$A$ particle of mass $1 \ kg$ is moving in $SHM$ with a path length of $0.01 \ m$ and frequency of $50 \ Hz$. The maximum force in newton,acting on the particle is (in $\pi^2$)

Five moles of hydrogen initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \, J/mol-K; \gamma=1.4$ for diatomic gas$)$

Phenol reacts with $CHCl_3$ and $NaOH$ at $340 \ K$ to give .......

The initial setting of cement is primarily due to which of the following?

$A$ person lives in a high-rise building at a height of $30 \, m$ on the bank of a river. Across the river is a well-lit tower of height $60 \, m$. When the person looks through a polarizer at an appropriate angle at the light from the top of the tower reflecting from the river surface,he finds the intensity of light is least. If the refractive index of water is $\frac{4}{3}$,the width of the river is......$m$.

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is