List of top Questions asked in UP Board XII

Find the value of \(\int \frac{1}{x^2 - a^2} dx\).

If \(R_1\) and \(R_2\) are equivalence relations in the set A, prove that \(R_1 \cap R_2\) is also an equivalence relation in A.

If two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}| = 2\), \(|\vec{b}| = 3\) and \(\vec{a} \cdot \vec{b} = 4\), find \(|\vec{a} - \vec{b}|\).

The Cartesian equation of a line is \(\frac{x+3}{2} = \frac{y-5}{4} = \frac{z+6}{2}\). Find its vector equation.

A die is thrown once. If the event 'the number obtained on the die is a multiple of 3' is represented by E and 'the number obtained on the die is even' is represented by F, tell whether the events E and F are independent.

Find the principal value of \(\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)\).

Find the value of \(\int x^3 e^{x^4} dx\).

Let \(\vec{a} = \hat{i} + 2\hat{j}\) and \(\vec{b} = 2\hat{i} + \hat{j}\). Is \(|\vec{a}| = |\vec{b}|\)? Are the vectors \(\vec{a}\) and \(\vec{b}\) equal?

If the orders of the matrices A and B are \(m \times n\) and \(n \times p\) respectively, then the order of AB will be

The direction cosines of the vector \(\hat{i} + \hat{j} - 2\hat{k}\) are

In which of the following places was the first atomic power station located?

Given below are statement and reason. Give answer by selecting correct option.
Statement: Alluvial soil is useful for paddy, wheat, and pulses.
Reason: Alluvial soil is famous for moisture.

Which of the following ports is not on the western coast of India?