List of top Questions asked in Mizoram (MBSE) Class XII

Find the derivative of \( (\sin x)^x + \sin^{-1}(\sqrt{x}) \) with respect to \(x\).
Find the principal value of \( \tan^{-1}(\sqrt{3}) - \sec^{-1}(-2) \).
Expand \( (2x-3y)^5 \) using the Binomial Theorem.
Solve the system of equations using Cramer's Rule: \[ 2x+3y=8, \qquad x-y=-1. \]
A box contains 5 red and 7 white balls. Two balls are drawn at random. What is the probability that both are red?
A merchant marks his goods 20% above the cost price and allows a discount of 10%. Find his profit percentage.
Evaluate the integral \[ \int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx . \]
Find the general solution of the differential equation \[ \frac{dy}{dx}+\frac{y}{x}=x^2 . \]
A and B start a business with capitals of ₹50,000 and ₹40,000 respectively. After 6 months, C joins them with ₹80,000. Find the share of each in a profit of ₹25,000 at the end of the year.
An agent is paid a 5% commission on all sales and an additional 2% del-credere commission on credit sales. If he sells goods worth ₹50,000 (of which ₹20,000 are credit sales), calculate his total earning.
Find the value of \(n\) if \[ {}^{n}P_{4} = 12 \times {}^{n}P_{2}. \]
Discuss the different viewpoints regarding the rights of minorities in the Constituent Assembly.
Analyze the contribution of Baba Guru Nanak to the religious and social landscape of India.
Show that the relation \(R\) in the set \(A = \{1,2,3,4,5\}\) given by \[ R=\{(a,b): |a-b| \text{ is even}\} \] is an equivalence relation.
If \[ A=\begin{bmatrix}2 & 3\\ 1 & -4\end{bmatrix} \quad \text{and} \quad B=\begin{bmatrix}1 & -2\\ -1 & 3\end{bmatrix}, \] verify that \( (AB)^{-1} = B^{-1}A^{-1} \).
Solve the following system of equations using the matrix method: \[ 2x+3y+3z=5,\qquad x-2y+z=-4,\qquad 3x-y-2z=3. \]
Explain the distinctive features of the Harappan drainage system.
Analyze the factors that contributed to the rise of Magadha as the most powerful Mahajanapada.
Discuss the role of the Alvars and Nayanars in the early Bhakti movement.
Describe the administrative and military features of the Amaranayak system in the Vijayanagar Empire.
Examine why the Sanchi Stupa survived while the Amaravati Stupa did not.
Discuss the social and economic status of the Jotedars in 18th-century Bengal.
Explain why Mahatma Gandhi launched the Salt Satyagraha as a symbol of protest.