List of top Questions asked in Maharashtra Board Class XII Exam

Derive an expression for maximum speed of a vehicle moving along a horizontal circular track.

Draft an E-mail to the manager of a company to request him/her to give you an opportunity as an apprentice to serve you as an experience for your career development.
Construct the truth table for the statement pattern: \[ [(p \rightarrow q) \land q] \rightarrow p \]

If the mean and variance of a binomial distribution are \( 18 \) and \( 12 \) respectively, then the value of \( n \) is __________.

Explain the buffer action of the sodium acetate-acetic acid buffer.
If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are the position vectors of the points \( A, B, C \) respectively and \[ 5\mathbf{a} - 3\mathbf{b} - 2\mathbf{c} = \mathbf{0}, \] then find the ratio in which the point \( C \) divides the line segment \( BA \) externally.
Explain the following terms:
(a) Grafting
(b) Apomixis
(c) Polyembryony
(d) Parthenocarpy
In \( \triangle ABC \), if \( a = 18 \), \( b = 24 \), and \( c = 30 \), then find the value of \[ \sin \left(\frac{A}{2} \right). \]
What are interhalogen compounds? Write the chemical reaction when chlorine reacts with dry slaked lime.

Predict the type of cubic lattice of a solid element having edge length of 400 pm and density of 6.25 g/ml. 
(Atomic mass of element = 60)

Define Lanthanide contraction. Write the balanced chemical equation when acidified \( K_2Cr_2O_7 \) reacts with \( H_2S \).

Staying in comfort at home gives one more happiness than travelling.
 

Match the persons given in column 'A' with opinions/characteristics given in column 'B' 



 

Review: 
You have recently read a famous book/magazine. Write a Review on the same with the help of the following points: 
- title, front page, back page 
- language, features, contents 
- Pictures, quality, presentation 
- Values, vision and variety 
 

The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.

Evaluate: \[ I = \int \frac{5e^x}{(e^x + 1)(e^{2x} + 9)} \, dx. \]
A box with a square base is to have an open top. The surface area of the box is 147 cm\(^2\). What should its dimensions be in order that the volume is largest?
If \( x = f(t) \) and \( y = g(t) \) are differentiable functions of \( t \), so that \( y \) is a function of \( x \) and \( \frac{dx}{dt} \neq 0 \), then prove that: \[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}. \] Hence find \( \frac{dy}{dx} \), if \( x = at^2 \), \( y = 2at \).

Solve the following L.P.P. by graphical method: 
Maximize: 
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]

Find the volume of the parallelepiped whose vertices are
\( A(3,2,-1), B(-2,2,-3), C(3,5,-2) \) and \( D(-2,5,4) \).

I like to ask questions of the places I visit. 
(Choose the correct tense form of the above sentence from the following options and rewrite.) 

I would come back to my apartment in New York. 
(Choose the correct option using ‘used to’ for the given sentence and rewrite.) 
 

Choose two correct alternatives which define the theme of the extract:

Select and write the two statements from the given list which justify the theme of the poem.
Mary Morstan encourages Dr. Watson to get involved in her case. Justify the statement with reference to 'The Sign of Four.'