List of top Questions asked in Maharashtra Board Class XII Exam

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 \( D(-2,5,4) \).

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

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:

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.)

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]

________novel is concerned with the protagonist’s overall growth from childhood to adulthood.
[Bildungsroman / Utopian / Gothic]

The novel that bears more than one level of meaning is called ________novel.
[Realistic / Allegorical / Historical]

Match the columns:

Appeal:
Prepare an ‘Appeal’ on the topic ‘Traffic Rules for Safety Measures’ with the help of the following points (100 to 150 words):
- Ignorance and lack of knowledge and information
- Purpose / need of obedience
- Avoid accidents / need of society
- Discipline

Blog:
Write a ‘Blog’ in a proper format on ‘Body Language’ with the help of the following points (100 to 150 words):
- Meaning and features
- Characteristics and scope
- Benefits / Importance
- Uses / Ways to utilize

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

Expand the following idea with the help of the points given below (100 to 150 words):
'Manners Maketh Man'
Essential Virtues
- Politeness
- Speech, tone, gestures, and action
- To be courteous and amiable

Imagine you are given the responsibility to 'compe' a programme by your college authorities. You need to prepare your script on the programme titled 'Cultural Fest 2024.' Draft the script to decide the flow of the programme. You may take help of the given points.