Q19. Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left( { } _ { 0 } ^ { 1 } \mathrm { n } \right)$ and uranium isotope $\left( { } _ { 92 } ^ { 235 } \mathrm { U } \right)$ is correct :
(1) ${ } _ { 56 } ^ { 144 } \mathrm { Ba } + { } _ { 36 } ^ { 89 } \mathrm { Kr } + 4 { } _ { 0 } ^ { 1 } \mathrm { n }$
(2) ${ } _ { 56 } ^ { 144 } \mathrm { Ba } + { } _ { 36 } ^ { 89 } \mathrm { Kr } + 3 _ { 0 } ^ { 1 } \mathrm { n }$
(3) ${ } _ { 56 } ^ { 140 } \mathrm { Xe } + { } _ { 38 } ^ { 94 } \mathrm { Sr } + 3 { } _ { 0 } ^ { 1 } \mathrm { n }$
(4) ${ } _ { 51 } ^ { 153 } \mathrm { Sb } + { } _ { 41 } ^ { 99 } \mathrm { Nb } + 3 { } _ { 0 } ^ { 1 } \mathrm { n }$

Q19.
Identify the logic gate given in the circuit: [Figure]
(1) NAND-gate
(2) AND gate
(3) NOR gate
(4) OR- gate

Q19. An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is :
(1) $\mathrm { E } = \mathrm { U }$
(2) $2 \mathrm { E } = \mathrm { U }$
(3) $2 \mathrm { E } = 3 \mathrm { U }$
(4) $\mathrm { E } = 2 \mathrm { U }$

Q19. The output $( Y )$ of logic circuit given below is 0 only when : [Figure]
(1) $\mathrm { A } = 1 , \mathrm {~B} = 0$
(2) $\mathrm { A } = 0 , \mathrm {~B} = 1$
(3) $\mathrm { A } = 0 , \mathrm {~B} = 0$
(4) $\mathrm { A } = 1 , \mathrm {~B} = 1$

Q19. The correct truth table for the following logic circuit is : [Figure]
(1)

$A$	$B$	$Y$
0	0	1
0	1	1
1	0	0
1	1	1

(2)

$A$	$B$	$Y$
0	0	0
0	1	1
1	0	0
1	1	1

(3)

$A$	$B$	$Y$
0	0	1
0	1	1
1	0	0
1	1	0

(4)

$A$	$B$	$Y$
0	0	0
0	1	0
1	0	0
1	1	1

Q19. The acceptor level of a p-type semiconductor is 6 eV . The maximum wavelength of light which can create a hole would be : Given $\mathrm { hc } = 1242 \mathrm { eVnm }$.
(1) 414 nm
(2) 103.5 nm
(3) 207 nm
(4) 407 nm

Q19. The output Y of following circuit for given inputs is : [Figure]
(1) $\Lambda \cdot B ( \Lambda + B )$
(2) 0
(3) $\overline { \mathrm { A } } \cdot \mathrm { B }$
(4) $A \cdot B$

Q19. Least count of a vernier caliper is $\frac { 1 } { 20 \mathrm {~N} } \mathrm {~cm}$. The value of one division on the main scale is 1 mm . Then the number of divisions of main scale that coincide with N divisions of vernier scale is :
(1) $( 2 \mathrm {~N} - 1 )$
(2) $\left( \frac { 2 \mathrm {~N} - 1 } { 2 \mathrm {~N} } \right)$
(3) $\left( \frac { 2 \mathrm {~N} - 1 } { 2 } \right)$
(4) $\left( \frac { 2 \mathrm {~N} - 1 } { 20 \mathrm {~N} } \right)$

Q19. A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42 eV . The wavelength of light emitted from the LED is :
(1) 1400 nm
(2) 650 nm
(3) 875 nm
(4) 1243 nm

Q19. The $I - V$ characteristics of an electronic device shown in the figure. The device is: [Figure]
(1) a diode which can be used as a rectifier
(2) a zener diode which can be used as a voltage regulator
(3) a transistor which can be used as an amplifier
(4) a solar cell
Q20. [Figure]

$A$	$B$	$E$
0	0	0
0	1	$X$
1	0	$Y$
1	1	0

In the truth table of the above circuit the value of X and Y are :
(1) 0,0
(2) 1,1
(3) 1,0
(4) 0,1

Q20. The value of net resistance of the network as shown in the given figure is : [Figure]
(1) $6 \Omega$
(2) $( 5 / 2 ) \Omega$
(3) $( 15 / 4 ) \Omega$
(4) $( 30 / 11 ) \Omega$

Q20. Which of the diode circuit shows correct biasing used for the measurement of dynamic resistance of p-n junction diode :
(1) [Figure]
(2) [Figure]
(3) [Figure]
(4) [Figure]

Q20. Following gates section is connected in a complete suitable circuit. [Figure]
For which of the following combination, bulb will glow (ON) :
(1) $\mathrm { A } = 0 , \mathrm {~B} = 0 , \mathrm { C } = 0 , \mathrm { D } = 1$
(2) $\mathrm { A } = 0 , \mathrm {~B} = 1 , \mathrm { C } = 1 , \mathrm { D } = 1$
(3) $\mathrm { A } = 1 , \mathrm {~B} = 0 , \mathrm { C } = 0 , \mathrm { D } = 0$
(4) $\mathrm { A } = 1 , \mathrm {~B} = 1 , \mathrm { C } = 1 , \mathrm { D } = 0$

Q20. A vernier callipers has 20 divisions on the vernier scale, which coincides with $19 { } ^ { \text {th } }$ division on the main scale. The least count of the instrument is 0.1 mm . One main scale division is equal to $\_\_\_\_$ mm.
(1) 0.5
(2) 2
(3) 5
(4) 1

Q20. While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is $\frac { x } { 50 } \mathrm {~mm}$. The value of $x$ is :
(1) 21
(2) 142
(3) 71
(4) 42

Q20. In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4 { } ^ { \text {th } }$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?
(1) 10
(2) 5
(3) 20
(4) 40

Q20. The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm . The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g , the density of the sphere is:
(1) $2.0 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
(2) $1.7 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
(3) $2.2 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
(4) $2.5 \mathrm {~g} / \mathrm { cm } ^ { 3 }$

Q20. There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm . With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :
(1) 3.35 mm
(2) 4.65 mm
(3) 4.55 mm
(4) 4.60 mm

Q20. One main scale division of a vernier caliper is equal to $m$ units. If $\mathrm { n } ^ { \text {th } }$ division of main scale coincides with $( n + 1 ) ^ { \text {th } }$ division of vernier scale, the least count of the vernier caliper is :
(1) $\frac { n } { ( n + 1 ) }$
(2) $\frac { 1 } { ( n + 1 ) }$
(3) $\frac { m } { ( n + 1 ) }$
(4) $\frac { m } { n ( n + 1 ) }$

Q21. Two forces $\bar { F } _ { 1 }$ and $\bar { F } _ { 2 }$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec { F } _ { 1 }$ and $\vec { F } _ { 2 }$ is $\cos ^ { - 1 } \left( \frac { 1 } { n } \right)$ . The value of $| n |$ is $\_\_\_\_$ .

Q21. A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x ^ { 2 } = 1 + t ^ { 2 }$. Its acceleration at any time t is $x ^ { - \mathrm { n } }$ where $\mathrm { n } =$ $\_\_\_\_$

Q21. Three vectors $\overrightarrow { \mathrm { OP } } , \overrightarrow { \mathrm { OQ } }$ and $\overrightarrow { \mathrm { OR } }$ each of magnitude A are acting as shown in figure. The resultant of the three [Figure] vectors is $\mathrm { A } \sqrt { x }$. The value of $x$ is $\_\_\_\_$。

Q21. A body of mass $M$ thrown horizontally with velocity $v$ from the top of the tower of height $H$ touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2 M thrown at a velocity $\frac { v } { 2 }$ from the top of the tower of height 4 H will touch the ground at a distance of $\_\_\_\_$ m .

Q22. A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $h _ { 1 }$ and $h _ { 2 }$, respectively, above the initial level. The ratio $h _ { 1 } : h _ { 2 }$ is $\frac { n } { 10 }$. The value of $n$ is $\_\_\_\_$。

Q22. A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac { x } { 5 }$. The value of $x$ is $\_\_\_\_$ .
Q23. [Figure]
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is $\_\_\_\_$ N.