The locus represented by the complex equation $$ \left| z-2-i \right|=\left| z \right|\,sin\left( \cfrac{\pi }{4}-\arg z \right) $$ is the part of

1) A circle
2) A parabola
3) A pair of straight lines
4) A rectangle hyperbola

An elevator weighing 6000 kg is pulled upward by a cable with an acceleration of  5ms^-2 . Taking g to be 10ms-2 , then the tension in the cable is  

1)  6000 N    2)  9000 N    3)  60000 N    4) 90000 N

An organic compound A upon reacting with NH₃ gives B . On heating , B gives C . C in the presence of KOH reacts with Br₂ to give CH₃CH₂NH₂.  A is

f(x) = ?x−1?+?x−3? then f′(2)=

1) ?−2? .
2) 2
3) 0
4) 1
.

Let f be a non-negative function defined on the interval [0,1] .If $$\int_0^x \sqrt{1-(f'(t))^2} dt = \int _0^x f(t) dt, 0 \leq x \leq 2,$$ and $$f(0) =0$$ then,

1) $$f\left(\frac{1}{2} \right) < \frac{1}{2} $$ and $$f\left( \frac{1}{3} \right) > \frac{1}{3}$$
2) $$f\left(\frac{1}{2} \right) > \frac{1}{2} $$ and $$f\left( \frac{1}{3} \right) > \frac{1}{3}$$
3) $$f\left(\frac{1}{2} \right) < \frac{1}{2} $$ and $$f\left( \frac{1}{3} \right) < \frac{1}{3}$$
4) $$f\left(\frac{1}{2} \right) > \frac{1}{2} $$ and $$f\left( \frac{1}{3} \right) < \frac{1}{3}$$

When Reactivity of Halogen atom is minimum in
 1. propyl oxide
 2. propyl chloride
 3. isopropyl chloride
 4. isopropyl bromide 
 

When 2 g of a gas A is introduced into an evacuated flask kept at 25°C, the pressure is found to be 1 atm. If 3g of another gas B is then added to the same flask, the pressure becomes 1.5 atm. Assuming ideal gas behavior, find the ratio of molecular masses MA : MB.

Select one:

1) 1?2
2) 3?1 
3) 2?1
4) 1?3

A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If μ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is

 A 60W light bulb emits spherical electromagnetic waves uniformly in all directions. If 50 percent of the power input to such a light bulb is emitted as electromagnetic radiation, what is the radiation intensity at a distance of 2:00m from the light bulb?

1) 4:8W/m²

2) 1:2W/m²  

3) 2:4W/m²

4) 0.6W/m²  

Calculate volume of the gases liberated at STP if 1 L of 0.2 molar solution of CuSO4 is electrolysed by 5.79 A current for 10000 seconds.

1)  5.6 L
2)  2.56 L
3)  50.6 L.
4)  none