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6 months ago

Class 12th Applications of Trigonometry

Let AB and PQ be two vertical poles, 160m apart from each other. Let C be the middle points of B and Q, which are feet of these two poles. Let $\frac{π}{8}$ and q be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan²q is equal to

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Payal Gupta

Contributor-Level 10

t a n \frac{π}{8} = \frac{2 h}{80} . . . . . . . . . (i)

$t a n θ = \frac{h}{80} . . . . . . . . . . (i i)$

$\Rightarrow t a n \frac{π}{8} = 2 t a n θ$

$t a n^{2} θ = \frac{3 - 2 \sqrt[]{2}}{4}$

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6 months ago

Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Three

The ionic radii of $O^{2 -}, F^{-}, {N a}^{+}$ and ${M g}^{2 +}$ are in the order:

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alok kumar singh

Contributor-Level 10

$O^{2 -} > F^{-} > {N a}^{+} > {M g}^{2 +}$ . Greater the Zeff, smaller is size.

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6 months ago

Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Ten

The probability, that in a randomly selected 3-digit number at least two digits are odd, is

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Payal Gupta

Contributor-Level 10

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6 months ago

Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Eight

On heating, lead (II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitrogen in solid $(C)$ is:

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alok kumar singh

Contributor-Level 10

$2 P b {({N O}_{3})}_{2} \overset{Δ}{?} 2 P b O + 2 {N O}_{2} + O_{2}$

$2 {N O}_{2} ? N_{2} O_{4}$ colourless

$N_{2} O_{4} + 2 N O ? 2 N_{2} O_{3}$

Oxidation state in $N_{2} O_{3}$ is +3

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6 months ago

Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Ten

Let the plane $P : \vec{r} . \vec{a} = d$ contains the line of intersection of two planes $\vec{r} . (\hat{i} + 3 \hat{j} - \hat{k}) = 6$ and $\vec{r} . (6 \hat{i} + 5 \hat{j} - \hat{k}) = 7 .$ If the plane P passes through the point $(2, 3, \frac{1}{2})$ , then the value of $\frac{{| 13 \vec{a} |}^{2}}{d^{2}}$ is equal to

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Payal Gupta

Contributor-Level 10

$P : (x + 3 y - z - 6) = λ (- 6 x + 5 y - z - 7) = 0$

Passes $(2, 3, \frac{1}{2})$

$\Rightarrow (2 + 9 - \frac{1}{2} - 6) = λ (- 12 + 15 - \frac{1}{2} - 7) = 0$

$\Rightarrow λ = 1$

$\frac{{| 13 \vec{a} |}^{2}}{d^{2}} = \frac{{(13)}^{2} (93)}{{(13)}^{2}} = 93$

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6 months ago

Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Ten

The acute angle between the planes P₁ and P₂, when P₁ and P₂ are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

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Payal Gupta

Contributor-Level 10

$(5 x + 8 y + 13 z - 29) + λ (8 x - 7 y + z - 20) = 0$

P₁ passing (2, 1, 3)

(10 + 8 + 39 – 29) + $λ (16 - 7 + 3 - 20) = 0$

$28 - 8 λ = 0 λ = 7 / 2$

$\Rightarrow$ 2X – Y + Z – 6 = 0 ….(i)

For P₂ passes (0, 1, 2)

$(8 + 26 - 29) + λ (- 7 + 2 - 20) = 0$

$5 - 25 λ = 0 \Rightarrow λ = \frac{1}{5}$

$P_{2} : x + y + 2 z - 5 = 0 . . . . . . . . (i i)$

Acute angle between the planes

$c o s θ = \frac{2 - 1 + 2}{\sqrt[]{4 + 1 + 1} \sqrt[]{1 + 1 + 4}} = \frac{1}{2}$

$\Rightarrow θ = \frac{π}{3}$

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6 months ago

Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Nine

The pair in which both the species have the same magnetic moment (spin only) is:

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alok kumar singh

Contributor-Level 10

${C r}^{2 +}$ and ${F e}^{2 +}$ both have 4 unpaired electrons.

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6 months ago

Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Nine

In experiment of find acceleration due to gravity (g) using simple pendulum, time period of 0.5s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, The accuracy in the determination of g is found to be x%. The value of x is_______.

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Vishal Baghel

Contributor-Level 10

T = 0.5 sec

No. of oscillation = 100

Resolution = 1 sec

$l = 10 c m \pm . 1 c m$

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6 months ago

Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Two

The region in the electromagnetic spectrum where the Balmer series lines appear is:

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alok kumar singh

Contributor-Level 10

Balmer series lies in the visible region.

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6 months ago

Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Ten

If two distinct points Q, R lie on the line of intersection of the planes x + 2y – z = 0 and 3x 5y + 2z = 0 and PQ = PR = $\sqrt[]{18}$ where the point P is (1, 2, 3), then the area of the triangle PQR is equal to

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Payal Gupta

Contributor-Level 10

Let vector along L is $\vec{x}$

$\vec{x} = | \begin{matrix} i & j & k \\ - 1 & 2 & - 1 \\ 3 & - 5 & 2 \end{matrix} |$

= $- \hat{i} - \hat{j} - \hat{k}$

Area of $Δ P Q R = \frac{1}{2} | \vec{P Q} * \vec{P R} |$

$= \frac{1}{2} | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 4 & - 1 \\ \frac{- 5}{3} & \frac{4}{3} & - \frac{11}{3} \end{matrix} |$

$= \frac{4}{3} \sqrt[]{38}$

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