A ball whose kinetic energy is E ,  is projected at an angle of 45^{\circ} to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

Option 1)

E

Option 2)

E/\sqrt{2}

Option 3)

E/2

Option 4)

Zero

Dimensions of    \frac{1}{\mu _{0}\varepsilon _{0}}   , where symbols have their usual meaning, are

Option 1)

\left [ L^{-1}T \right ]

Option 2)

\left [ L^{-2}T^{2} \right ]

Option 3)

\left [ L^{2}T^{-2} \right ]

Option 4)

\left [ LT^{-1} \right ]

Identify the pair whose dimensions are equal.

Option 1)

torque and work

Option 2)

stress and energy

Option 3)

force and stress

Option 4)

force and work.

 Some energy levels of a molecule are shown in the figure.  The ratio of the wavelengths r=λ12, is given by :

  • Option 1)

    r= \frac{4}{3}

  • Option 2)

    r= \frac{2}{3}

  • Option 3)

    r= \frac{3}{4}

  • Option 4)

    r= \frac{1}{3}

 

Arrange the following electromagnetic radiations per quantum in the order of increasing energy :

A : Blue light      B : Yellow light
C : X-ray             D : Radiowave.

 

  • Option 1)

    D, B, A, C

     

  • Option 2)

    A, B, D, C

     

  • Option 3)

    C, A, B, D

     

  • Option 4)

     B, A, D, C

     

 

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

  • Option 1)

     its kinetic energy increases but potential energy and total energy decrease
     

  • Option 2)

     kinetic energy, potential energy and total energy decrease

  • Option 3)

     kinetic energy decreases, potential energy increases but total energy remains same

     

  • Option 4)

     kinetic energy and total energy decrease but potential energy increases

 

A radioactive nucleus A with a half life T, decays into a nucleus B.  At t=0, there is no nucleus B.  At sometime t, the ratio of the number of B to that of A is 0.3.  Then, t is given by :

  • Option 1)

    t= \frac{T}{2}\: \: \frac{\log 2}{\log 1.3}

  • Option 2)

    t= T\frac{\log 1.3}{\log 2}

  • Option 3)

    t= T\log \left ( 1.3 \right )

  • Option 4)

    t= \frac{T}{\log 1.3}

 

‘n’ moles of an ideal gas undergoes a process A→B as shown in the figure.  The maximum temperature of the gas during the process will be :

  • Option 1) (9P0V0/4nR) 
  • Option 2) (3P0V0/2nR)  
  • Option 3) (9P0V0/2nR)  
  • Option 4)(9P0V0/nR)  
 

 A solid body of constant heat capacity 1 J/0C is being heated by keeping it in contact with reservoirs in two ways : 

  (i)    Sequentially keeping in contact with 2 reservoirs such that each reservoir      
          supplies same amount of heat.       
  (ii)    Sequentially keeping in contact with 8 reservoirs such that each reservoir       
          supplies same amount of heat.          
          In both the cases body is brought from initial  temperature  1000C  to  final   
         temperature 2000C. Entropy change of the body in the two cases respectively is :                    

 

  • Option 1)

    ln2,4ln2

  • Option 2)

    ln2,ln2

  • Option 3)

    ln2,2ln2

  • Option 4)

    2ln2,8ln2

 

 The following observations were taken for determining surface tension T of water by capillary method :

diameter of capillary, D=1.25×10−2 m rise of water, h=1.45×10−2 m. Using g=9.80 m/s2 and the simplified

relation T= \frac{rhg}{2}\times 10^{3} N/m  , the possible error in surface tension is closest  to:

 

 

  • Option 1)

    0.15%

     

  • Option 2)

    1.5%

     

  • Option 3)

    2.4%

     

  • Option 4)

    10%

 

 A train is moving on a straight track with speed 20 ms -1. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms-1) close to :

 

  • Option 1)

    6%

  • Option 2)

    12 %

  • Option 3)

    18 %

  • Option 4)

    24 %

 

 For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly ?

