\({ }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q\)
In the nuclear emission stated above, the mass number and atomic number of the product \(Q\) respectively, are:
1. \(286,80\)
2. \(288,82\)
3. \(286,81\)
4. \(280,81\)

Subtopic:  Types of Decay |
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In a vernier callipers, \((N+1)\) divisions of the vernier scale coincide with \(N\) divisions of the main scale. If \(1\) \(\text{MSD}\) represents \(0.1~\text{mm}\), the vernier constant (in \(\text{cm}\)) is:
1. \(\dfrac{1}{100(N+1)} \) 2. \(100N\)
3. \(10(N+1) \) 4. \(\dfrac{1}{10 N}\)
Subtopic:  Measurement & Measuring Devices |
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If \(x = 5 \mathrm {sin }\left(\pi t+ {\dfrac {\pi} 3}\right)~\text m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are:
1. \(5~\text m, 2~\text s\)
2. \(5~\text {cm}, 1~\text s\)
3. \(5~\text m, 1~\text s\)
4. \(5~\text {cm}, 2~\text s\)
Subtopic:  Simple Harmonic Motion |
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In the above diagram, a strong bar magnet is moving towards solenoid-\(2\) from solenoid-\(1\). The direction of induced current in solenoid-\(1\) and that in solenoid-\(2\), respectively, are through the directions:
                        
1. \(BA\) and \(CD\)
2. \(AB\) and \(CD\)
3. \(BA\) and \(DC\)
4. \(AB\) and \(DC\)
Subtopic:  Bar Magnet |
From NCERT
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A logic circuit provides the output \(Y\) as per the following truth table:
\(A\) \(B\) \(Y\)
0
0
1
1
0
1
0
1
1
0
1
0
The expression for the output \(Y\) is : 
1. \(A \cdot \overline{B}+\overline{A} \)
2. \(\overline{B} \)
3. \(B \)
4. \(A \cdot B+\overline{A}\)
Subtopic:  Logic gates |
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A wire of length \('l'\) and resistance \(100 ~\Omega\) is divided into \(10\) equal parts. The first \(5\) parts are connected in series while the next \(5\) parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
1. \(52~ \Omega\) 2. \(55~ \Omega\)
3. \(60 ~\Omega\) 4. \(26~ \Omega\)
Subtopic:  Combination of Resistors |
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The output (\(Y\)) of the given logic gate is similar to the output of an/a: 
                    
1. \(\text{NOR}\) gate 
2. \(\text{OR}\) gate 
3. \(\text{AND}\) gate 
4. \(\text{NAND}\) gate 
Subtopic:  Logic gates |
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A thin spherical shell is charged by some source. The potential difference between the two points \(C\) and \(P\) (in V) shown in the figure is: 
( Take \(\dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9\) SI units)

1. \(1 \times 10^5\)
2. \(0.5 \times 10^5\)
3. \(\text{zero}\) 
4. \(3 \times 10^5\)
Subtopic:  Electric Potential |
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The mass of a planet is \(\left ( \dfrac{1}{10} \right )^{\text{th}} \) that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:
1. \(9.8 ~\text{ms}^{-2}\) 2. \(4.9 ~\text{ms}^{-2}\)
3. \(3.92 ~\text{ms}^{-2}\) 4. \(19.6~\text{ms}^{-2}\)
Subtopic:  Acceleration due to Gravity |
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The minimum energy required to launch a satellite of mass \(m\) from the surface of earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\) from the surface of the earth is:
1. \(\dfrac{2 G m M}{3 R} \) 2. \(\dfrac{G m M}{2 R} \)
3. \(\dfrac{G m M}{3 R} \) 4. \( \dfrac{5 G m M}{6 R}\)
Subtopic:  Satellite |
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