List of top Questions asked in MHT CET

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).
Which of the following shows maximum hydrogen bonding?
A particle in SHM has a speed of \(6\,cm/s\) at the mean position and an amplitude of \(4\,cm\). Find its position when its velocity is \(2\,cm/s\).
Evaluate: \(\tan^{-1}(1) + \tan^{-1}(4) + \tan^{-1}(5) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\). Find the value of \(\alpha\).
The normal value of Tidal Volume (TV) in a healthy adult is approximately:
A particle moves with a constant velocity of \(5\ \text{m/s}\) in a circular path of radius \(2\ \text{m}\); calculate its centripetal acceleration.
A train moving at 20 m/s approaches a stationary observer. The frequency of the whistle emitted by the train is 640 Hz. If the velocity of sound is 340 m/s, the apparent frequency heard by the observer is:
The process during double fertilization in which non motile male gametes are carried through hollow pollen tube is called
What is the primary site of sperm production?
Name the phenomenon that proves the transverse nature of light.
The term used for species in which the last individual has died or is not recorded is
Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).
Which transition element among the following shows the highest number of oxidation states?
Eight identical spherical liquid drops, each falling with a terminal velocity $v$, coalesce to form a single large drop. The terminal velocity of the new large drop is:
For a weak base of concentration \(C\) and degree of dissociation \(\alpha\), what is the correct relation between \(K_b\) and \(C\)?
Evaluate the integral: \(\int \frac{x}{x + 2} \, dx\).
Outer layer of microspore is made up of:
In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the number of bacteria present in the beginning are:
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its centre and perpendicular to its length is:
Find the energy of a photon with a wavelength of \(4000\,\text{\AA}\). (Take \( h = 6.63 \times 10^{-34}\,\text{Js} \), \( c = 3 \times 10^8\,\text{m/s} \)).
Evaluate the integral: \( \displaystyle \int \frac{x}{x+2}\,dx \)
Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).
If a polygon has 54 diagonals, find the number of sides of the polygon.
Where is sperm produced?
Which hormone is primarily responsible for the relaxation of pelvic ligaments during childbirth?