$A$ $500 \ kg$ car takes a round turn of radius $50 \ m$ with a velocity of $36 \ km/h$. The centripetal force acting on the car is (in $N$)

If $\operatorname{cosec} \theta = \frac{p+q}{p-q}$,then $\cot \left(\frac{\pi}{4} + \frac{\theta}{2}\right)$ is equal to

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number,then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$,$\lambda \vec{b}+4 \vec{c}$,and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

$1+\frac{2}{4}+\frac{2 \cdot 5}{4 \cdot 8}+\frac{2 \cdot 5 \cdot 8}{4 \cdot 8 \cdot 12}+\frac{2 \cdot 5 \cdot 8 \cdot 11}{4 \cdot 8 \cdot 12 \cdot 16}+\ldots \ldots$ is equal to :

Which of the following cannot be used in Friedel-Crafts reactions?

The major product of the following reaction is: