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Class 12th Physics

The binding energy (in MeV) of a nitrogen nucleus $(_{7}^{14} N)$ is :

(Given mass of nucleus $m (_{7}^{14} N) = 14.00307 u$ , mass of proton $m_{p} = 1.00783 u$ , mass of neutron $m_{n} = 1.00867 u$ and $1 u = 931.5 M e V / c^{2}$ )

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Raj Pandey

Contributor-Level 9

$_{7}^{14} N$ contains 7 protons and 7 neutrons.

Mass defect, $(_{}_{}) (\begin{matrix} \end{matrix})$ $Δ m = (7 m_{H} + 7 m_{n}) - m (\begin{matrix} 14 \\ 7 \end{matrix}) = (7 * 1.00783 u) + (7 * 1.00867 u) - 14.00307 u$

$= 0.11243 u$

Binding energy $= 0.11243 * 931.5 M e V = 104.7 M e V$

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Class 12th Physics

The circuit shown in the figure is in steady state for a long time. The connection to battery is suddenly broken (switch S is opened up). What is the charge (in $μ C$ ) on the capacitor after 0.001 sec.?

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alok kumar singh

Contributor-Level 10

$i_{i} = \frac{84}{140} = 0.6 A$

$i_{2} = \frac{84}{60} = 1.4 A$

p.d across capacitor = 20 v

Q = CV = 5 * 20 = 100 $? C$

After S is open

Q = Q . e^-t/RC

=100 e^-4

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Class 12th Physics

Which of the following transitions of He⁺ ion will give rise to spectral line which has same wavelength as some spectral line in hydrogen atom?

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alok kumar singh

Contributor-Level 10

If n₂ -> n₁ in H (Z = 1) gives $λ$ then $z n_{2} \to z n_{1}$ give same $λ$ H-like ion for He⁺ ion (z = 2)

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Class 12th Physics

In the figure shown below, the maximum and minimum possible unknown resistance (X), that can be measured by the post office box are X_max and X_minrespectively. Then the ratio of these two resistances is: (In this experiment, we take out only one plug in arm AB and only one plug in arm BC, but in arm AD we can take any no. of plugs):

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alok kumar singh

Contributor-Level 10

$\frac{P}{Q} = \frac{R}{X} X_{m a x} = \frac{R_{m a x} . Q_{m a x}}{P_{m i n}}$

$= 9000 * \frac{1000}{10} = 9 * 1 0^{5} o h m$

$x_{m i n} = \frac{R_{m i n} . Q_{m i n}}{P_{m a x}} = 100 * \frac{10}{1000} = 1 o h m$

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Class 12th Electromagnetic Induction

A copper ring of radius $R = 8 c m$ and circular cross-sectional $A = 2 {m m}^{2}$ is in a homogeneous magnetic field whose induction is perpendicular to its plane and changes uniformly. At $t = 0$ the induction is $B_{0} = 0$ and in $t = 0.2 s$ it increases to $B = 2 T$ . The angular velocity $ω$ at which the ring should be rotated uniformly in order not to have tensile stress in it at time instant $t_{1} = 0.1 s$ is approximately: (mass of the ring $m = 9$ gram, Resistance $= 5 m Ω$ , self-induction and gravity can be neglected)

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Raj Pandey

Contributor-Level 9

$R = 8 c m, A = 2 {m m}^{2}, B_{0} = 0$ at $t = 0 s e c$

$B = 2$ Tat $t = 0.2 s e c$

$| ε | = \frac{2 - 0}{0.2} π * 64 * 10^{- 4}$ volts

$i = \frac{| ε |}{r} = \frac{64 π * 10^{- 3}}{5 * 10^{- 3}}$ ampere

$i = \frac{64 π}{5}$ ampere

$d F = i d l B =$ magnetic force

$d m ω^{2} R =$ centrifugal force

$\begin{array}{l} ∴ & i d l B = d m ω^{2} R \\ \Rightarrow & i d l \cdot B = \frac{m}{2 π R} \cdot d l ω^{2} R \\ \Rightarrow & ω = \sqrt[]{\frac{2 π i B}{m}} = \sqrt[]{\frac{2 π * 64 π * 1}{5 * 9 * 10^{- 3}}} \\ ω = \frac{16 π}{3} * 10 r a d / s e c = 170 r a d / s e c \end{array}$

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Class 12th Maths

Let g(x) = x+2|-3|. If a denotes the number of relative minima, b denotes the number of relative maxima and c denotes the product of the zeros. Then the value of (a+2b-c) is

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Vishal Baghel

Contributor-Level 10

c = -5, a = 2, b = 1

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Class 12th Continuity and Differentiability

If 1+x⁴-x⁵ = Σ_i=0⁵ a?(1+x)ⁱ, for all x ∈ R, then a² is equal to ____________

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Vishal Baghel

Contributor-Level 10

1 + x? - x? = a? (1+x)? + a? (1+x) + a? (1+x)² . + a? (1+x)?
Differentiate
4x³ - 5x? = a? + 2a? (1+x) + 3a? (1+x)².
12x² - 20x³ = 2a? + 6a? (1+x).
Put x = -1
12 + 20 = 2a? ⇒ a? = 16

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Class 12th Matrices

Let A be a square matrix of order 2 such that A² – 4A + 4I = 0, where I is an identity matrix of order 2. If B = A? + 4A? + 6A³ + 4A² + A – 162 I, then det(B) is equal to

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