The velocity and acceleration vectors of a particle moving in a magnetic field are given by : \(\vec{v}=3 \hat{i}+4 \hat{j}\) and \(\vec{a}=2 \hat{i}+\hat{j}\) respectively, Then :
(A) the magnetic field is along \(z\)-direction
(B) \(v=3\)
(C) the kinetic energy of the particle is constant
(D) the acceleration is in x-z plane
(E) the particle is moving in \(x-y\) plane

In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{\pi}{3} \). If capacitor is removed from the circuit instead of inductor, the phase difference is again \( \frac{\pi}{3} \). What is the power factor of the circuit?

An electric motor is driven by d.c. supply of emf \( V_0 \) and internal resistance r. The current when output power is maximum will be

A voltage \( V = 200 \sin(400t) \) V AC source is connected to a series combination of an inductance 20 mH and resistance \( 6 \, \Omega \). The rms current in the AC circuit is:

The current sensitivity of a galvanometer increases by 10%. If its resistance also increases by 20%, the voltage sensitivity will

A series LCR circuit is connected to a 230 V, 50 rad/s source. Given L = 5 H, C = 80 \( \mu \)F and R = 40 \( \Omega \). Impedance of the circuit is

A metallic wire of uniform area of cross section has a resistance R, resistivity \(\rho\) and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity and power rating at V volts are now denoted by R', and P' respectively. The corresponding values are correctly related as __________ . Fill in the blank with the correct answer from the options given below

Arrange the following amines in increasing order of basicity in aqueous solution
(A)\(\left( CH _3\right)_2 NH\)
(B) \(CH _3 NH _2\)
(C)\(\left( CH _3\right)_3 N\)
(D) \(NH _3\)
Choose the correct answer from the options given below :

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis.
Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Animal starch is popularly known as

A displacement current of 1.0 A is established in the space between the two parallel plates of 1 \( \mu\text{F} \) capacitor. The rate of change of voltage across the capacitor is:

Potassium (K) and Rubidium (Rb) forms

The ratio of the Nuclear density of the gold isotope \(^{197}_{79}\text{Au}\) and the silver isotope \(^{107}_{47}\text{Ag}\) is :

The value of \(k\) for which the function \(f(x)=\left\{\begin{array}{ll}\frac{1-\cos 8 x}{16 x^2} & , \text { if } x \neq 0 \\ k & , \text { if } x=0\end{array}\right.\) is continuous at \(x=0\) is :