List of top Mathematics Questions asked in MHT CET

Bacteria increases at the rate proportional to the number of bacteria present. If the original number \( N \) doubles in \( 4 \) hours, then the number of bacteria will be \( 4N \) in

If \( A = \begin{pmatrix} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 0 & 3 & -5 \end{pmatrix} \) where \( A_{ij} \) is the cofactor of the element \( a_{ij} \) of matrix \( A \), then \( a_{21}A_{21} + a_{22}A_{22} + a_{23}A_{23} = \)

\( y = c^2 + \dfrac{c}{x} \) is the solution of the differential equation

The area of the region bounded by the curve \( y = \log x \), x-axis and the lines \( x = 1 \), \( x = e \) is

If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots \), then \[ \frac{dy}{dx} = \]

Evaluate the integral \( \int_0^1 \frac{x^2}{1 + x^2} dx \)

If \( \sqrt{x + y} + \sqrt{y - x} = 5 \), then \( \frac{d^2y}{dx^2} = \)

The particular solution of the differential equation \( \cos \left( \frac{dy}{dx} \right) = a \), under the conditions \( a \in \mathbb{R} \) and \( y(0) = 2 \) is

20 meters of wire is available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, then the radius of the circle is

The equation of the normal to the curve \( 2x^2 + 3y^2 - 5 = 0 \) at \( P(1, 1) \) is

If \( f(x) = x^2 - 3x + 4 \) and \( f(x) = f(2x + 1) \), then \( x = \)

The minimum value for the LPP \( Z = 6x + 2y \), subject to \( 2x + y \geq 16, x \geq 6, y \geq 1 \) is

Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink

The principal value of \( \sin^{-1} \left( -\frac{1}{2} \right) \) is

Evaluate \( 2 \tan^{-1} \left( \frac{1}{3} \right) - \tan^{-1 \left( \frac{3}{4} \right) \)}

If \( f(x) = \frac{|x - 2|}{x - 2} \) for \( x \neq 2 \), and \( f(x) = 1 \) for \( x = 2 \), then which of the following statements is true?

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

The probability distribution of a discrete r.v. \( X \) is: \[ \begin{array}{c|ccccc} X = x & 0 & 1 & 2 & 3 & 4 \\ P(X = x) & k & 2k & 4k & 2k & k \\ \end{array} \] Then, the value of \( P(X \leq 2) \) is:

If \( \frac{x}{x-y} = \log \left( \frac{a}{x-y} \right) \), then \( \frac{dy}{dx} = \)

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

Evaluate the integral: \[ \int_{-1}^{1} \left[ \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right] dx \]

The co-ordinates of the foot of the perpendicular from the point \( (0, 2, 3) \) on the line
\[ \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \]

The approximate value of \( \log_{10}99 \) is (Given \( \log_{10}e = 0.4343 \))

The maximum value of \(Z = 10x + 25y\) subject to \[ 0 \le x \le 3,\; 0 \le y \le 3,\; x + y \le 5,\; x \ge 0,\; y \ge 0 \] is

Evaluate the integral: \[ \int \frac{\sin x}{\sin\left(x-\frac{\pi}{4}\right)}\,dx \]