HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find `dy/(dx)` if, `x = e^(3t),  y = e^sqrtt`.

Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`

Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.

[(p→q) ∧ q]→p

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`

Write the dual of the following statements: (p ∨ q) ∧ T

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.

Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 

Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.

Find `dy/dx if x^3 + y^2 + xy = 7`

Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )

Find `"dy"/"dx"` ; if x = sin³θ , y = cos³θ

Find `"dy"/"dx"` ; if y = cos^-1 `("2x" sqrt (1 - "x"^2))`

If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )

Differentiate e^{4x + 5} w.r..t.e^3x

A manufacturing company produces x items at the total cost of Rs (180 + 4x). The demand function of this product is P = (240 − x). Find x for which profit is increasing.

Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.

If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid.