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अमेजन घाटी दक्षिणी अमेरिका महाद्वीप में स्थित है।

एशिया महाद्वीप स्थित है।

पूर्व दिशा में स्थित है।

‘संसार की छत’ तिब्बत के पठार को कहा जाता है।

विश्व का सबसे बड़ा महाद्वीप एशिया और सबसे छोटा महाद्वीप आस्ट्रेलिया है।

हमारी पृथ्वी पर जलीय भाग अधिक है इसीलिए इसे नीला ग्रह कहते हैं।

(c) Zero
There is no current flowing in external loop so B = 0

(b) infinite and zero respectively
The resistance of an ideal voltmeter should be infinite and resistance of an ideal ammeter should be zero.

(a) high resistance connected in series
A high resistance is connected in series to convert a moving coil galvanometer into voltmeter.

For cyclotron
\(\frac{m v^{2}}{r}\) = qvB
Here m is mass of charge particle, v is velocity of particle, Bis magnetic field.
∴ Radius of the path
r = \(\frac{m v}{q B}\)
Periodic time, T = \(\frac{2 \pi r}{v}=\frac{2 \pi m}{q B}\)
∴ Time spent in semicircle
\(\frac{T}{2}=\frac{\pi m}{q B}\)

Time period remains constant.
∵ \(t=\frac{\pi m}{q B}\)

When the energy of light charged particles is increased, their mass increases due to relativistic effect.

Pole pieces of permanent magnet are used in a galvanometer of concave shape to produce radial magnetic field.

Plane of coil will be perpendicular to magnetic field.

Principle:

Cyclotron works on the principle that a charged particle moving normal to a magnetic field experiences magnetic Lorentz force due to which the particle moves in a circular path. Cyclotron uses the fact that the frequency of revolution of the charged particle in a magnetic field is independent of its energy. Here, the magnetic field moves the charged particles in a circular path and electric field increases their energy in each frequency.

The mathematical principle is given by the Lorentz force in both perpendicular electric and magnetic field:

\(\vec{F}=q \vec{E}+q(\vec{v} \times \vec{B})\)

By increasing the number of turns in the coil and taking soft iron core.

(c) the number of flux lines entering the surface must be equal to the number of flux lines leaving it.

(d) all charges must necessarily be outside the surface.

(b) ∮_sE.dS = 0 if the charge is outside the surface.

(d) ∮_sE.dS =q/ɛ_o  if charges of magnitude q were inside the surface.

(c) the dominant electric field is ∝1/r³ , for large r, where r is the distance from a origin in this region. 

(d) the work done to move a charged particle along a closed path, away from the region, will be zero.

Correct option is a. On the job training

B) optic centre

C) 1 → r,2 → s,3 → q,4 → p

C) optic centre

(c) potential energy

Explanation:- 

The Potential energy of a system is due to its configuration. When conservative internal forces do work on the system, the potential energy changes to kinetic energy. So negative of work done by the conservative internal forces will be the change in potential energy.

(a) total energy

Explanation:- 

External forces will either change KE or PE or both of a system. Since total mechanical energy (KE+PE) of a system is conserved when no external force acts, hence work done by external force will change total mechanical energy.

The magnetic moment of a current loop is defined as the product of current I and the area vector of the loop. 

We define the magnetic moment m to have a magnitude IA, 

If the loop has N closely wound turns, the expression for torque, Eq. still holds, with m = NIA

(d)  -1/4kx².

Explanation:- 

The work done by the spring on both of the masses is equal to the potential energy stored in the spring. The potential energy stored in the spring = -½kx². 

Since the masses are pulled out symmetrically, the work done by the string on each mass

 =½(-½kx²) =-¼kx². 

The negative sign is for the fact that displacement is opposite to the force.

(c) potential energy

Explanation:- 

The Potential energy of a system is due to its configuration. When conservative internal forces do work on the system, the potential energy changes to kinetic energy. So negative of work done by the conservative internal forces will be the change in potential energy.

(c) The recoiling nucleus at a time t after the decay as measured by the passenger is x .

(a)F₁ = F₂ = F for t < 0.

Explanation:

(a) is correct because as seen in the figure for t<0, F₁ = F₂ =F. For the same reason (b) is incorrect.  Since at t=0 the force on the left rope is withdrawn so at t>0, F₁ ≠ F, F₂ ≠ F. So (c) is in correct.  Since force on the left rope is withdrawn at t=0, so at t>0 force by the right rope on the block will not change ie. F₁ will not be less than F. So (d) is incorrect. 

