If the percentage errors in measuring the length and the diameter of a wire are \(0.1 \%\) each. The percentage error in measuring its resistance will be _______.

For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})\), \(\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0\), them value of \(\mathrm{x}\) is _______.

A uniform rod of mass m and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _________.(g acceleration due to gravity)

Two particles, of masses \(M\) and \(2M\), moving as shown, with speeds of \(10\, m/s\) and \(5\, m/s\), collide elastically at the origin. After the collision, they move along the indicated directions with speeds \(v_1\) and \(v_2\) respectively. The value of \(v_1\) and \(v_2\) are nearly

A point charge of \(+\,12 \,\mu C\) is at a distance \(6 \,cm\) vertically above the centre of a square of side \(12\, cm\) as shown in figure. The magnitude of the electric flux through the square will be ....... \(\times 10^{3} \,Nm ^{2} / C\)

In the experiment of \(Ohm's law,\) a potential difference of \(5.0\, V\) is applied across the end of a conductor of length \(10.0\, cm\) and diameter of \(5.00\, mm .\) The measured current in the conductor is \(2.00\, A\). The maximum permissible percentage error in the resistivity of the conductor is

In an experiment of determine the Young's modulus of wire of a length exactly \(1\; m\), the extension in the length of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.02\,mm\) when a load of \(1\,kg\) is applied. The diameter of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.01\,mm\). The error in the measurement of Young's modulus \((\Delta Y)\) is found to be \(x \times 10^{10}\,Nm ^{-2}\). The value of \(x\) is \(\left[\right.\) Take \(\left.g =10\,m / s ^{2}\right]\)

Two circuit are shown in the figure \((a)\) and \((b).\) At a frequency of \(....\,rad/s\) the average power dissipated in one cycle will be same in both the circuits.

By what percentage will the illumination of the lamp decrease if the current drops by \(20 \%\) ?

A body of mass \(2\, kg\) is driven by an engine delivering a constant 10.Power \(1\, J / s\). The body starts from rest and moves in a straight line. After \(9\) seconds, the body has moved a distance (in \(m )\)

The maximum speed of a boat in still water is \(27 \mathrm{~km} / \mathrm{h}\). Now this boat is moving downstream in a river flowing at \(9 \mathrm{~km} / \mathrm{h}\). A man in the boat throws a ball vertically upwards with speed of \(10 \mathrm{~m} / \mathrm{s}\). Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))