Boron has two isotopes ${}_{5}B^{10}$ and ${}_{5}B^{11}$. If atomic weight of Boron is 10.81 then ratio of ${}_{5}B^{10}$ to ${}_{5}B^{11}$in nature will be: 

1. 15 : 16 

2. 19: 81

3. 81 : 19 

4. 20: 53

The following table is for which logic gate?

1. AND
2. OR
3. NAND
4. NOT

For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)

Two pendulums suspended from the same point have lengths of \(2\) m and \(0.5\) m. If they are displaced slightly and released, then they will be in the same phase when the small pendulum has completed:
1. \(2\) oscillations
2. \(4\) oscillations
3. \(3\) oscillations
4. \(5\) oscillations

For protecting a magnetic needle, it should be placed:

A circular ring of mass M and radius R is rotating about its axis with constant angular velocity ω. Two particles, each of mass m are attached gently to the opposite ends of the diameter of the ring. The angular velocity of the ring will now become:

1. \(\frac{m \omega}{M   +   2 m}\)

2. \(\frac{m \omega}{M   -   2 m}\)

3.  \(\frac{M \omega}{M   +   2 m}\)

4. \(\frac{M   +   2 m}{M \omega}\)

If $x$ $=$ $3$ $-4t^2$ $+$ $t^3$, then work done in the first 4s will be:
(Mass of the particle is 3 gram)
1.  384 mJ
2.  168 mJ
3.  192 mJ
4.  None of the above

If force \(F=500-100t,\) then the function of impulse with time will be:
1. \( 500 t-50 t^2 \)
2. \( 50 t-10 \)
3. \( 50-t^2 \)
4. \( 100 t^2\)