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Given equation 

x/1 = y/3 = z/0 and plane eq. 2x + y = 5

line (x - x₁)/l = (y - y₁)/m = (z - z₁)/n plane ax + by + cz + d = 0

here angle of them sin = (al + bm + cn)/√(a² + b² + c²) √(l² + m² + n²)

Here, l = 1, m = 3, n = 0

a = 2, b = 1, c = 0

then, sin θ = (2 x 1 + 3 x 1 + 0 x 0)/√(2² + 1² + 0²) x √(1² + 3²)

sin θ = (2 + 3 + 0)/√(4 + 1) √(1 + 9)

sin θ = 5/(√5 x √10)

sin θ = 5/√50

sin θ = 5/5√2 = 1√2

sin θ = sin π/4

θ = π/4

Given lines are (x - 1)/k = (y - 2)/2 = (z - 3)/3 = λ ...(i)

and (x - 2)/3 = (y - 3)/k = (z - 1)/2 = μ ...(ii)

Any point on line (i) is (kλ + 1,2λ + 2,3λ + 3) and any point on line (ii) (3μ + 2,μk + 3,2μ + 1)

If these line interest, these points must coincide for some value of and .

So, λk + 1 = 3μ + 2, 2λ + 2 = μk + 3, 3λ + 3 = 2μ + 1

λk - 3λ - 1 = 0, 2λ - μk - 1 = 0, 3λ - 2μ + 2 = 0

taking first two, we get 

λ/(3 - k) = μ/(-2 + k) = 1/(-k² + 6) 

λ = (3 - k)/(6 - k²), μ = (k - 2)/(6 - k²)

Putting these value of λ & μ in 3λ - 2μ + 2 = 0

3(3 - k)/(6 - k²) - 2(k - 2)/(6 - k²) + 2 = 0

9 - 3k - 2k + 4 + 12 - 2k² = 0

2k² + 5k - 25 = 0

2k(k + 5) - 5(k + 5) = 0

(2k - 5)(k - 5) = 0

k = 5/2, -5

k = -5 satisfy both the equation.

Hence, k = - 5 is require value.

Answer is (c) 3/4

Answer is (d) x/√(1 + x²)

The correct option is B) nt.

A path length t in a glass plate of refractive index n is equivalent to nt path length in vacuum.

The correct option is C) (n+1) A.

The thin prism of refractive index n and angle of prism A is (n+1) A.

The correct option is A) Frequency.

Of course, it is frequency that specifies the color of light or spectral radiation. For example, you can make the red light have the same wavelength as green light by passing red light through glass or air.

The correct option is D) Diamond.

Diamond has a very high refractive index (about 2.42 compared to about 1.5 for glass). 

Diamonds are cut so that a light ray falling on the diamond is reflected multiple times inside the diamond and therefore sends light out in all direct.

The correct option is A) Conversing lens.

A convex lens n = 1.5 is immersed in water n = 1.33 then it will behave as a Conversing lens.

The correct option is (B) λ = h/p.

The relationship between momentum and wavelength for matter waves is given by p = h/λ, and the relationship energy and frequency is E = hf. 

The wavelength λ = h/p is called the de Broglie wavelength, and the relations λ = h/p and f = E/h are called the de Broglie relations.

It states that the dimensions of each term on both sides of an equation are same.

The principle of homogeneity of dimensions states that the dimensional formula of all the terms in an equation must be the same.

This principle states that a physical equation will dimensionally correct if the dimensions of all the terms occurring on both sides of the equation are the same.

According to this principle, the dimensions of the fundamental quantities of two sides of a physical relation must be the same.

When both the cyclists are moving with equal velocities. That is, they move with equal speeds in the same direction.

Correct Answer is: B) 3 x 10^-9

The stat coulomb is the unit of electric charge quantity in the cgs (centimetre/gram/second) system. It is approximately equal to the charge contained in 2.082 x 10⁹ electrons.

When two objects, carrying like electrical charges of 1 stat coulomb each, are placed so their charge centers are one centimetre (1 cm) apart, the objects repel each other with a force of one dyne (1 dyne).

Correct Answer is: D) A rectifier

Diode is a device which allows passing a current only when it is forward biased. That's why if we use one alternating voltage source instead of a battery during the negative cycles the diode will be reverse biased and will not allow the current to flow. Hence it can be used as a rectifier.

Correct Answer is: B) sm^-1

We know that unit of electric field is: Newton per coulomb or volt per meter…… (i)

And for magnetic field: tesla which is equal to: Newton second per coulomb meter... (ii)

Equation (ii) divided by eq (i):

Ratio inverse of meter per second.

Correct Answer is: C) Photon 

The energy in a hydrogen atom depends on the energy of the electron. When the electron changes levels, it decreases energy and the atom emits photons. The photon is emitted with the electron moving from a higher energy level to a lower energy level.

The given convex lens is made up of five different materials. So they have different refractive indices / different focal lengths. Hence they form five different images.

Water is one compound which is decomposed into hydrogen and oxygen by using the chemical effect of electric current.

