HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Important Questions

Using the rules in logic, write the negation of the following:

(p ∨ q) ∧ (q ∨ ∼r)

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q → p

Consider the following statements.

1. If D is dog, then D is very good.
2. If D is very good, then D is dog.
3. If D is not very good, then D is not a dog.
4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

Negation of “Some men are animal” is ______.

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

If p ∨ q is true, then the truth value of ∼ p ∧ ∼ q is ______.

Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."

Draw Venn diagram for the following:

No policeman is thief

Draw Venn diagram for the following:

Some doctors are rich

Draw Venn diagram for the following:

Some students are not scholars

Conditional of p → q is equivalent to p → ∼ q.

Converse of the statement q `rightarrow` p is ______.

Find `dy/dx if y=cos^-1(sqrt(x))`

find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

find dy/dx if x=e^{2t ,} y=`e^sqrtt`

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`

If x=at², y= 2at , then find dy/dx.