List of top Mathematics Questions asked in CBSE CLASS XII

Integrate the function: \(\frac {1}{\sqrt {(2-x)^2+1}}\)
Integrate the function: \(\frac {3x^2}{x^6+1}\)
Find the integrals of the function: \(\frac{1}{cos(x-a)cos(x-b)}\)
Find the integrals of the function: \(sin^{-1} (cos x)\)
Find the integrals of the function: \(\frac {cos\  2x}{(cos \ x+sin \ x)^2}\)
Find the integrals of the function: \(\frac {1}{sin \ x\  cos^3 x}\)
Find the integrals of the function: \(\frac {cos 2x+2 sin^2x}{cos^2x}\)
Find the integrals of the function: \(\frac {sin^3 x+cos^3 x}{sin^2 x .cos^2 x}\)

From the differential equation of the family of circles touching the y-axis at the origin.

From the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

From the differential equation of the family of circles having centre on y-axis and radius 3 units.

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts(in kg) of nitrogen, phosphoric acid, potash and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240kg of phosphoric acid at least 270kg of potash and at most 310kg of chlorine. If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
 

kg per bag

 Brand PBrand Q

Nitrogen

Phosphoric acid

Potash

Chlorine

3

1

3

1.5

3.5

2

1.5

2

Let R be the relation in the set N given by R={\((a,b):a=b−2,b>6\)}.Choose the correct answer
Let R be the relation in the set {1,2,3,4} given by R= {(1,2), (2,2), (1,1), (4,4), (1,3), (3,3), (3,2)}. Choose the correct answer.
Find an anti derivative (or integral) of the following functions by the method of inspection: sin2x - 4e3x

For each of the differential equations given below, indicates its order and degree (if defined).

\((i) \frac {d^2y}{dx^2}+5x(\frac {dy}{dx})^2-6y=log\ x\)

\((ii)(\frac {dy}{dx})^3-4(\frac{dy}{dx})^2+7y=sin\ x\)

\((iii) \frac {d^4y}{dx^4}-sin(\frac {d^3y}{dx^3})=0\)

Find a particular solution satisfying the given condition:\(\frac {dy}{dx}-3y\  cot\ x=sin2x;\ y=2 \ when\  x=\frac \pi2\)
For the differential equations, find the particular solution satisfying the given condition:\(2xy+y^2-2x^2\frac{dy}{dx}=0;y=2\) when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\(\frac{dy}{dx}-\frac{y}{x}+cosec(\frac{y}{x})=0;y=0\) when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\([xsin^2(\frac{x}{y})-y]dx+xdy=0;y=\frac{π}{4},\)when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\(x^2dy+(xy+y^2)dx=0;y=1\) when \(x=1\)
For the differential equations, find the particular solution satisfying the given condition:\((x+y)dy+(x-y)dy=0;y=1\) when \(x=1\)
Show that the given differential equation is homogeneous and solve:\((1+e^{\frac{x}{y}})dx+e^{\frac{x}{y}}(1-\frac{x}{y})dy=0\)
Show that the given differential equation is homogeneous and solve:\(y\,dx+xlog(\frac{y}{x})dy-2x\,dy=0\)
Show that the given differential equation is homogeneous and solve:\(x\frac{dy}{dx}-y+sinx(\frac{y}{x})=0\)