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General Solution of tan theta = tan alpha

Q.3 If k ∈ N...

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Q.3 If k ∈ N is a divisor of n! + 1, then the number of values of k satisfying 2 < k < n, is/ar

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Q. The value of the expression

2^{k} (\frac{n}{0}) (\frac{n}{k}) - 2^{k - 1} (\frac{n}{1}) (\frac{n - 1}{k - 1}) + 2^{k - 2} (\frac{n}{2}) (\frac{n - 2}{k - 2}) . . + (- 1)^{k} (\frac{n}{k}) (\frac{n - k}{0})

N

be the set of natural numbers. Suppose

f : N \to N

is a function satisfying the following conditions :

(a) f (m + n) = f (m) + f (n) (b) f (2) = 2

Then the value of

\frac{1}{7} 20 \sum k = 1 f (k)

Q. If total number of runs scored in

n

(\frac{n + 1}{4}) (2^{n + 1} - n - 2)

n > 1,

and the runs scored in the

k^{th}

match are given by

k \cdot 2^{n + 1 - k}

1 \leq k \leq n,

then the value of

n

Q. If total number of runs scored in

n

(\frac{n + 1}{4}) (2^{n + 1} - n - 2)

n > 1,

and the runs scored in the

k^{th}

match are given by

k \cdot 2^{n + 1 - k}

1 \leq k \leq n,

then the value of

n

A_{1}, A_{2}, A_{3}, . . ., A_{11}

11

arithmetic means and

H_{1}, H_{2}, H_{3}, . . ., H_{11}

11

harmonic means and

G_{1}, G_{2}, G_{3}, . . ., G_{11}

11

geometric means between

1

9

, and the value of

5 \prod k = 1 A_{k} \cdot G_{12 - 2 k} \cdot H_{12 - k}

N

. Then which of the following is\are correct?

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General Solution of tan theta = tan alpha

Standard XII Mathematics

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