The correct answer is (a) (c)

Explanation:

Only in the reason AB and CD the displacement is directly proportional to time, it means that the particle is moving with a uniform velocity. So in this reason force on the particle is zero.

The correct answer is (d) F₁ = 0, F₂ = 0.

Explanation:

(a), (b) and (c) are possible under different values of accelerations of the frames S₁ and S₂ with respect to another inertial frame. But (d) is not possible because due to difference in accelerations of frames the pseudo forces in both frames cannot be equal. 

(b) F₁ may be equal to F₂ 

Explanation:

Neither the time nor the distance for accelerating and decelerating journey is mentioned. So both forces may or may not be equal.  

(a) Both the frames are inertial.
(b) Both the frames are noninertial.

Explanation:

S₁ is moving with constant velocity w.r.t frame S₂ . So, if S₁ is inertial, then S₂ will be inertial and if S₁ is non-inertial, then S₂ will be non-inertial.

(c) the frame may be inertial but the resultant force on the particle is zero
(d) the frame may be noninertial but there is a nonzero resultant force.

Explanation:

 (a) is incorrect because if the particle and the non-inertial frame both are moving with same acceleration, the particle will be seen at rest from this frame. So we cannot conclude that the frame is inertial.  (b) is  also not correct. Suppose as viewed from an inertial frame a force F produces an acceleration a in a particle. If  this particle be seen from a non-inertial frame that too is moving with same acceleration in the same direction, it will seem to be at rest. But the force on the particle is not zero.  (c) and (d) are possible conditions.

Since the required numbers are greater than 1000000, then the number is begin with either 1,2 or 4

∴ Number of numbers begin with 1

= 6!/3!2! = (6 x 5 x 4 x 3!)/3!(2 x 1) = 60

Total numbers beginning with 2

= 6!/2!2! = (3 x 4 x 5 x 6)/2 = 180

Total numbers beginning with 4

= 6!/3! = 6 x 5 x 4 = 120

Required number of numbers 

= 60+ 180 + 120 = 360 

Alternative 

Required number of numbers

= 7!/3!2! - 6!/3!2! = 420 - 60 = 360

Let the mother’s present age be x years. 

Let her son’s present age be y years. 

Then, we have: 

x + 2y = 70 …….(i) 

And, 2x + y = 95 ……(ii)

On multiplying (ii) by 2, we get: 

4x + 2y = 190 ……..(iii) 

On subtracting (i) from (iii), we get: 

3x = 120 

⇒ x = 40 

On substituting x = 40 in (i), we get: 

40 + 2y = 70 

⇒ 2y = (70 – 40) = 30 

⇒ y = 15 

Hence, the mother’s present age is 40 years and her son’s present age is 15 years.

Let the mother’s present age be x years. 

Let her son’s present age be y years. 

Then, we have: 

x + 2y = 70 …….(i) 

And, 2x + y = 95 ……(ii)

On multiplying (ii) by 2, we get: 

4x + 2y = 190 ……..(iii) 

On subtracting (i) from (iii), we get: 

3x = 120 

⇒ x = 40 

On substituting x = 40 in (i), we get: 

40 + 2y = 70 

⇒ 2y = (70 – 40) = 30 

⇒ y = 15 

Hence, the mother’s present age is 40 years and her son’s present age is 15 years.

(d) 40 years

Let the man’s present age be x years. 

Let his son’s present age be y years. 

Five years later: 

(x + 5) = 3(y + 5) 

⇒ x + 5 = 3y + 15 

⇒ x – 3y = 10 ………..(i) 

Five years ago: 

(x – 5) = 7(y – 5) 

⇒ x – 5 = 7y – 35 

⇒ x – 7y = –30 ………..(ii) 

On subtracting (i) from (ii), we get: 

-4y = -40 

⇒ y = 10 

On substituting y = 10 in (i), we get:

x – 3 × 10 = 10 

⇒ x – 30 = 10 

⇒ x = (10 + 30) = 40 years 

Hence, the man’s present age is 40 years.

Correct answer = (d) 40 years

Let the man’s present age be x years. 

Let his son’s present age be y years. 

