List of top Mathematics Questions asked in MHT CET

The length of the altitude through the point \( D \) of the tetrahedron where the vertices of the tetrahedron are
\[ A(2, 3, 1), B(4, 1, -2), C(6, 3, 7), D(-5, -4, 8), \] is

The volume of the tetrahedron whose coterminous edges are represented by
\[ \mathbf{a} = -12\hat{i} + p\hat{k}, \quad \mathbf{b} = -3\hat{j} - \hat{k}, \quad \mathbf{c} = -2\hat{i} + \hat{j} - 15\hat{k}, \] is 570 cu. units, then \( p = \)

The direction ratios of the line of intersection of the planes \( x - y + z - 5 = 0 \) and \( x - 3y - 6 = 0 \), are:

In a culture, the bacteria count is 1,00,000 initially. The number increases by 10% in the first 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

If \( y = ax^r - bx^{r-1} \), then \[ \frac{d^2y}{dx^2} = ? \]

The points \( (1, 3) \) and \( (5, 1) \) are two opposite vertices of a rectangle. The other two vertices lie on the line \[ y = 2x + c, \quad \text{where} \quad c \text{ is the constant}, \quad \text{then the co-ordinates of the other two vertices are} \]

Angle between the parabola \[ y^2 = 4(x - 1) \quad \text{and} \quad x^2 + 4(y - 3) = 0 \quad \text{at the common end of their latus rectum is} \]

A wire of length 8 units is cut into two parts which are bent respectively in the form of a square and a circle. The least value of the sum of the areas so formed is

Evaluate the integral \[ \int \frac{x^3}{(x+1)^2} \, dx. \]

Evaluate the integral \[ \int \cos \left( \frac{\pi x}{6} \right) \cos \left( \frac{\pi x}{3} \right) \, dx. \]

Let \( x \) be the length of each of the equal sides of an isosceles triangle and \( \theta \) be the angle between these sides. If \( x \) is increasing at the rate \( \frac{1}{2} \) m/hour and \( \theta \) is increasing at the rate \( \frac{\pi}{3} \) rad/hour, then the rate at which area of the triangle is increasing when \( x = 12 \) m and \( \theta = \frac{\pi}{4} \) is

The abscissae of the points of the curve \[ y = x^3 \quad \text{are in the interval} \quad [-2, 2], \] where the slope of the tangents can be obtained by the mean value theorem for the interval \( [-2, 2] \), are

The solution set for minimizing the function \( z = x + y \) with constraints \[ x + y \geq 2, \quad x + 2y \leq 8, \quad x \leq 3, \quad x, y \geq 0 \] contains

The distance of the point \( P(3, 8, 2) \) from the line \[ \frac{x}{2} = \frac{y - 3}{4} = \frac{z - 3}{3}, \quad \text{measured parallel to the plane} \quad 3x + 2y - 2z + 15 = 0, \] is

The angle between the lines \[ \frac{x-1}{1} = \frac{y+1}{2} = \frac{z-3}{-1}, \quad \frac{x-1}{2} = \frac{y-3}{3} = \frac{z-1}{4}, \] where \( l, m, n \) are roots of the equation \[ x^2 + x^2 - 4x - 4 = 0, \] is

If \( I(\theta) = \cos \theta_1 \cos \theta_2 \cos \theta_3 \dots \cos \theta_n \), then \[ \tan \theta_1 + \tan \theta_2 + \tan \theta_3 + \cdots + \tan \theta_n = ? \]

Evaluate the limit: \[ \lim_{n \to \infty} \left[ \frac{1}{1 - \pi} + \frac{8}{1 + \pi} + \cdots + \frac{x^2}{n\pi} \right]. \]

The correct simplified circuit diagram for the logical statement \[ \left[ (q \land ( \sim q \lor r)) \land (\sim p \lor (p \land r)) \right] \] is

If \( n^+ C_{n+1} - n^3 C_n = 15(n + 2) \), then \( n = \)

In a triangle ABC, with usual notations, \[ \tan \left( \frac{A}{4} \right) = \frac{5}{6}, \quad \tan \left( \frac{C}{2} \right) = \frac{2}{5}, \] then

If \( \{ (p \land \sim q) \land (p \land r) \} \rightarrow (p \lor q) \) has truth value false, then truth values of the statements \( p, q, r \) are respectively

Evaluate the integral \[ \int_0^{\pi/2} \frac{\cos^2 x \sin^2 x}{\cos^2 x + \sin^2 x} \, dx. \]