List of top Mathematics Questions asked in MHT CET

The Cartesian equation of the curve given by \[ x = 6 \cos \theta, \quad y = 6 \sin \theta \] is

If the equation \[ x^2 - 3xy + y^2 + 3x - 5y + 2 = 0 \] represents a pair of lines, where \( \theta \) is the angle between them, then the value of \( \csc^2 \theta \) is

The line through the points \( (1, 4), (-5, 1) \) intersects the line \( 4x + 3y - 5 = 0 \) in the point

If \[ y = \tan^{-1}(\sec x + \tan x), \quad \text{then} \quad \frac{dy}{dx} = \]

If \(\displaystyle \sin\!\left(\frac{x+y}{x-y}\right) = \tan \frac{\pi}{5}\), then find \(\displaystyle \frac{dy}{dx}\).

A particle moves according to the law \( s = t^3 - 6t^2 + 9t + 25 \). The displacement of the particle at the time when its acceleration is zero is

If the population grows at the rate of \( 8% \) per year, then the time taken for the population to be doubled is \([ \log 2 = 0.6912 ]\)

If \[ A = \begin{bmatrix} 1 & 3 \\ 2 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ B^{-1} A^{-1} = \]

Given \(A = \{1,2,3,4,5\}\), \(B = \{1,4,5\}\). If \(R\) is a relation from \(A\) to \(B\) such that \((x,y) \in R\) with \(x>y\), then the range of \(R\) is

The radius of a circle is increasing at the rate of \( 2 \,\text{cm/sec} \). Find the rate at which its area is increasing when the radius of the circle is \( 5 \) decimeters.

The feasible region of the L.P.P.
\[ \text{Maximize } z = 70x + 50y \] subject to \[ 8x + 5y \le 60,\quad 4x + 5y \le 40,\quad x \ge 0,\; y \ge 0 \] is

The angle between the lines \[ \mathbf{r_1} = (i + 2j + 3k) + \lambda (i + j + 2k) \quad \text{and} \quad \mathbf{r_2} = (3i + k) + \lambda' (2i + j - k), \quad \lambda, \lambda' \in \mathbb{R} \] is

The focal distance of the point \( (4, 4) \) on the parabola with vertex at \( (0, 0) \) and symmetric about the y-axis is

Evaluate the integral \( \displaystyle \int \frac{e^x}{\sqrt{x}}(1+2x)\,dx \)

If \[ p \rightarrow \left( \sim p \vee q \right) \text{ is false, then the truth values of } p \text{ and } q \text{ are respectively} \]

In a triangle ABC, if \[ \frac{\sin A - \sin C}{\cos C - \cos A} = \cot B, \text{ then A, B, C are in} \]

The odds in favour of drawing a king from a pack of 52 playing cards is

A plane \( E_1 \) makes intercepts \( 1, -3, 4 \) on the coordinate axes. The equation of a plane parallel to \( E_1 \) and passing through \( (2,6,-8) \) is

If \( f(x) = e^{x}g(x) \), \( g(0) = 4 \), and \( g'(0) = 2 \), then \( f'(0) = \)

Evaluate the integral \( \int \frac{4e^x + 6e^{-x}}{9e^x - 4e^{-x}} dx = Ax + B \log |9e^{2x} - 4| + c \), then (where \( c \) is the constant of integration)

The p.d.f. of a continuous random variable \( X \) is given by \[ f(x) = \frac{x + 2}{18}, \quad \text{if} \, -2<x<4, \quad f(x) = 0, \, \text{otherwise}. \] Then \( P[ |x|<1 ] = \)

If the p.m.f. of a random variable \( X \) is \[ \begin{array}{|c|c|c|c|c|} X & 1 & 2 & 3 & 4 & 5
P(X = x) & k & \frac{k}{3} & \frac{k}{4} & \frac{k}{2} & \end{array} \] then \( k = \)

Evaluate \( \int \frac{x^2}{(x+1)^2(x+2)^2} \, dx \)

Evaluate the integral \[ \int \frac{\sec x}{\sqrt{\log(\sec x + \tan x)}}\, dx \]

The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is