Study questions platform-wide or filter by specific tests with correct answers revealed.
Two cards are drawn one after another with replacement from a well-shuffled standard deck of 52 cards. Let $X$ be the number of aces obtained. Find $P(X=1)+P(X=2)$.
$p=P(\text{ace})=\dfrac{4}{52}=\dfrac{1}{13}$, $q=\dfrac{12}{13}$. Binomial with $n=2$.
$P(X=1)=\binom{2}{1}\cdot\dfrac{1}{13}\cdot\dfrac{12}{13}=\dfrac{24}{169}$
$P(X=2)=\binom{2}{2}\cdot\left(\dfrac{1}{13}\right)^2=\dfrac{1}{169}$
$P(X=1)+P(X=2)=\dfrac{24}{169}+\dfrac{1}{169}=\dfrac{25}{169}$
- Among the alkali metals, only Lithium ($Li$) is small enough and has sufficient polarizing power to react directly with $N_{2}$ to form a stable nitride ($Li_{3}N$).
- This is a characteristic diagonal relationship property between Lithium and Magnesium.
- Spring constant $k$: $F = kx \Rightarrow [k] = \frac{[F]}{[x]} = \frac{MLT^{-2}}{L} = MT^{-2} = M^1L^0T^{-2}$ → (3)
- Pascal (pressure): $[P] = \frac{Force}{Area} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} = M^1L^{-1}T^{-2}$ → (4)
- Hertz (frequency): $[f] = T^{-1} = M^0L^0T^{-1}$ → (2)
- Joule (energy): $[E] = ML^2T^{-2} = M^1L^2T^{-2}$ → (1)
Correct match: A-3, B-4, C-2, D-1
Using the Relativistic Doppler Effect formula for an approaching source:
$f' = f \sqrt{\frac{1 + v/c}{1 - v/c}}$
Given $v = 0.5c$:
$f' = 10 \sqrt{\frac{1 + 0.5}{1 - 0.5}} = 10 \sqrt{\frac{1.5}{0.5}} = 10 \sqrt{3} \approx 10 \times 1.732 = 17.32 \text{ GHz}$.
Sign in to join the conversation and share your thoughts.
Log In to Comment