List of top Mathematics Questions asked in MHT CET

Maximize \( z = x + y \) subject to: \[ x + y \leq 10, \quad 3y - 2x \leq 15, \quad x \leq 6, \quad x, y \geq 0. \] Find the maximum value.
Using the rules in logic, write the negation of the following: \[ (p q) \land (q \lor \sim r) \]
A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:
The integral \( \int \frac{\csc x}{\cos^2\left(1 + \log \tan \frac{x}{2}\right)} \, dx \) is equal to:
The value of \( \sqrt{3} \csc 20^\circ - \sec 20^\circ \) is:

The radius of a cylinder is increasing at the rate 2 cm/sec and its height is decreasing at the rate 3 cm/sec, then find the rate of change of volume when the radius is 3cm and the height is 5 cm.

If x = 3 tan t and y = 3 sec t, then find \(\frac{d^2y}{dx^2} \, at\,t=\frac{\pi}{4}\), is:

Find ∑(x-xi)2=100, no. of observations = 20, ∑xi=20.

Find ∫(cos√x) dx=?

Two lines \(2x=3y=-z\) and \(6z=-y=-4z\) intersect at a point, then find the angle between them.
If \(A=\begin{bmatrix} 2a & -3b\\ 3 & 2\end{bmatrix}\) and \(\text{adj}A = AA^T\), then 2a+3b is?

The sum of mean and variance of a given set is 15/2 and their number of trials is 10, then find the value of variance?

Area of the Region bounded by the curve y=√49-x2 and x-axis is .

In a certain culture of bacteria the rate of increase is proportional to the no.of bacteria present at that instant it is found that there are 10000 bacteria present in 3 hours and 40000 bacteria at the 5 hours the number of bacteria present in the beginning is?

Ki are possible values of K for which lines \(Kx + 2y + 2 = 0\), \(2x + Ky + 3 = 0\), \(3x + 3y + K = 0\) are concurrent, then \(∑k_i\) has value.
The solution of ey-x dy/dx = y(sinx + cosx)/(1 + ylogy)
The negation of inverse of the statement \((p \wedge q)→(p\vee\sim q)\)
Find k if \(\int_{0}^{\frac{1}{2}}[\frac{x^2dx}{(1-x^2)^{\frac{3}{2}}}]=\frac{k}{6}\).

∫ (x2 - 1)dx/(x3(2x4 - 2x2 1)1/2) = ?

The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is? 
 
If \(\int_0^{\pi/2} \log(\cos x) \, dx = \frac{\pi}{2} \log\left(\frac{1}{2}\right)\), then find \(\int_0^{\pi/2} \log(\sec x) \, dx\).

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

If \(X\sim(5,p)\) \(P(X=3) = 5P(X=4)\), find variance.

\(\int \frac{1}{\cos^3 x \sqrt{\sin 2x}} \, dx\)

\( \int \left( \frac{1}{7} - 6x - x^2 \right) \, dx \)