Copper sulphate is one chemical compound which is produced by using the chemical effect of electric current.

Copper and Gold are purified by using the chemical effect of current (or electrolysis).

Carbon and hydrogen are extracted by using the chemical effect of electric current.

C. C and D 

Both Aluminum and Sodium metals are produced by the electrolysis of their molten compounds because they are not freely available. They need to be extracted from their sources.

Virtual  type of image

d) Perisperm

Formation of convergent faults, deviation of plates and vulcanicity are the major reasons for evolution of earthquakes in the Atlantic Ridge belt.

Intensity of earthquakes is measured on the Richter scale. It contains numbers from 0 to 9.

1000 mL of.0.75 M HCl have 0.75 mol of HCl = 0.75 x 36.5 g = 24.375 g
(Molar mass of HCl is 36.5)
Mass of HCl in 25 mL of 0.75 M
HCl = 24.375/1000 x 25 g = 0.6844 g
According to the given chemical equation,
CaCO₃ (s) + 2HCl(ag) →CaCl₂ (aq) + CO₂(g) + H₂O(Z)
2 mol of HCl i.e. 73 g HCl react completely with 1 mol of CaCO₃g i.e. 100 g
.’. 0.6844 g HCl reacts completely with CaCO₃ = 100/73 x 0.6844 g = 0.938 g

38% by mass = 38 g HCl in 100 g solution
38 g HCl in 100/1.19 mL = 84 mL solution = 0.084 L .
Molarity = \(\frac{38}{36.5}\) × \(\frac{1}{0.084}\) = 12.39 M.
Thus, the molarity of solution is 12.39 M.

1 mol of MnO₂ = (Atomic mass of Mn + 2 x atomic mass of oxygen)
= 55 + 32 g = 87 g
87g of MnO₂ react with 4 moles of HCl i.e. 4 x 36.5 g
= 146 g of HCl.
(Molar mass of HCl is 36.5)
5.0 g of MnO₂ will react with HCl = 146/87 x 5.0 g
=8.40 g.

Na₂O₂+2H₂O → 2NaOH + H₂O₂

2 KO₂+2H₂O→ 2KOH + H₂O₂+O₂

Answer: (c) Sr

Answer: (b) +2

(c) (iii) only

According to Boyle’s law,

V ∝ \(\frac{1}{P}\) (at constant T and n) ………..(1)

According to Charles’ law,

V ∝ T (at constant P and n) …….(2)

According to Avogadro’s law, 

V ∝ n (at constant P and T) …….(3) 

Combining relations (1), (2) and (3), we get

V ∝ \(\frac{nT}P\)

Converting this proportionality into an equation by introducing a constant of proportionality (‘R’ known as gas constant), we get

∴ V = \(\frac{nRT}P\)

On rearranging the above equation, we get PV = nRT

where, 

P = Pressure of gas, 

V = Volume of gas, 

n = number of moles of gas, 

R = Gas constant,

T = Absolute temperature of gas. 

This is the ideal gas equation or equation of state.

[Note: In the ideal gas equation, R is called gas constant or universal gas constant, whose value is same for all the gases. In this equation, if three variables are known, fourth can be calculated. The equation describes the state of an ideal gas. Hence, it is also called as equation of state.]

Correct option is: (C) V ∝ T

Charles's law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure V ∝ T

Correct option is (C) V ∝ T

Correct option is: (C) 112 g mol^-1

PV = nRT = PV = \(\frac WM RT\)

= PM = \(\frac WV RT\) 

= PM = \(\rho\)RT ....(i)

Let say density of \(N_2\) at 4 bat = \(\rho\)

then the density of unknown gas at 2 atm = 2\(\rho\)

Using equation (i) 

For \(N_2\) gas 

4 \(\times\) 28 = \(\rho\) \(\times\) R \(\times\) 300 ...(ii)

for unknown gas 

2 \(\times\) M = 2e \(\times\) R \(\times\) 300 ....(iii)

iii ÷ ii, we got

\(\frac {2M}{4\times28} = \frac {2\rho\times R\times300}{\rho\times r\times 300}\)

M = \(\frac {2 \times 4\times 28}{2}\) 

M = 112 g/mol

(C) 112 g mol^-1

Correct option is : (A) 2 atm

Using ideal gas equation

PV = nRT

P = \(\frac {2\times0.082\times546}{44.8}\) 

= 2 atm

Correct option is (A) 2 atm

The answer is (a) 2 atm

Its unit and the number of times the unit is contained in the physical quantity.

No, it is a unit of distance.

One light year is defined as the distance traveled by light in one year.

1 light year = 9.46 x 10¹⁵ m.

1 light year = 9.46 x 10¹⁵ m

Hence 1 A.U./1 L.Y. = (1.496 x 10¹¹/9.46 x 10¹⁵) = 10^-5.

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299, 792, 458 of a second.

1 light year = 3 x 10⁸ ms^-1 x (365 x 24 x 60 x 60 ) s

= 9.46 x 10¹⁵ m

Thus 1 m = 1/(9.46 x 10¹⁵)1.y.

= 1.057 x 10^-16 light year.