List of top Questions asked in MHT CET

Two monkeys off mass 10 kg and 8 kg are moving along a vertical light rope the former climbing up with an acceleration of 2 m/second square while the latter coming down with a uniform velocity of 2 m/sec square find the tension in the rope at the fixed support

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

The negation of inverse of the statement \((p \wedge q)→(p\vee\sim q)\)

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.

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.

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?

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

At the pure inductive stage, find e_max.

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

In which forest does average rainfall occur?

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

If at depth ‘\(d\)’ the gravitational force acting on a particle is 300 N, then what is the force on a particle at depth ‘\(\frac d2\)’ ?

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