HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Important Questions for Mathematics and Statistics

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.

If y =1 − cos θ, x = 1 − sin θ, then `dy/dx  "at"  θ =pi/4` is ______

If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`

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`

Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`

If x = cos t (3 – 2 cos² t) and y = sin t (3 – 2 sin² t), find the value of dx/dy at t =4/π.

Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`

If X = f(t) and Y = g(t) Are Differentiable Functions of t ,  then prove that y is a differentiable function of x and

`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`

Hence find `"dy"/"dx"` if x = a cos² t and y = a sin² t.

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

If y = sin ^-1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`