maths

# An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $$1, 2, 3, .., 9$$ is randomly picked and the number on the card is noted. The probability that the noted number is either $$7$$ or $$8$$ is?

A .
$$\dfrac{13}{36}$$
B .
$$\dfrac{19}{36}$$
C .
$$\dfrac{19}{72}$$
D .
$$\dfrac{15}{72}$$
physics

# A radioactive nucleus (initial mass number A and atomic number Z) emits $$3$$ $$\alpha$$-particles and $$2$$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A .
$$\displaystyle \frac{\mathrm{A}-\mathrm{Z}-8}{\mathrm{Z}-4}$$
B .
$$\displaystyle \frac{\mathrm{A}-\mathrm{Z}-4}{\mathrm{Z}-8}$$
C .
$$\displaystyle \frac{\mathrm{A}-\mathrm{Z}-12}{\mathrm{Z}-4}$$
D .
$$\displaystyle \frac{\mathrm{A}-\mathrm{Z}-4}{\mathrm{Z}-2}$$
physics

A .
d a c b
B .
a d c b
C .
a d b c
D .
d a b c
physics

# A nucleus A, with a finite de - broglie wavelength $$\lambda_A$$. undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B The deBroglie wavelengths $$\lambda_B$$ and $$\lambda_C$$ of B and C are respectively :-

A .
$$2 \lambda_A , \lambda_A$$
B .
$$\lambda_A , 2 \lambda_A$$
C .
$$\lambda_A, \dfrac{ \lambda_A}{2}$$
D .
$$\dfrac{\lambda_A}{2} , \lambda_A$$
chemistry

biology

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biology