Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Let z_{1}\: and \: z_{2}  be two roots of the equation z^{2}+az+b=0,z being complex further, assume that the origin ,z_{1}\: and \: z_{2}  form an equilateral triangle then

  • Option 1)

    a^{2}= 2b

  • Option 2)

    a^{2}= 3b

  • Option 3)

    a^{2}= 4b

  • Option 4)

    a^{2}= b

 

The locus of the centre of a circle which touches the circle \left | z-z_{1} \right |= a\: and \: \left | z-z_{2} \right |= b externally

\dpi{100} \left ( z,z_{1},z_{2}\: are \: complex\: number\: \right ) will be

  • Option 1)

    an ellipse

  • Option 2)

    a hyperbola

  • Option 3)

    a circle

  • Option 4)

    none of these

 

The number of complex numbers z such that

\left | z-1 \right |= \left | z+1 \right |= \left | z-i \right | equals

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    \infty

 

The point represented by 2+i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there
2\sqrt{2} units in the south-westwards direction.  Then its new position in the Argand plane is at the point represented by

  • Option 1)

     2+2i

  • Option 2)

    1 + i

  • Option 3)

    −1− i

  • Option 4)

    −2−2 i

 

The largest value of r for which the region represented by the set   \left \{ w\epsilon C/\left | w-4-i \right |\leq r \right \}      

is contained in the region represented by the set \left \{ z\epsilon C/\left | z-1 \right |\leq\left | z+i \right | \right \}  is equal to:

  • Option 1)

    \sqrt{17}

  • Option 2)

    2\sqrt{2}

  • Option 3)

    \frac{3}{2}\sqrt{2}

  • Option 4)

    \frac{5}{2}\sqrt{2}

 

CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following expressions is correct ?

  • Option 1)

    r_{Cs^{+}}+r_{CI^{-}}=3a

  • Option 2)

    r_{Cs^{+}}+r_{CI^{-}}=\frac{3a}{2}

  • Option 3)

    r_{Cs^{+}}+r_{CI^{-}}=\frac{\sqrt{3}}{2}a\;

  • Option 4)

    r_{Cs^{+}}+r_{CI^{-}}=\sqrt{3}a

 

 A ball of mass 160 g is thrown up at an angle of 600 to the horizontal at a speed of 10 ms-1. The angular momentum of the ball at the highest point of the trajectory  with respect to the point from which the .ball is thrown is nearly (g=10 ms-2)                

 

  • Option 1)

    1.73 kg m2/s

  • Option 2)

    3.0 kg m2/s

  • Option 3)

    3.46 kg m2/s

  • Option 4)

    6.0 kg m2/s

 

 Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out  from  under  it  with  acceleration  ‘a’ perpendicular to the axis of the cylinder.  What is Ffriction at point P ? It is assumed that the cylinder does not slip.         

                      

 

  • Option 1) Mg

     

  • Option 2) Ma

     

  • Option 3) Ma/2

     

  • Option 4) Ma/3

     

 

A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed \omega rad/s about the vertical. About the point of suspension :

 

  • Option 1)

    angular momentum is conserved.

  • Option 2)

    angular momentum changes in magnitude but not in direction.

  • Option 3)

    angular momentum changes in direction but not in magnitude.

  • Option 4)

     angular momentum changes both in direction and magnitude.

 

A hoop of radius r and mass m rotating with an angular velocity \omega _{0}  is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velociy of the centre of the hoop when it ceases to slip ?

 

 

  • Option 1)

    r\omega _{0}\;

  • Option 2)

    \frac{r\omega _{0}}{4}

  • Option 3)

    \frac{r\omega _{0}}{3}

  • Option 4)

    \frac{r\omega _{0}}{2}

 

A thin bar of length L has a mass per unit  length\lambda, that increases linearly with distance from one end.If its total mass is M and its mass per unit length at the lighter end is \lambda _{0}, then the distance of the centre of mass from the lighter end is :

  • Option 1)

    \frac{L}{2}-\frac{\lambda _{0}L^{2}}{4M}

  • Option 2)

    \frac{L}{3}+\frac{\lambda _{0}L^{2}}{8M}

  • Option 3)

    \frac{L}{3}+\frac{\lambda _{0}L^{2}}{4M}

  • Option 4)

    \frac{2L}{3}-\frac{\lambda _{0}L^{2}}{6M}

 

 An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now ?

