Among the following the least unit for length is

A block of mass 10 kg moving with a speed of \(5 \hat{\mathrm{i}} \mathrm{m} \mathrm{s}^{-1}\) on a frictionless horizontal surface suddenly explodes into two pieces. If one piece with mass 4 kg moves with a speed of \(10 \hat{\mathrm{i}} \mathrm{m} \mathrm{s}^{-1}\), then the velocity of the second piece is

In a system, unit of mass is \(A \mathrm{~kg}\), length is \(B \mathrm{~m}\) and time is \(C \mathrm{~s}\), then the value of \(10 \mathrm{~N}\) in this system is

In the figure shown, \(\mathrm{AB}\) is a rod of length \(30 \mathrm{~cm}\), area of cross-section \(1 \mathrm{~cm}^2\) and thermal conductivity \(336 \mathrm{SI}\) units. The ends \(\mathrm{A}\) and \(\mathrm{B}\) are at constant temperatures \(20^{\circ} \mathrm{C}\) and \(40^{\circ} \mathrm{C}\) respectively. A point \(\mathrm{C}\) of the rod is connected to ice at \(0^{\circ} \mathrm{C}\) in a thermally insulated box \(\mathrm{D}\) through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is \(\left(\mathrm{L}_{\mathrm{ice}}=80 \mathrm{cal} \mathrm{g}^{-1}\right)\)

The temperature of the system decreases in the process of

If the cold junction is held at \(0^{\circ} \mathrm{C}\), the same thermo emf \(V\) of a thermocouple varies as \(V=10 \times 10^{-6} t-\frac{1}{40} \times 10^{-6} t^2\), where \(t\) is the temperature of the hot junction in \({ }^{\circ} \mathrm{C}\). The neutral temperature and the maximum value of thermo emf are respectively :

In \(n-p-n\) transistor, in CE configuration:
1. The emitter is heavily doped than the collector.
2. Emitter and collector can be interchanged.
3. The base region is very thin but is heavily doped.
4. The conventional current flows from base to emitter.

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 \(\mathrm{P}^{\mathrm{T}}-\mathrm{Q}^{\mathrm{T}}=\)

The energy of a photon is equal to the kinetic energy of a proton. If \(\lambda_1\) is the de-Broglie wavelength of a proton, \(\lambda_2\) the wavelength associated with the proton and if the energy of the photon is \(E\), then \(\left(\lambda_1 / \lambda_2\right)\) is proportional to

The protective power of a lyophilic colloidal sol is expressed in terms of

From the given reaction
\(2 \mathrm{KMnO}_4 +3 \mathrm{H}_2 \mathrm{SO}_4+5 \mathrm{H}_2 \mathrm{O}_2 \longrightarrow \mathrm{K}_2 \mathrm{SO}_4+2 \mathrm{MnSO}_4 +8 \mathrm{H}_2 \mathrm{O}+5 \mathrm{O}_2\)
Find the normality of \(\mathrm{H}_2 \mathrm{O}_2\) solution, if \(20 \mathrm{~mL}\) of it is required to react completely with 16 \(\mathrm{mL}\) of \(0.02 \mathrm{M} \mathrm{KMnO}_4\) solution.
\(\left(\right.\) Molar mass of \(\mathrm{KMnO}_4=158 \mathrm{~g} \mathrm{~mol}^{-1}\) )

Match the following
\(\begin{array}{llll}
& \text {List - I} & & \text {List - II} \\
\text {a)} & \text {See Saw Shape} & \text {i)} & \mathrm{XeF}_4 \\
\text {b)} & \text {Square Pyramidal} & \text {ii)} & \mathrm{CF}_3 \\
\text {c)} & \text {T-Shape} & \text {iii)} & \mathrm{PbCl}_2 \\
\text {d)} & \text{Bent Shape} & \text {iv)} & \mathrm{SF}_4 \\
& & \text {v)} & \mathrm{BrF}_5
\end{array}\)
The correct answer is

The curve \(f(x)=e^x \sin x\) is defined in the interval \([0,2 \pi]\). The value of \(x\) for which the slope of the tangent drawn to the curve at \(x\) is maximum, is