List of top Questions asked in Maharashtra Board Class XII Exam

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.

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

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

Select and write the two statements from the given list which justify the theme of the poem.

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.) 

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

Mary Morstan encourages Dr. Watson to get involved in her case. Justify the statement with reference to 'The Sign of Four.'
The most interesting part of the extract 'Around the World in Eighty Days' is its climax. Discuss.
Appreciate Phileas Fogg as the protagonist of 'Around the World in Eighty Days.'
Consider 'student-teacher relationship' as one of the themes of "To Sir With Love."
Write a character-sketch of the narrator E.R. Braithwaite in "To Sir With Love."

The novel based on an imaginary community possessing the ideal qualities is called _________ novel.
[ Utopian/Epistolary /Picaresque ]

________novel is a novel based on the author’s life. 
[Epistolary / Psychological / Autobiographical]