For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?
(1) $\hat j + \hat k, \hat j + \hat k $
(2) $-\hat j + \hat k, -\hat j – \hat k $
(3) $\hat j + \hat k, -\hat j – \hat k $
(4) $-\hat j + \hat k,-\hat j+\hat k $ Continue reading For a plane electromagnetic wave propagating in x-direction ….
A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let $S_n$ be the distance travelled by the block in the interval t = n-1 to t = n. Then, the ratio $\frac {S_n}{S_{n+1}}$ is:
(1) $\frac {2n-1}{2n}$
(2) $\frac {2n-1}{2n+1}$
(3) $\frac {2n+1}{2n-1}$
(4) $\frac {2n}{2n-1}$ Continue reading A small block slides down on a smooth inclined plane ….
A particle is released from height H above the ground. At a certain instant its kinetic energy is three times its potential energy. The height h above the ground and the speed of the particle v at that instant are respectively:
(1) $\frac {H}{4},\frac {3gH}{2}$
(2) $\frac {H}{4},\frac {\sqrt {3gH}}{2}$
(3) $\frac {H}{2},\frac {\sqrt {3gH}}{2}$
(4) $\frac {H}{4},\sqrt {\frac {3gH}{2}}$ Continue reading A particle is released from height H above the ground ….
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? ($g=10 m/s^2$)
(1) 10.2 kW
(2) 8.1 kW
(3) 12.3 kW
(4) 7.0 kW Continue reading Water falls from a height of 60 m at the rate of 15 kg/s ….
We have, $(x-1)^{100}+(x-2)^{200}=(x-1)(x-2)q(x)+r(x)$
Since divisor is quadratic, the remainder must be linear.
So, $r(x)=ax+b$
$(x-1)^{100}+(x-2)^{200}=(x-1)(x-2)q(x)+ax+b$
Putting $x=1$ above yields $a+b=1$
Substituting $x=2$, yields $2a+b=1$
Clearly, a=0 & b=1
So, remainder $=ax+b=1$.
A radioactive nucleus ${}_Z^AX$ undergoes spontaneous decay in the sequence ${}_Z^AX \to {}_{Z – 1}B \to {}_{Z – 3}C \to {}_{Z – 2}D$ where Z is the atomic number of element X. The possible decay particles in the sequence are:
(1) $\alpha,\beta^-.\beta^+$
(2) $\alpha,\beta^+,\beta^-$
(3) $\beta^+,\alpha,\beta^-$
(4) $\beta^-,\alpha,\beta^+$ Continue reading A radioactive nucleus ${}_Z^AX$ undergoes ….
In a potentiometer circuit, a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs?
(1) 60 cm
(2) 21.6 cm
(3) 64 cm
(4) 62 cm Continue reading In a potentiometer circuit, a cell of EMF 1.5 V ….