Five years later: 

(x + 5) = 3(y + 5) 

⇒ x + 5 = 3y + 15 

⇒ x – 3y = 10 ………..(i) 

Five years ago: 

(x – 5) = 7(y – 5) 

⇒ x – 5 = 7y – 35 

⇒ x – 7y = –30 ………..(ii) 

On subtracting (i) from (ii), we get: 

-4y = -40 ⇒ y = 10 

On substituting y = 10 in (i), we get: 

x – 3 × 10 = 10 ⇒ x – 30 = 10 

⇒ x = (10 + 30) = 40 years 

Hence, the man’s present age is 40 years

Let the man’s present age be x years. 

Let his son’s present age be y years. 

According to the question, we have: 

Two years ago: 

Age of the man = Five times the age of the son 

⇒ (x – 2) = 5(y – 2) 

⇒ x – 2 = 5y – 10 

⇒ x – 5y = –8 …….(i) 

Two years later: 

Age of the man = Three times the age of the son + 8 

⇒ (x + 2) = 3(y + 2) + 8 

⇒ x + 2 = 3y + 6 + 8 

⇒ x – 3y = 12 …………(ii) 

Subtracting (i) from (ii), we get: 

2y = 20 

⇒ y = 10 

On substituting y = 10 in (i), we get: 

x – 5 × 10 = -8 

⇒ x – 50 = -8 

⇒ x = (-8 + 50) = 42 

Hence, the present age of the man is 42 years and the present age of the son is 10 years.

Let the woman’s present age be x years. 

Let her daughter’s present age be y years. 

Then, we have: 

x = 3y + 3 

⇒ x – 3y = 3 …….(i)

After three years, we have: 

(x + 3) = 2(y + 3) + 10 

⇒ x + 3 = 2y + 6 + 10 

⇒ x – 2y = 13 ……(ii) 

Subtracting (ii) from (i), we get: 

-y = (3 – 13) = -10 

⇒ y = 10 

On substituting y = 10 in (i), we get: 

x – 3 × 10 = 3 

⇒ x – 30 = 3 

⇒ x = (3 + 30) = 33 

Hence, the woman’s present age is 33 years and her daughter’s present age is 10 years.

Correct option is (B) 10 years

Let the present age of woman be x years and present age of her daughter be y years.

After 5 years, the age of woman is (x+5) years

and the age of her daughter is (y+5) years

\(\therefore\) According to given conditions, we have

x = 4y                      __________(1)

and (x+5) = 3 (y+5)

\(\Rightarrow\) 4y + 5 = 3y + 15       (From (1))

\(\Rightarrow\) 4y - 3y = 15 - 5

\(\Rightarrow\) y = 10

\(\therefore\) The present age of her daughter is 10 years.

Correct option is B) 10 years

A typical volcano is a cone-shaped hill with a pit like opening at the top. This opening which acts as the mouth of the volcano is called a crater.

Correct option is (D) 12%

Let principal amount be Rs x and rate of interest be R%.

Given that total amount after applying simple interest on principal amount in 4 years is Rs 7400 & in 7 years Rs 9200.

\(\therefore\) \(x+\frac{4xR}{100}=7400\)       __________(1)

and \(x+\frac{7xR}{100}=9200\)   __________(2)

From (1), we obtain

xR = 25 (7400 - x)

\(\Rightarrow\) xR = 185000 - 25x   __________(3)

Then from (2) & (3), we get

\(x+\frac{7(185000 - 25x)}{100}=9200\)

\(\Rightarrow\) 4x + 51800 - 7x = 36800    (Multiplying both sides by 4)

\(\Rightarrow\) -3x = 36800 - 51800

\(\Rightarrow\) -3x = -15000

\(\Rightarrow x=\frac{-15000}{-3}=5000\)

Then from (3), we get

5000R = 185000 - 125000

\(\Rightarrow\) 5000R = 60000

\(\Rightarrow R=\frac{60000}{5000}=\frac{60}{5}=12\)

Hence, rate of interest is 12%.

Correct option is D) 12%

Vent refers to the passage in the earth’s crust through which lava and other volcanic materials are ejected. The vent, generally, occurs in the weaker part of the earth’s crust.

Volcanic materials are ejected through the mouth of the volcano. The ejected volcanic materials accumulate around the vent, and give rise to the volcanic cone.

The word volcano is derived from a hill located in the island ‘Volcano’ north of Sicily. 

Volcanoes which erupts frequently even now as known as “active volcanoes”. E.g. Mt. Etna in Sicily, Stromboli inLipati islands. Paricutin in Mexico, Cotopaxi in Andes etc. There are about 500 active volcanoes all over the world.