A block of mass \(5\,kg\) starting from rest pulled up on a smooth incline plane making an angle of \(30^{\circ}\) with horizontal with an affective acceleration of \(1\,ms ^{-2}\). The 10.Power delivered by the pulling force at \(t =10\,s\) from the start is \(.....\,W.\) \(\left[\right.\) Use \(\left.g =10\,ms ^{-2}\right]\) (calculate the nearest integer value)  

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

Name the logic gate equivalent to the diagram attached

In the circuit shown, current (in \(A\)) through \(50\; V\) and \(30\; V\) batteries are, respectively

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density \(d.\) The area of the base of both vessels is \(S\) but the height of liquid in one vessel is \(x_{1}\) and in the other, \(x_{2}\). When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is

The horizontal component of earth's magnetic field at a place is \(3.5 \times 10^{-5} \mathrm{~T}\). A very long straight conductor carrying current of \(\sqrt{2} A\) in the direction from South east to North West is placed. The force per unit length experienced by the conductor is _______ \(\times 10^{-6} \mathrm{~N} / \mathrm{m}\).

When a resistance of \(5\,\Omega\) is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of \(250\,mA\), however when \(1050\,\Omega\) resistance is connected with it in series, it gives full scale deflection for \(25\) volt. The resistance of galvanometer is \(......\,\Omega\).

A concave mirror for face viewing has focal length of \(0.4\,m.\) The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is......\(m\)

The value of \( \frac{^{100}C_{50}}{51} + \frac{^{100}C_{51}}{52} + \dots + \frac{^{100}C_{100}}{101} \) is:

If both the means and the standard deviation of \(50\) observations \(x_1, x_2, ………, x_{50}\) are equal to \(16\) , then the mean of \((x_1 - 4)^2, (x_2 - 4)^2, …., (x_{50} - 4)^2\) is

The resistance per centimeter of a meter bridge wire is \(\mathrm{r}\), with \(\mathrm{X}\  \Omega\) resistance in left gap. Balancing length from left end is at \(40 \mathrm{~cm}\) with \(25\  \Omega\) resistance in right gap. Now the wire is replaced by another wire of \(2 \mathrm{r}\) resistance per centimeter. The new balancing length for same settings will be at _______.

Let \(\vec a,\,\vec b,\) and \(\vec c\) be three unit vectors, out of which vectors \(\vec b\) and \(\vec c\) are non-parallel. If \(\alpha \) and \(\beta \) are the angles which vector \(\vec a\) makes with vectors \(\vec b\) and \(\vec c\) respectively and \(\vec a\,\, \times \,\,(\vec b\,\, \times \,\,\vec c)\,\, = \,\,\frac{1}{2}\,\,\vec b,\) then \(\left| {\alpha  - \beta } \right|\) is equal to .............. \(^o\)

Dimensions of universal gravitational constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are _______.