The acceleration due to gravity at a height of \((\sqrt{2}-1) \mathrm{R}\) from the surface of the earth is
(Acceleration due to gravity on the surface of the earth \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) and R is radius of the earth)

A force \(\overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}-15 \hat{\mathrm{j}} \mathrm{N}\), acts on a body resulting in a displacement of \(6 \hat{i}\). If the body had a kinetic energy of 7 joules at the beginning of the displacement, the kinetic energy at the end of the displacement is

Water stands upto height \(h\) behind the dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. Density of water is \(\rho\) and acceleration due to gravity is \(g\). If atmospheric pressure force is also considered, then the point of application of total force acting on the dam due to water above \(O\) is

Kepler's second law (law of areas) is nothing but a statement of

Figure shows an equilateral triangle \(A B C\) of side ' \(l\) ' carrying currents as shown and placed in a uniform magnetic field ' \(B\) ' perpendicular to the plane of triangle. The magnitude of magnetic forces on triangle is

A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has speed of \(54 \mathrm{kmh}^{-1}\) while the other has the speed of \(36 \mathrm{kmh}^{-1}\). The bird starts moving from first car towards
the other and is moving with the speed of \(36 \mathrm{kmh}^{-1}\) where the two cars were separated by \(36 \mathrm{~km}\). The total distance covered by the bird before the cars meet each other is

The transition of an electron in hydrogen atom that emits a photon whose wavelength lies in the ultraviolet region of the electromagnetic spectrum is

Which of the following is not an example of allylic halide?

As shown in the figure, two infinitely long straight parallel wires \(P\) and \(Q\) carrying equal currents in opposite directions are arranged parallel to \(\mathrm{Y}\)-axis. If the magnetic field due to wire \(\mathrm{P}\) at the origin ' \(\mathrm{O}\) ' of the co-ordinate system is B, then match the resultant magnetic fields at various points given in column \(A\) with the points given in column \(B\).
\(\begin{array}{ll}
\text{Column A} & \text{Column B} \\
\text{A)} \frac{B}{4} & \text{i)} (0,0) \\
\text{B)} \frac{B}{2} & \text{ii)} (a, 0) \\
\text{C)} \frac{2 \mathrm{~B}}{3} & \text{iii)} (2a, 0) \\
\text{D)} 2 \mathrm{~B} & \text{iv)} (3 \mathrm{a}, 0) \\
\end{array}\)


The correct answer is

If \(l, m, n\) are the direction cosines of a line that is perpendicular to the lines having the direction ratios \(1,2,-1\) and \(1,-2,1\) then \((l+m+n)^2=\)

A capacitor of capacitance \(2 \mu \mathrm{~F}\) is charged with the help of a 60 V battery. After disconnecting the battery, if this capacitor is connected in parallel with another uncharged capacitor of capacitance \(1 \mu \mathrm{~F}\), then the potential difference across the plates of \(2 \mu \mathrm{~F}\) capacitor is

The changes in bond length with respect to \(\mathrm{N}-\mathrm{N}\) and \(\mathrm{O}-\mathrm{O}\), when \(\mathrm{N}_2\) becomes \(\mathrm{N}_2^{+}\)and \(\mathrm{O}_2\) becomes \(\mathrm{O}_2^{+}\)are respectively

\(\int \frac{2 t+1}{t^2+t+1} d t=\)