Let $f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule,$\int_0^2 f(x) dx$ is equal to

Which of the following has a cup-shaped thalamus?

Assertion $(A)$: Cyclohexane is the most stable cycloalkane.
Reason $(R)$: Cyclopropane and cyclobutane are less stable due to angle strain and torsional strain.
The correct answer is:

$\frac{\sin \theta}{1 - \cot \theta} + \frac{\cos \theta}{1 - \tan \theta} = $

The direction ratios of the normal to the plane passing through $(0,0,1)$, $(0,1,2)$, and $(1,0,3)$ are

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is: