List of top Mathematics Questions asked in MHT CET

The probability that a person wins a prize on a lottery ticket is \( \frac{1}{4} \). If he purchases 5 lottery tickets at random, then the probability that he wins at least one prize is

If the vectors \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar, then \( \dfrac{\left| \vec{a} + 2\vec{b} \;\; \vec{b} + 2\vec{c} \;\; \vec{c} + 2\vec{a} \right|} {\left| \vec{a} \;\; \vec{b} \;\; \vec{c} \right|} \) is

The joint equation of a pair of lines passing through \((2,3)\) and parallel to the lines \[ x^2 - y^2 = 0 \] is

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

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

The approximate value of the function \( f(x) = x^3 + 5x^2 - 7x + 10 \) at \( x = 1 \) is

If \[ \tan u = \frac{\sqrt{1 - x}}{\sqrt{1 + x}}, \quad \cos v = 4x^3 - 3x, \quad \text{then} \quad \frac{du}{dv} = \text{?}

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

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

If \( f(x) = \frac{|x|}{x} \) for \( x \neq 0 \) and \( f(x) = 1 \) for \( x = 0 \), then the function is

The volume of a tetrahedron whose vertices are \( A = (-1, 2, 3) \), \( B = (3, -2, 1) \), \( C = (2, 1, 3) \), and \( D = (-1, -2, 4) \) is

If $f(x)=\dfrac{4\sin \pi x}{5x}$ for $x\neq 0$ and $f(x)=2k$ for $x=0$, and $f(x)$ is continuous at $x=0$, then the value of $k$ is

With usual notations in \( \triangle ABC \), if \( C = 90^\circ \), then \( \tan^{-1}\left(\dfrac{a}{b+c}\right) + \tan^{-1}\left(\dfrac{b}{c+a}\right) \) is

If the planes \[ 2x - 5y + z = 8 \quad \text{and} \quad 2 \lambda x - 15y + 2z + 6 = 0 \] are parallel to each other, then the value of \( \lambda \) is

If line \( x + y = 0 \) touches the curve \( ax^2 = 2y^2 - b \) at \( (1, -1) \), then the values of \( a \) and \( b \) are respectively

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

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

The differential equation whose solution is \( y = c_1 \cos ax + c_2 \sin ax \) (where \( c_1 \) and \( c_2 \) are arbitrary constants) is

Evaluate \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{\tan x}{\tan x + \cot x} \, dx \]

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

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

ABCD is a parallelogram. \(P\) is the midpoint of \(AB\). If \(R\) is the point of intersection of \(AC\) and \(DP\), then \(R\) divides \(AC\) internally in the ratio

The length of the latus rectum of the parabola \( x^2 + 2y = 8x - 7 \) is

If \[ \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{9 + 16 \sin 2x} \, dx = k \log 3, \text{ then } k = \]

If \( x + y = \frac{\pi}{2} \), then the maximum value of \( \sin x \cdot \sin y \) is