(graphs are schematic and not drawn to scale)

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

The period of oscillation of a simple  pendulum isT=2\pi \sqrt{\frac{L}{8}} Measured value of L is 20.0 cm known to 1 mm accuracy   and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution.  The accuracy in the determination of g is

  • Option 1)

    2%

  • Option 2)

    3%

  • Option 3)

    1%

  • Option 4)

    5%

 

A uniform string of length 20 m is suspended from a rigid support.  A short wave pulse is introduced at its lowest end. It starts moving up the string.  The time taken to reach the support is : (take g = 10 ms−2)

  • Option 1)

    2\pi \sqrt{2}\: \: s

  • Option 2)

    2s

  • Option 3)

    2\sqrt{2}s

  • Option 4)

    \sqrt{2}s

 

A particle performs simple harmonic motion with amplitude A.  Its speed is trebled at the instant that it is at a distanc

\frac{2A}{3} from equilibrium position.  The new amplitude of the motion is :

  • Option 1)

    \frac{A}{3}\sqrt{41}

  • Option 2)

    3A

  • Option 3)

    A\sqrt{3}

  • Option 4)

    \frac{7A}{3}

 

A pendulum clock loses 12 s a day if the temperature is 400C and gains 4 s a day if the temperature is 200C.  The temperature at which the clock will show correct time, and  the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively :

  • Option 1)

     250C;  α = 1.85×10−5/0C

     

  • Option 2)

     600C; α =1.85×10−4/0C

     

  • Option 3)

     300C; α=1.85×10−3/0C

     

  • Option 4)

     550C;  α = 1.85×10−2/0C

 

A student measures the time period of 100 oscillations of a simple pendulum four times.  The data set is 90 s, 91 s, 95 s and 92 s.  If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

  • Option 1)

    92 ± 2 s

  • Option 2)

    92 ± 5.0 s

  • Option 3)

    92 ± 1.8 s

  • Option 4)

    92 ± 3 s

     

 

A red LED emits light at 0.1 watt uniformly around it.The amplitude of the electric field of the light at a distance of 1 m from the diode is :

  • Option 1)

    1.73 V/m

  • Option 2)

    2.45 V / m

  • Option 3)

    5.48 V / m             

  • Option 4)

    7.75 V / m

 

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be :

  • Option 1)

    450

  • Option 2)

    900

  • Option 3)

    1350

  • Option 4)

    1800

 

 The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6,7 and 8, without repetition, is :

  • Option 1)

    216

  • Option 2)

    192

  • Option 3)

    120

  • Option 4)

    72

 

If the number of terms in the expansion of

\left ( 1-\frac{2}{x} +\frac{4}{x^{2}}\right )^{n},\: x\neq 0

28, then the sum of the coefficients of all the terms in this expansion, is

  • Option 1)

    64

  • Option 2)

     2187

     

  • Option 3)

     243

     

  • Option 4)

     729

     

 

The sum of coefficients of integral powers of  x  in  the  binomial  expansion  of

\left ( 1-2\sqrt{x} \right )^{50}\; is:

  • Option 1)

    \frac{1}{2}\left ( 3^{50}+1 \right )

  • Option 2)

    \frac{1}{2}\left ( 3^{50} \right )

  • Option 3)

    \frac{1}{2}\left ( 3^{50}-1 \right )

  • Option 4)

    \frac{1}{2}\left ( 2^{50}+1 \right )

 

In a compound, atoms of element Y from ccp lattice and those of element occupy 2/3rd  of tetrahedral voids. The formula of the compound will be

  • Option 1)

    X_{3}Y_{4}

  • Option 2)

    X_{4}Y_{3}

  • Option 3)

    X_{2}Y_{3}

  • Option 4)

    X_{2}Y

 

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens’ principle leads us to conclude that as it travels, the light beam :

  • Option 1)

     becomes narrower
     

     

  • Option 2)

    goes horizontally without any deflection

  • Option 3)

     bends downwards

     

  • Option 4)

    bends upwards

 

 Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is\mu, a ray, incident at an angle \Theta, on the face AB would get transmitted through the face AC of the prism provided :

  • Option 1)

    \Theta > \sin ^{-1}\left [ \mu \sin \left ( A-\sin ^{-1} \left ( \frac{1}{\mu } \right )\right ) \right ]

  • Option 2)

    \Theta < \sin ^{-1}\left [ \mu \sin \left ( A-\sin ^{-1} \left ( \frac{1}{\mu } \right )\right ) \right ]

  • Option 3)

    \Theta >\cos ^{-1}\left [ \mu \sin \left ( A+\sin ^{-1} \left ( \frac{1}{\mu } \right )\right ) \right ]

  • Option 4)

    \Theta < \cos ^{-1}\left [ \mu \sin \left ( A+\sin ^{-1} \left ( \frac{1}{\mu } \right )\right ) \right ]

 
Exams
Articles
Questions