A projectile can have the same range \(R\) for two angles of projection. If \(t_1\) and \(t_2\) be the times of flight in two cases, then their product

A region contains a uniform electric field \(\mathbf{E}=(10 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}) \mathrm{Vm}^{-1} . A\) and \(B\) are two points in the field at \((1,2,0) \mathrm{m}\) and \((2,1,3) \mathrm{m}\), respectively. The work done when a charge of \(0.8 \mathrm{C}\) moves from \(A\) to \(B\) in a parabolic path is

A proton of velocity a \((3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-1}\) enters field of magnetic induction \((2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})\) tesla, the acceleration produced in the proton in \(\mathrm{ms}^{-2}\) is \(\left(\right.\) Specific charge of proton \(=0.96 \times 10^8 \mathrm{Ckg}^{-1}\) )

A crystal of intrinsic silicon at room temperature has a carrier concentration of \(1.6 \times 10^{16} / \mathrm{m}^3\). If the donor concentration level is \(4.8 \times 10^{20} / \mathrm{m}^3\), then the concentration of holes in the semiconductor is

In a region, the intensity of an electric field is given by \(\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}) \mathrm{NC}^{-1}\). The electric flux through a surface of area \(10 \hat{\mathrm{i}} \mathrm{m}^2\) in the region is

Identify the incorrect statement regarding Reynold's number $\left(R_e\right):$

A rubber cube of side $5 \mathrm{cm}$ has one face fixed while a tangential force $1800 \mathrm{N}$ is applied on its opposite face. If modulus of rigidity of rubber is $2.4\times {10}^6 \mathrm{N} {\mathrm{m}}^{-2}$, then the lateral displacement of the strained face is______.

Identify the correct statements from the following:
i. In the extraction of \(\mathrm{Ag}\) and \(\mathrm{Au}\), zinc is used as reducing agent.
ii. Impure zinc can be refined by distillation method.
iii. Malachite is an ore of nickel.

If \(A=\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]\) is expressed as a sun of a symmetric matrix \(\mathrm{P}\) and skew symmetric matrix \(\mathrm{Q}\), then \(\mathrm{P}^{\mathrm{T}}-\mathrm{Q}^{\mathrm{T}}=\)

If \(A\) and \(B\) are two events of a random experiment such that \(P(A)=0.6, P(B)=0.3\) and \(P(A \mid B)=0.5\) then \(P(\bar{B} \mid \bar{A})=\)

Glucose + ? ____ Sucrose

The correct decreasing order of priority for the functional group of organic compounds in the IUPAC method of nomenclature is

Let ' \(\mathrm{O}\) ' be the origin, \(\mathrm{A}\) and \(\mathrm{B}\) be two points with position vectors \(-3 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(4 \hat{i}-4 \hat{j}-3 \hat{k}\) respectively. Let \(P\) be a point such that the line drawn through \(P\) parallel to \(\overrightarrow{\mathrm{OB}}\) meets \(\mathrm{OA}\) in \(\mathrm{L}\) and another line through \(\mathrm{P}\) parallel to \(\overrightarrow{\mathrm{OA}}\) meets \(\mathrm{OB}\) in \(\mathrm{M}\). If \(\mathrm{L}\) divides \(\mathrm{OA}\) in the ratio \(2: 3\) and \(\mathrm{M}\) divides \(\mathrm{OB}\) in the ratio \(3: 2\), then the distance from 0 to \(\mathrm{P}\) is