(Atmospheric pressure =76 cm of Hg)

  • Option 1)

    16 cm

  • Option 2)

    22 cm

  • Option 3)

    38 cm

  • Option 4)

    6 cm

 

 Water is flowing at a speed of 1.5 ms-1 through a horizontal tube of cross-sectional area 10-2 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water=103 kgm-3).

 

  • Option 1)

    15 N

  • Option 2)

    22.5 N

  • Option 3)

    33.7

  • Option 4)

    45 N

 

The figure shows a system of two concentric spheres of radii r_{1}\: and\: r_{2} and kept at temperatures T_{1}\: and\: T_{2} respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

  • Option 1)

    \frac{r_{1}r_{2}}{\left ( r_{2}-r_{1} \right )}

  • Option 2)

    \left ( r_{2}-r_{1} \right )

  • Option 3)

    \frac{\left ( r_{2}-r_{1} \right )}{r_{1}r_{2}}

  • Option 4)

    \ln \left ( \frac{r_{2}}{r_{1}} \right )

 

A cylindrical vessel of cross-section A contains water to a height h.There is a hole in the bottom of radius 'a'.The time in which it will be emptied is :

  • Option 1)

    \frac{2A}{\pi a^{2}}\sqrt{\frac{h}{g}}

  • Option 2)

    \frac{\sqrt{2}A}{\pi a^{2}}\sqrt{\frac{h}{g}}

  • Option 3)

    \frac{2\sqrt{2}A}{\pi a^{2}}\sqrt{\frac{h}{g}}

  • Option 4)

    \frac{A}{\sqrt{2}\pi a^{2}}\sqrt{\frac{h}{g}}

 

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3 m and that of kerosene 2 m. When the hole is opened the velocity of fluid coming out from it is nearly : (take g=10 ms-2 and density of water =103 kg m-3)

  • Option 1)

    10.7 ms-1

  • Option 2)

    9.6 ms-1

  • Option 3)

    8.5 ms-1

  • Option 4)

    7.6 ms-1

 

Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S the change  in total surface area, T is the surface  tension and P atmospheric pressure, which  of the following relation is correct ?        

 

  • Option 1)

    4PV+3ST=0

  • Option 2)

    3PV+4ST=0

  • Option 3)

    2PV+3ST=0

  • Option 4)

    3PV+2ST=0

 

 A spring of unstretched length l has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is :

  • Option 1) (1/2)mv2   
  • Option 2) mv2 
  • Option 3) (1/3)mv2   
  • Option 4) (1/6)mv2   
 

 A line drawn through the point P(4, 7) cuts the circle x2+y2=9 at the points A and B. Then PA⋅PB is equal to :

  • Option 1)

    53

  • Option 2)

    56

  • Option 3)

    74

  • Option 4)

    65

 

 The machine as shown has 2 rods of length 1 m connected by a pivot at the top.  The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot.  As the roller goes back and forth, a 2 kg weight moves up and down.  If the roller is moving towards right at a constant speed, the weight moves up with a :

 

  • Option 1)

     constant speed

  • Option 2)

     decreasing speed

  • Option 3)

     increasing speed

     

  • Option 4)

    speed which is    \frac{3}{4}  th of that of the roller when the weight is 0.4 m above the ground

 

If in a p-n  junction diode, a square input signal of 10 V is applied as shown

Then the output signal across R_L will be

 

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be

  • Option 1)

    100 Hz

  • Option 2)

    70.7 Hz

  • Option 3)

    50 Hz

  • Option 4)

    25 Hz

 

The circuit has two oppositely connect ideal diodes in parallel. What is the current following in the circuit?

  • Option 1)

    1.33 A

  • Option 2)

    1.71 A

  • Option 3)

    2.00 A

  • Option 4)

    2.31 A.

 Interference pattern is observed at ‘P’ due to superimposition of two rays coming out 
from a source ‘S’ as shown in the figure.The value of ‘l’ for which maxima is
obtained at ‘P’ is : (R is perfect reflecting surface) :    

  • Option 1)

    l= \frac{2n\lambda }{\sqrt{3}-1}

  • Option 2)

    l= \frac{\left ( 2n-1 \right )\lambda }{2\left ( \sqrt{3}-1 \right )}

  • Option 3)

    l= \frac{\left ( 2n-1 \right )\lambda\sqrt{3} }{4\left ( 2-\sqrt{3} \right )}

  • Option 4)

    l= \frac{\left ( 2n-1 \right )\lambda }{\sqrt{3}-1}

 

test

Exams
Articles
Questions