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Line is intersection of plane x - 2y + z = 2 and 4x + 3y - z = 0

Let direction ratios of that line are a, b and c.

Then that line is perpendicular to both planes.

\(\therefore\) a - 2b + c = 0

4a + 3b - c = 0

\(\therefore\) \(\frac{a}{2-3} = \frac {b}{4+1}=\frac{c}{3+8}\) (By cross multiplication method)

⇒ a/-1 = b/5 = c/11

Hence, direction ratios of that line are -1, 5 and 11.

Since, line is perpendicular to the required plane. It means line is parallel to the normal of the plane i.e., direction ratios of the normal of the plane are -1, 5 and 11.

\(\therefore\) Equation of the plane is

-x + 5y + 11z = d----(1)

Given the required plane is passing through point (1, 1, 1).

 \(\therefore\) -1 + 5 + 11 = d

⇒ d = 15

\(\therefore\) Equation of required plane is -x + 5y + 11z = 15.

Correct option (A) 2πrh    

Explanation:

C.S.A. of one rupee coin (cylinder) = 2πrh.

Correct answer is (b) 1

Correct option is (c) 128 cm²

Correct answer is (d) 3/4

Correct answer is (d) None

Correct answer is (b) 2

Correct option is: (a) Coprime

Correct answer is (c) 7.5 cm

Correct answer is (a) 1000

Correct answer is (b) 2 : 5

Correct answer is (d) non-terminating but repeating.

Correct option is: (b) a = 9, b = -5

Correct option is: (C) 3

Correct answer is (A) sec 30°

Correct option is: (A) 3

Correct answer is (a) both negative

Given:

276x1 is divisible by 3

Concept used:

Divisibility rule of 3:

A number is completely divisible by 3 if the sum of its digits is divisible by 3.

Calculation:

Addition of digits of the given number = 2 + 7 + 6 + x + 1

⇒ 16 + x

⇒ values of x will be,

x= 2, 5, 8

Sum of the possible numbers = 2 + 5 + 8

∴  Sum of the possible numbers is 15

Given:

71, 63, 55, ?

Calculation:

Let the number be 'x'

71 – 63 = 8

63 – 55 = 8

Now we can see that the difference between,

1st and 2nd is same as of the difference between,

2nd and 3rd, that is 8.

⇒ 55 – x = 8

⇒ x = 55 – 8

⇒ x = 47

∴ The next value is 47

Calculation:

Prime factorisation of each, 

⇒ 5a² = 5 × a × a 

⇒ 10a³p = 2 × 5 × a × a × a × p 

⇒ 15ap = 3 × 5 × a × p 

So, HCF = 5a 

∴ The required answer is 5a

Given:

5x2 – 6x + 5 – (– x2 – x + 8)

Calcualtion:

⇒ 5x2 – 6x + 5 – (– x2 – x + 8)

⇒ 5x2 – 6x + 5  + x2 + x – 8

⇒ 6x2 – 5x – 3 

∴ You will get 6x2 – 5x – 3. 

Correct answer is (A) 0

(A) reflection by inosphere 

(D) AND,OR,NOT

(A) a-i, b-ii, d-iii, c-iv 

Correct option (B) ABA

Explanation:

ABA (Abscisic acid) is a naturally occurring growth inhibitor in plants. 

Correct Answer is: (a) μ₀nAi/2rR

Correct Answer is: (c) The cell will lose some electrical energy but never gain any energy.

Correct Answer is: (d) It will move with variable acceleration less than the acceleration due to gravity.

Correct Answer is: (c) It will show deflections first to one side and then to the other.

Correct Answer is: (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Both the statements are true, but Statement II is not the correct explanation of Statement I. 

(A) Both the statements are true and statement II is the correct explanation of Statement I. 

(A) Both the statements are true and statement II is the correct explanation of Statement I. 

(a) U₂ = U₁ + q +w 

U₂ – U₁ = q + w 

or ∆U = q + w 

(b) w= -p∆V

(c) q = 200J 

w = -315J 

∆U = ? 

