List of top Questions asked in CBSE CLASS XII

For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?
Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4  \end{bmatrix}\)

What is the Planning Process?

Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 &  3\\ 5 & 7 \end{bmatrix}\)
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix}  -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that 
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)n=anI+nan-1bA,where I is the identity matrix of order 2 and n∈N

Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta  &-sin\alpha \\   -sin\beta&cos\beta  &0 \\   sin\alpha cos\beta&sin\alpha\sin\beta  &cos\alpha  \end{vmatrix}\)

Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).
The coordinates of the foot of the perpendicular drawn from the point \( (0, 1, 2) \) on the \( x \)-axis are given by:
A particle moves along the curve \(6y=x^3+2\).Find the points on the curve at which the y coordinate is changing 8 times as fast as the \(x\) coordinate
Pass necessary journal entries relating to the issue of debentures and to write off discount/loss on issue of debentures in the books of Ajanta Ltd. in the following cases: 200, 9\% debentures of \rupee1,000 each are issued at 10\% discount and redeemable at par. Balance in Securities Premium account is \rupee15,000. 300, 11\% debentures of \rupee1,000 each are issued at 5\% discount and redeemable at a premium of 10\%. Balance in Securities Premium account is \rupee35,000.
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
The month of September is celebrated as the Rashtriya Poshan Maah across the country. Following a healthy and well-balanced diet is crucial in order to supply the body with the proper nutrients it needs. A balanced diet also keeps us mentally fit and promotes improved level of energy.
\includegraphics[width=\linewidth]{latex1.png} A dietician wishes to minimize the cost of a diet involving two types of foods, food \( X \) (in kg) and food \( Y \) (in kg), which are available at the rate of \( \text{₹} 16/\text{kg} \) and \( \text{₹} 20/\text{kg} \), respectively. The feasible region satisfying the constraints is shown in Figure-2. On the basis of the above information, answer the following questions: [(i)] Identify and write all the constraints which determine the given feasible region in Figure-2. [(ii)] If the objective is to minimize cost \( Z = 16x + 20y \), find the values of \( x \) and \( y \) at which cost is minimum. Also, find the minimum cost assuming that minimum cost is possible for the given unbounded region.
Is Saheb happy working at the tea-stall? Explain.
Why did Sophie like her brother Geoff more than any other person? From her perspective, what did he symbolise?
Find: \[ \int \frac{(3 \cos x - 2) \sin x}{5 - \sin^2 x - 4 \cos x} \, dx. \]

What is the coordination entity formed when excess of aqueous \(KCN\) is added to an aqueous solution of copper sulphate? Why is it that no precipitate of copper sulphide is obtained when \(H_2S(g)\) is passed through this solution?

Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
\includegraphics[width=\linewidth]{latex.png} The relation between fuel consumption \( F \) (liters per 100 km) and speed \( V \) (km/h) under some constraints is given as: \[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \] On the basis of the above information, answer the following questions: [(i)] Find \( F \), when \( V = 40 \, \text{km/h} \). [(ii)] Find \( \frac{dF}{dV} \). [(iii)] (a) Find the speed \( V \) for which fuel consumption \( F \) is minimum.
\hspace*{0.8cm} OR
(b) Find the quantity of fuel required to travel \( 600 \, \text{km} \) at the speed \( V \) at which \( \frac{dF}{dV} = -0.01 \).
The vertices of triangle \( \triangle ABC \) are \( A(1, 1, 0), B(1, 2, 1) \), and \( C(-2, 2, -1) \). Find the equations of the medians through A and B. Use the equations so obtained to find the coordinates of the centroid.
Minimise Z=x+2y
Subject to 2x+y≥3,x+2y≥6,x,y≥0.
How would you describe the character and temperament of Sophie’s father?
Integrate the function: \(\frac {1}{\sqrt {(x-a)(x-b)}}\)

Draw the structures of all isomeric alcohols of molecular formula C5H12O and give their IUPAC names. (ii)Classify the isomers of alcohols in question 11.3(i)as primary, secondary and tertiary alcohols.

Find: \[ \int \frac{e^{4x} - 1}{e^{4x} + 1} \, dx. \]