List of top Mathematics Questions asked in CBSE CLASS XII

Find the general solution of the differential equation \( 2x^2 \frac{dy}{dx} = y^2 + 2xy \).

If the lines \(\frac{x - 3}{1} = \frac{1 - y}{1} = \frac{z + 2}{p}\) and \(\frac{2 - x}{3} = \frac{y + 1}{5} = \frac{z + 56}{2p}\) are perpendicular to each other, then find the value(s) of \(p\).

Evaluate : \( \int_{0}^{\pi} \frac{\sin^{2026} x}{\sin^{2026} x + \cos^{2026} x} \, dx \)

Find the vector equation of a line passing through the origin and perpendicular to both the lines \(\vec{r} = 2\hat{i} - \hat{j} + 2\hat{k} + \lambda(3\hat{i} + 4\hat{j} + 2\hat{k})\) and \(\vec{r} = \mu(\hat{i} - \hat{j} + \hat{k})\).

Find : \( \int \frac{dx}{x^{1/2} + x^{1/3}} \)

Find : \( \int \tan^{-1} \left( \sqrt{\frac{1-x}{1+x}} \right) \, dx \)

Find : \( \int \frac{x + 3}{x^2 + 4x + 5} \, dx \)

Assertion (A) : One of the particular solutions of the differential equation \(\frac{dy}{dx} = e^{x+y}\) can be \(e^x + e^{-y} = -2\).
Reason (R) : \(e^x + e^{-y} = C\) is the general solution of the differential equation \(\frac{dy}{dx} = e^{x+y}\).

Find the value of \(\sin [\cot^{-1} \sqrt{2} (\cos (\tan^{-1} 1))]\).

Find the sub-interval(s) of \((0, \frac{\pi}{2})\) in which \(f(x) = \tan x - 4x\) is increasing.

If \(x = t + \frac{1}{t}\) and \(y = t - \frac{1}{t}\), find \(\frac{dy}{dx}\) at \(t = 2\).

Assertion (A) : The vectors \(\vec{a}\) and \((-2\vec{a})\), where \(\vec{a} \neq \vec{0}\) are collinear vectors.
Reason (R) : \(\vec{a} \cdot (-2\vec{a}) = 0\).

If for two unit vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a} + 2\vec{b}| = |2\vec{a} - \vec{b}|\), then find the angle between \(\vec{a}\) and \(\vec{b}\).

Direction ratios of lines \(l_1\) and \(l_2\) are \(\) and \(\) respectively. The values of \(p\) and \(q\) for which \(l_1\) and \(l_2\) are parallel are respectively :

For any two vectors \( \vec{a} \) and \( \vec{b} \), which of the following statements is always true ?

If \(l_1, m_1, n_1\) and \(l_2, m_2, n_2\) are direction cosines of lines \(L_1\) and \(L_2\) respectively and \(\theta\) is the acute angle between them, then :

If \( (\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 198 \) and \( |\vec{a}| = 10|\vec{b}| \), then :

\( \int_{-1}^{1} (1 - |x|) \, dx \) is equal to :

\(\int \frac{dx}{2^x + 2^{-x}}\) is equal to :

The area of the shaded region of the circle given below is equal to :

The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is :

If \(A\) and \(B\) are skew-symmetric matrices of same order, then \(AB' + BA'\) is a/an :

If a square matrix \(A\) is such that \(A^2 = A\) and \((I - A)^3 = xA + I\), then value of \(x\) must be :

If \(\sin^{-1} x = y\), then \(\frac{dy}{dx}\) is :

If \(\begin{bmatrix} 4 1 3 \end{bmatrix} A = \begin{bmatrix} -4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3 \end{bmatrix}\), then order of \(A\) must be :