List of top Mathematics Questions asked in CBSE CLASS XII

Find: \[ \int \frac{e^{4x} - 1}{e^{4x} + 1} \, dx. \]

(a) If \( x^{30} y^{20} = (x + y)^{50} \), prove that
\[ \frac{dy}{dx} = \frac{y}{x}. \]

Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
\includegraphics[width=\linewidth]{latex.png} The relation between fuel consumption \( F \) (liters per 100 km) and speed \( V \) (km/h) under some constraints is given as: \[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \] On the basis of the above information, answer the following questions: [(i)] Find \( F \), when \( V = 40 \, \text{km/h} \). [(ii)] Find \( \frac{dF}{dV} \). [(iii)] (a) Find the speed \( V \) for which fuel consumption \( F \) is minimum.
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(b) Find the quantity of fuel required to travel \( 600 \, \text{km} \) at the speed \( V \) at which \( \frac{dF}{dV} = -0.01 \).

Integrate the function: \(\frac{e^{2x}-1}{e^{2x}+1}\)

A particle moves along the curve \(6y=x^3+2\).Find the points on the curve at which the y coordinate is changing 8 times as fast as the \(x\) coordinate

The month of September is celebrated as the Rashtriya Poshan Maah across the country. Following a healthy and well-balanced diet is crucial in order to supply the body with the proper nutrients it needs. A balanced diet also keeps us mentally fit and promotes improved level of energy.
\includegraphics[width=\linewidth]{latex1.png} A dietician wishes to minimize the cost of a diet involving two types of foods, food \( X \) (in kg) and food \( Y \) (in kg), which are available at the rate of \( \text{₹} 16/\text{kg} \) and \( \text{₹} 20/\text{kg} \), respectively. The feasible region satisfying the constraints is shown in Figure-2. On the basis of the above information, answer the following questions: [(i)] Identify and write all the constraints which determine the given feasible region in Figure-2. [(ii)] If the objective is to minimize cost \( Z = 16x + 20y \), find the values of \( x \) and \( y \) at which cost is minimum. Also, find the minimum cost assuming that minimum cost is possible for the given unbounded region.

Find: \[ \int \frac{(3 \cos x - 2) \sin x}{5 - \sin^2 x - 4 \cos x} \, dx. \]

The vertices of triangle \( \triangle ABC \) are \( A(1, 1, 0), B(1, 2, 1) \), and \( C(-2, 2, -1) \). Find the equations of the medians through A and B. Use the equations so obtained to find the coordinates of the centroid.

Minimise Z=x+2y
Subject to 2x+y≥3,x+2y≥6,x,y≥0.

Integrate the function: \(\frac {1}{\sqrt {(x-a)(x-b)}}\)

Find the local maximum value and local minimum value (whichever exists) for the function \[ f(x) = 4x^2 + \frac{1}{x}, \quad (x \neq 0). \]

Find the integrals of the function: \(sin^3 (2x+1)\)

Integrate the function: \(\frac {1}{\sqrt {8+3x-x^2}}\)

If a matrix has 36 elements, the number of possible orders it can have, is:

If \( y = (\tan x)^x \), then find \( \frac{dy}{dx} \).

A function \( f \) is defined from \( R \to R \) as \( f(x) = ax + b \), such that \( f(1) = 1 \) and \( f(2) = 3 \). Find the function \( f(x) \). Hence, check whether the function \( f(x) \) is one-one and onto.

Integrate the function: \(\frac {3x}{1+2x^4}\)

Prove that the greatest integer function defined by f(x)=[x],0<x<3 is not differentiable at x=1 and x=2.

Evaluate: \[ \int_1^3 (|x - 1| + |x - 2| + |x - 3|) \, dx. \]

Evaluate the definite integral: \(∫^4_1[|x-1|+|x-2|+|x-3|]dx\)

Find the value of \( p \) for which the lines \[ \vec{r_1} = \hat{i} + (2\lambda + 1) \hat{j} + (3\lambda + 2) \hat{k} \] and \[ \vec{r_2} = \hat{i} - 3 \hat{j} + (p\mu + 7) \hat{k} \] are perpendicular to each other and also intersect. Also, find the point of intersection of the given lines.