Class 12th

Let total work is 60 (LCM of 20, 12 & 15)

Per day work 

(Raj + Mohan) = 3 units

(Mohan + Sohan) = 5 units

(Raj + Shohan) = 4 units

(Raj + Mohan + Sohan) = (3 + 5 + 4)/2 = 6 units

Raj's per day work = 6 – 5 = 1 unit

Total time taken by Raj = 60 days

Total days taken by Mahesh alone = 45*4 = 180 days

Let the total work = 180 units (LCM of 180 and 60)

Mahesh per day work = 1 units

Mahesh and Anand per day work = 180/60 = 3 units

Anand per day work = 3 – 1 = 2

Time taken = 180/2 = 90 days

$Current in circuit i=\frac{10}{4+1}=2 A$

$Terminal voltage =E-iR$

$=10-2*1=8 V$

Food for 80 person = 150 days

Food for 1 person = 150 * 80

Food for 150 person = (150 * 80/150)

= 80 days

Let the total work is 300 units (LCM of 150,100 and 60)

A's per day work = 2 units

B's per day work = 3 units

C's per day work = 5 units

(A+ B + C)'s per day work = 2 + 3 + 5 = 10 units

Time taken = 300/10 = 30 Days

de-Broglie wavelength $\lambda =\frac{h}{P}=\frac{h}{mv}=\frac{h}{\sqrt[]{2mE}}$ where $E=\frac{1}{2}m{v}^2$

Squaring both sides,

${\lambda }^2=\frac{h^2}{4m^{2}E}$

$\Rightarrow \frac{1}{{\lambda }^2}=\left( constant \right)E$

Graph passes through origin with constant slope.

Solar cell characteristics

B: In reverse biased $pn$ junction diode, the current measured in $\left(?A\right)$ , is due to minority charge carrier.

Let y = 2^111x then, $\frac{1}{4}{y}^3+4y=2y^2+1$  

y³ – 8y² +16y – 4 = 0

Let three real roots be a, b and c then abc = and corresponding values of x be x₁,   x₂, and x_3\

$2^{111 (x_1 + x_2 + x_3)}= 4$

111 (x₁ + x₂ + x₃) = 2

x₁ + x₂ + x₃ = 2/111

m + n = 2 + 111 = 113