List of top Mathematics Questions asked in CBSE CLASS XII

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \(y=cos x + C  : y'+ sin x=0\)
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \(y=x^2+2x+C     : y'-2x -2= 0\)
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=ex+1 : y''-y'=0

The corner points of the feasible region are determined by the following system of linear inequalities:
2x+y≤10,x+3y≤15,xy≥0 are (0,0),(5,0),(3,4)and(0,5)Let Z=px+qy,where p,q >0.Condition on p and q so that the maximum of Z occurs at both (3,4)and (0,5) is

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If A,B are symmetric matrices of same order,then AB−BA is a
  1. Find equation of line joining (1,2) and (3,6) using determinants 
  2. Find equation of line joining (3,1) and (9,3) using determinants

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time(in minutes)required for each toy on the machines is given below:
A manufacturer makes two types of toys
Each machine is available for a maximum 6 hours per day.If the profit on each toy of type A is Rs7.50 and that on each toy of type B is Rs5, show that 15 toys of type A and 30 toys of type B should be manufactured in a day to get maximum profit.

Differentiate the functions with respect to x.
\(sin(x^2+5)\)

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

determine whether the given planes are parallel or perpendicular,and in case they are neither, find the angles between them. (a)7x+5y+6z+30=0 and 3x-y-10z+4=0 

(b)2x+y+3z-2=0 and x-2y+5=0 

(c)2x-2y+4z+5=0 and 3x-3y+6z-1=0 

(d)2x-y+3z-1=0 and 2x-y+3z+3=0 

(e)4x+8y+z-8=0 and y+z-4=0

Find \(\frac{dy}{dx} y=sin^{-1}(\frac{1-x^2}{1+x^2}),0<x<1\)
Find the second order derivatives of the function
\(x^2+3x+2\)

Differentiate the functions with respect to x.
\(cos\ x^3.sin^2(x^5)\)

Differentiate the functions with respect to x.
\(sec(tan(\sqrt x))\)

Differentiate the functions with respect to x.
\(cos(sin\ x)\)

A manufacturer produces three products \(x,y,z\) which he sells in two markets. Annual sales are indicated below:
MarketProducts
I10000200018000
II6000200008000
(a)If unit sale prices of \(x,y\) and \(z\) are Rs 2.50,Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market with the help of matrix algebra.
(b) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.
Compute the following:
\((i)\begin{bmatrix}a&b\\-b&a\end{bmatrix}+\begin{bmatrix}a&b\\b&a\end{bmatrix}\)
\((ii)\begin{bmatrix}a^2+b^2& b^2+c^2\\ a^2+c^2& a^2+b^2\end{bmatrix}+\begin{bmatrix}2ab& 2bc \\-2ac& -2ab\end{bmatrix}\)
\((iii)\begin{bmatrix}-1&4&-6\\ 8&5&16\\ 2&8&5\end{bmatrix}+\begin{bmatrix}12&7&6 \\8&0&5\\ 3&2&4\end{bmatrix}\)
\((iv)\begin{bmatrix}cos^2x& sin^2x\\ sin^2x& cos^2x\end{bmatrix}+\begin{bmatrix}sin^2x& cos^2x\\ cos^2x& sin2x\end{bmatrix}\)
Express the following matrices as the sum of a symmetric and a skew-symmetric matrix:
\((i)\begin{bmatrix}3&5\\1&-1\end{bmatrix}\)
\((ii)\begin{bmatrix}6&-2&2\\ -2&3&-1\\ 2&-1&3\end{bmatrix}\)
\((iii)\begin{bmatrix}3&3&-1\\ -2&-2&1\\ -4&-5&2\end{bmatrix}\)
\((iv)\begin{bmatrix}1&5\\-1&2\end{bmatrix}\)
Maximise Z=-x+2y
subject to the constraints:
x≥3,x+y≥5,x+2y≥6,y≥0.
Minimise and Maximise Z=x+2y
Subject to x+2y≥100,2x-y≤0,2x+y≤200;x,y≥0.
Minimise and Maximise Z=5x+10y
Subject to x+2y≤120,x+y≥60,x-2y≥0,x,y≥0.

Prove that \(x^2-y^2=c(x^2+y^2)\)is the general solution of differential equation(\(x^3-3xy^2)dx=(y^3-3x^2y)dy\),where \(c\) is parameter.

Show that the points \(A(1,2,7),B(2,6,3)\),and \(C(3,10,-1)\) are collinear.