r)}

Write the dual of the following.

∼ p ∨ (q ∧ r) ∧ t

Write the dual of the following.

(p ∨ q) ∨ c

Choose correct alternatives:

If the equation 4x² + hxy + y² = 0 represents two coincident lines, then h = _______

If the lines represented by kx² − 3xy + 6y² = 0 are perpendicular to each other, then

Choose correct alternatives:

The difference between the slopes of the lines represented by 3x² - 4xy + y² = 0 is 2

If log (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.

If `log_10((x^3 - y^3)/(x^3 + y^3))` = 2, show that `dy/dx = -(99x^2)/(101y^2)`.