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

Find `dy/dx if, x = e^(3t),y=e^((4t+5))`

 Find `dy/dx` if,

`x = e ^(3^t), y = e^((4t + 5))`

Find `dy/dx` if, `x=e^(3t), y=e^((4t+5))`

 Find `dy/dx if,x = e^(3^T), y = e^((4t + 5)`

Find `dy/dx` if x= `e^(3t)`, y =`e^((4t+5))`

Find `dy/dx` if,  `x = e^(3t), y = e^((4t + 5))`

Find `dy/dx if, x= e^(3t)"," y = e^((4t+5))`

Find `dy/dx` if, x = `e^(3t)`, y = `e^((4t + 5))`.

Express the truth of each of the following statements by Venn diagram:

(a) Some hardworking students are obedient.

(b) No circles are polygons.

(c) All teachers are scholars and scholars are teachers. 

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

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Draw a Venn diagram for the truth of the following statement : 

All rational number are real numbers. 

Draw Venn diagram for the truth of the following statements : 

Some rectangles are squares. 

Express the truth of each of the following statements using Venn diagrams: 

(a) No circles are polygons

(b) Some quadratic equations have equal roots 

If x⁷ . y⁹ = (x + y)¹⁶ then show that `"dy"/"dx" = "y"/"x"`

Express the truth of the following statements with the help of Venn diagram:
(a) No circles are polygon
(b) If a quadrilateral is rhombus , then it is a parallelogram .

Using the Venn diagram, examine the logical equivalence of the following statements: 

(a) Some politicians are actors.

(b) There are politicians who are actors.

(c) There are politicians who are not actors.

If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`

Express the truth of each of the following statements by Venn diagram :
(a) Some hardworking students are obedient.
(b) No circles are polygons.
(c) All teachers are scholars and scholars are teachers.

Express the truth of each of the following statements using Venn diagram.
(1) All teachers are scholars and scholars are teachers.
(2) If a quadrilateral is a rhombus then it is a parallelogram..