∆U = q + w 

= 200 + {315} 

= 200 - 315 = -115J

1. First law: 

Energy can neither be created nor be destroyed. Energy in one form can be converted into another form without any loss or gain. 

Second law: 

Entropy of the universe increases during a spontaneous process. 

Third law: 

Entropy of a perfect crystalline substance is zero at absolute zero of temperature. 

2. Entropy: 

Entropy is a measure of randomness or disorder of a system.

3. Spontaneous process: 

A spontaneous process is defined as an irreversible process which has a natural tendency to occur either of its own or after proper initiation under the given set of conditions.

1. The state of a system refers to the conditions of existence of a system when its macroscopic properties have definite values. If any of the macroscopic properties of the system changes, the state of the system will change. The measurable properties required to describe the state of a system are called state variables or state functions. A state function is a property of a system whose value depends only upon the initial and final states of the system and is independent of the path by which this state has been reached. Properties whose values depend on the path followed are called path functions.

2. State variables/State functions – Temperature, Pressure, Enthalpy, Entropy.

1. If ∆H is -ve and ∆S is +ve, ∆G would certainly be -ve and the process will be spontaneous at all temperatures. 

If both ∆H and ∆S are – ve ∆G would be -ve if ∆H > T∆S 

If both ∆H and ∆S are + ve ∆G would be -ve if T∆S > ∆H 

If ∆H is +ve and AS is -ve, ∆G would certainly be +ve and the process will be non-spontaneous at all temperatures.

2. According to Gibbs equation, 

∆G = ∆H – T∆S ∆G 

= (-20.5 × 10³) - (298 ×-50.4) 

= – 20500 + 15019.2 = – 5480.8 J mol^-1 

Since ∆G is -ve, the process is spontaneous.

1. The Zeroth law of thermodynamics states that if two bodies say, ‘A’ and ‘B’ are in thermal equilibrium with another body say, ‘C’, then the bodies A’ and ‘B’ will also be in thermal equilibrium with each other. It provides the basis for the measurement of temperature.

2. The two important modes of transference of energy are heat and work. 

Heat: The exchange of energy, which is a result of temperature difference between system and surroundings is called heat (q). 

Work: The exchange of energy between system and surroundings can occur in the form of work which can be mechanical work, electrical work or pressure-volume work. The exchange of energy as pressure volume work can occur if system consists of gaseous substance and there is a difference of pressure between system and surroundings.

The second law of thermodynamics provides explanation for the spontaneity of chemical reactions. In exothermic reactions heat released by the reaction increases the disorder of the surroundings and overall 1 entropy change is positive which makes the reaction spontaneous.

In the case of endothermic reactions, since heat is ‘ absorbed by the system from the surroundings, the entropy change of the surroundings becomes negative (∆S_surr < 0). In this case the process will be spontaneous only if the entropy change of the reacting system is positive (∆S_sys > 0) and is also greater than ∆S_surr in magnitude so that the overall entropy change (∆S_total) is positive.

• In order for cyclones to develop various conditions need to be fulfilled.
• There must be a plentiful supply of moisture, and for this reason distribution of cyclones is closely related to those regions where the highest sea - surface temperatures are found. i.e. the western portions of the tropical oceans in late summer with a temperature of at least 27°C.
• This moisture provides the necessary latent heat to drive the storm and to provide the rainfall. 

It is mentioned in the 4th line of the paragraph that 27°C temperature is ideal for the formation of a tropical cyclone.

"There must be a plentiful supply of moisture, and for this reason distribution of cyclones is closely related to those regions where the highest sea - surface temperatures are found. i.e. the western portions of the tropical oceans in late summer with a temperature of at least 27°C. This moisture provides the necessary latent heat to drive the storm and to provide the rainfall. Tropical cyclones tend to occur mainly in between the Tropic of Capricorn and Tropic of cancer except the equatorial region i.e.5° on both side of the equator because closer than that to the Equator the Coriolis parameter approaches Zero. The main cyclone activity in the Northern Hemisphere is in late summer and autumn during the time of the equatorial trough's northern displacement."

• The main cyclone activity in the Northern Hemisphere is in late summer and autumn during the time of the equatorial trough's northern displacement.