List of top Questions asked in UP Board XII

Who have classified culture into material and non-material cultures?

Mention the three characteristics of the Rural Society.

Define ‘Kinship’.

What is ‘Social Stratification’?

What is ‘Communalism’?

'Chipko Movement' is related to:

Which of the following is called the fourth pillar of democracy?

Who is the founder of Arya Samaj?

Which of the following is not the characteristic of culture?

Liberalization is related with:

Who was the originator of the ‘Cyclical Theory’?

The main basis for separating rural and urban communities is:

Who among the following is not a sociologist?

Solve: \(\frac{dy}{dx} = \frac{x+y+1}{2x+2y+3}\).

Solve: \((1+y^2) dx = (\tan^{-1} y - x) dy\).

Prove that \( \int_{0}^{\pi/2} \sqrt{\frac{1+\cos 4x}{2}} \, dx = 1 \).

If \( I = \int_{0}^{\pi} \frac{x \, dx}{a^2 \cos^2 x + b^2 \sin^2 x} \), find the value of I.

For the two vectors \( \vec{a} \) and \( \vec{b} \), prove that \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) when \( \vec{a} \neq \vec{0} \) and \( \vec{b} \neq \vec{0} \).

If \( I = \int_{\pi/6}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}} \), then prove that \( I = \frac{\pi}{12} \).

A car is started to move from a point P at time t = 0 and is stopped at the point Q. The distance x metre covered by the car in t second is given by \(x = t^2\left(3-\frac{t}{2}\right)\). Find the time required by the car to reach at the point Q and also find the distance between P and Q.

Find the shortest distance between the lines \(\vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})\) and \(\vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(3\hat{i} - 5\hat{j} + 2\hat{k})\).

If x, y, z are three independent events, then prove that \(P(X \cap Y \cap Z) = P(X) \cdot P\left(\frac{Y}{X}\right) \cdot P\left(\frac{Z}{X \cap Y}\right)\).

Solve the following system of equations by matrix method :
2x + 3y + 3z = 5
x - 2y + z = -4
3x - y - 2z = 3

Find the vector equation of a straight line passing through the point (5, 2, -4) and parallel to the vector \( 3\hat{i} + 2\hat{j} - 8\hat{k} \).

Without cover a box is formed by 6 m x 16 m rectangular steel sheet on cutting the squares of length x m from its each corner. Then find the maximum volume of the box.