List of top Questions asked in MHT CET

A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes $(\frac{1}{4})^{th}$ of the original in time ?t? and ?n? revolutions are made in that lime. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three heats. The length of open pipe is made $\frac{1}{2}^{nd}$ and closed pipe is made three times the original, the number of beats produced will be

A lift of mass $m$ is connected to a rope which is moving upward with maximum acceleration $a$. For maximum safe stress, the elastic limit of the rope, is $T$. The minimum diameter of the rope is (g = gravitational acceleration)

The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $V$ is the velocity of sound and $n$ is the frequency emitted by the source then the difference between apparent frequencies heard by the observer is

Identify the weakest oxidising agent among the following.

Aldehydes or ketones when treated with $\ce{C_6H_5 - NH - NH_2}$, the product formed is

If the function \[ f(x) = \begin{cases} [ tan (\frac {\pi}{4}+x)]^{1/x} & \quad for\, x \neq 0\\ K \,\,\,\,\,\,\,\,\,\text{if } x =0 \end{cases} \] is continuous at $x = 0$, then $K = ?$

The objective function of $LPP$ defined over the convex set attains its optimum value at

A molecule of Stachyose contains how many carbon atoms ?

A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is

If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $

Two spherical black bodies have radii $?r_1?$ and $'r_2'$ . Their surface temperatures are $'T_1'$ and $'T_2'$. If they radiate same power then $\frac{r_2}{r_1}$ is

The area of the region bounded by the lines $y = 2x + 1, y = 3x + 1$ and $x = 4$ is

Which of the following statements is INCORRECT in case of Hofmann bromamide degradation ?

Solubility of which among the following solids in water changes slightly with temperature ?

Which of following coordinate complexes is an exception to $EAN$ rule ? (Given At. No. Pt = 78, Fe = 26, Zn = 30, Cu = 29)

The equation of the plane through $(-1, 1 , 2 ) $ whose normal makes equal acute angles with co-ordinate axes is

If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $

If $c$ denotes the contradiction then dual of the compound statement $\sim p \wedge ( q \vee c)$ is

If vector $\vec{r}$ with d.c.s. $l, m, n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is

The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is

The value of $\cos^{-1} \left(\cot\left(\frac{\pi}{2}\right)\right) + \cos^{-1} \left(\sin\left(\frac{2\pi}{3}\right)\right) $ is

$\int^1_0 x \, \tan^{-1} x\,dx = $

The maximum value of $f(x) = \frac{\log \, x }{x} (x \neq 0 , x \neq 1)$ is

The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point