Set of value of r of which- 18Cr - 2 - 2- 18Cr - 1 - 18Cr- 20C13 contains -

The correct option is C 7 elements a2(1+cos2θ)+hsin^12θ+b2(1 cos 2θ) =α^2+2bαβ+bβ^2 1 (a+b)2+[√((a b2)^2+h^2)]cos(2θ+ϕ) which is independent ...

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Standard XII

Physics

Energy Levels

Set of value ...

Question

Set of value of $r$ of which, $^{18} C_{r - 2} + 2.^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}$ contains -

4

elements

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5

elements

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7

elements

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10

elements

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Solution

The correct option is C $7$ elements
$\frac{a}{2} (1 + cos 2 θ) + h {sin}^{1} 2 θ + \frac{b}{2} (1 - cos 2 θ)$
$= α^{2} + 2 b α β + b β^{2} - 1$
$\frac{(a + b)}{2} + ⎡ ⎣ \sqrt{{(\frac{a - b}{2})}^{2} + h^{2}} ⎤ ⎦ cos (2 θ + ϕ)$
which is independent of $q$ if ${(\frac{a - b}{2})}^{2} + b^{2} = 0$
& $a = b$ $h = 0$
hence given curve is circle
$^{18} C_{r - 2} +^{18} C_{r - 1} +^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}$
$^{19} C_{r - 2} +^{19} C_{r} \geq^{20} C_{13}$
$^{20} C_{r} \geq^{20} C_{13}$
$^{20} C_{0}^{20} C_{1} C_{2} C_{3} C_{4} C_{5} C_{6} C_{7} C_{8} C_{9} C_{10} C_{11} C_{12} C_{13}$
$r = 7, 8, 9, 10, 11, 12, 13$

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Similar questions

Q. Number of elements in set of values of

r

for which

^{18} C_{r - 2} + {2.}^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}

is satisfied is:

Q. Set of values of r for which

^{18} C_{r - 2} + 2 \cdot^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}

contains

Each set X, contains 5 elements and each set Y, contains 2 elements and $⋃_{r = 2}^{20} X_{r} = S = ⋃_{r = 1}^{n} Y_{r}$ . If each element of S belongs to exactly 10 of the $X_{r}^{^{'} s}$ and to exactly 4 of $Y_{r}^{^{'} s}$ then find the value of n.

Q. Each set X, contains 5 elements and each set Y, contains 2 elements and

\cup_{r = 1}^{20} X_{r} = S = \cup_{r = 1}^{n} Y_{r}

. If each element of S belong to exactly 10 of the X_r's and to eactly 4 of Y_r's, then find the value of n.

Q. Each set X_r contains 5 elements and each set Y_r contains 2 elements and

\cup_{r = 1}^{20} X_{r} = S = \cup_{r = 1}^{n} Y_{r}

. If each element of S belongs to exactly 10 of the

X_{r}^{' s}

and to exactly 4 of the

Y_{r}^{' s},

then n is
(a) 10
(b) 20
(c) 100
(d) 50

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Set of value of r of which, 18Cr−2+2. 18Cr−1+18Cr≥ 20C13 contains -

Set of value of $r$ of which, $^{18} C_{r - 2} + 2.^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}$ contains -