MCQ
If $\left(1-x+x^2\right)^n=a_0+a_1 x+a_2 x^2+\ldots+a_{2 n} x^{2 n}$, then $a_0+a_2+a_4+\ldots+a_{2 n}$ equals.
- A$3^n+\frac{1}{2}$
- B$\frac{3^n+1}{2}$
- C$\frac{3^n-1}{2}$
- D$\frac{1-3^n}{2}$
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Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is:
The value of $\sin\frac{\pi}{10}\sin\frac{13\pi}{10}$ is:
$\frac{1}{2}$
$-\frac{1}{2}$
$-\frac{1}{4}$
$1$
[Hint: Use $\sin18^\circ=\frac{\sqrt{5}-1}{4}$ and $\cos36^\circ=\frac{\sqrt{5}+1}{4}$]
Two dice are thrown together. The probability that neither they show equal digits nor the sum of their digits is 9 will be: