For Maximum no. Of vectors required to make the resultant zero can be upto infinity . And the minimum no. of unequal vectors required to do so is 3

Ans:- (B) principle of superstition Gravitation force is a central force so to find net force we can add different forces on the object with the help of superposition principle

To achieve a current of 2A in phase with the supply voltage, the impedance of the series combination of the capacitor and resistor must be equal to the resistance of the load. The impedance of the capacitor is given by: Zc = 1/(jωC) where j is the imaginary unit, ω is the angular frequency (2πf), and C is the capacitance in farads. Substituting the given values, we get: Zc = 1/(j(2π50)(25π^2×10^-6)) Zc = -j12.73 kΩ where the negative sign indicates a phase shift of -90 degrees. The impedance of the resistor is simply its resistance, which is 50Ω. To find the value of the additional component/s to be connected in series with C and R, we need to find the impedance that will make the total impedance equal to 50Ω at 0 degrees phase angle. Let's call this impedance Zx. Then: Ztotal = Zc + R + Zx = 50∠0° Substituting the values of Zc and R, we get: Zx = 50∠0° - (-j12.73 kΩ) - 50Ω Zx = (50 + j12.73) kΩ Therefore, the additional component to be connected in series with C and R is a capacitor with a capacitance of: Cx = 1/(2πfZx) = 1/(2π×50×(50 + j12.73)×10^3) = 0.181μF And a phase angle of: θx = -90° - arctan(12.73/50) = -110.53° Alternatively, the additional component could be an inductor with an inductance of: Lx = Zx/(2πf) = (50 + j12.73)×10^3/(2π×50) = 1.273H And a phase angle of: θx = 90° - arctan(12.73/50) = 69.47° Both options would result in a total impedance of 50Ω at 0 degrees phase angle, which would allow a current of 2A in phase with the supply voltage.

P(total) = 100 W

A speed multiplier is a device used to increase the speed of a machine or system. An example of a speed multiplier is a gearbox, which is commonly used in automobiles to increase the speed of the wheels relative to the engine. For example, if an automobile has an engine that rotates at 3000 revolutions per minute (RPM) and the wheels have a diameter of 24 inches, the car would have a maximum speed of around 45 miles per hour. However, by using a gearbox with a speed multiplier of 3, the wheels can rotate at 9000 RPM, which would increase the car's maximum speed to around 135 miles per hour. Another example of a speed multiplier is a turbocharger, which is commonly used in high-performance engines to increase the amount of air that can be delivered to the engine, allowing it to produce more power. The turbocharger uses exhaust gas to drive a turbine, which in turn drives a compressor that compresses the air going into the engine. This increases the air density and allows more fuel to be burned, resulting in a higher output power. The speed of the turbine can be many times higher than the engine speed, which effectively acts as a speed multiplier for the compressor.

Ans:       Please refer to the attached file

The factors affecting Brownian movemt are the temperature of the system, size of the particles, number of particles present in the system and also the viscosity.

The average speed of a body may be given as the total distance travelled by the body by the total time taken by it. It is a scalar quantity.

Use simple distance/time formula, but since sound goes and come back in echo so we take double distance.

Since R1=R2(same resistance) so the total current will divide equally in each branch, hence use 10th class combination formula to find total current and divide it by2( short trick for competition)