Explore topic-wise InterviewSolutions in Current Affairs.

(i) Yes. Sum of the length of any two sides of a triangle is greater than the length of the 3 side.

(ii) Yes, Sum of the length of any two sides of a triangle is greater than the length of the 3^rd side.

(iii) Yes, Sum of the length of any two sides of a triangle is greater than the length of the 3^rd side.

Comparing this equation with the general equation of the conic 

Ax² + Bxy + Cy² + Dx + Ey + F = 0 

We get A = C also B = 0 

So the given conic is a circle.

Comparing this equation with the general equation of the conic 

Ax² + Bxy + Cy² + Dx + Ey + F = 0 

We get A ≠ C also C are of the same sign. 

So the given conic is an ellipse.

(i) Hyperbola 

(ii) Parabola 

(iii) Hyperbola 

(iv) Ellipse

(v) Ellipse 

(vi) Ellipse 

(vii) Circle

(d) 9

Slope of normal = -1 and 

Slope of tangent = -1 

The condition for y = mx + c to be a tangent to the parabola 

y² = 4ax is c = a/m

Here the parabola is y² = 12x ⇒ a = 3 and m = 1 

∴ c = 3/1 = 3

∴ Equation of tangent is y = x + 3 

Solving the parabola and tangent we get the points (3, 6) and (3,-6) 

∴ k = -3 or k = 9

(a) 2

The normals are x ± y = 3 

Distance from (3, -2) on both normal is r

(i.e.,) r = |(3 - 2 - 3/√2)| = √2 

r² = 2

(c) 18

The given parabola is y² = 4ax

Since it passes through (2, -6) 

∴ (-6)² = 4a(2) 

⇒ 36 = 8a 

a = 36/8 = 9/2

Length of the latus rectum = 4a = 4(9/2) = 18

y² = 8x. 

Comparing this equation with y² = 4ax 

we get 4a = 8 ⇒ a = 2 

Now, the parametric form for y² = 4ax is x = at², y = 2at 

Here a = 2 and t = 2 

⇒ x = 2(2)² = 8 and y = 2(2) (2) = 8 

So the point is (8, 8) 

Now eqution of tangent to y² = 4 ax at (x₁, y₁) is yy₁ = 2a(x + x₁) 

Here (x₁, y₁) = (8, 8) and a = 2 

So equation of tangent is y(8) = 2(2) (x + 8) 

(ie.,) 8y = 4 (x + 8) 

(÷ by 4) ⇒ 2y = x + 8 ⇒ x – 2y + 8 = 0 

Alternative

The equation of tangent to the parabola y² = 4ax at ‘t’ is 

yt = x + at² 

Here t = 2 and a = 2 

So equation of tangent is 

(i.e.,) y(2) = x + 2(2)² 

2y = x + 8 ⇒ x – 2y + 8 = 0

(a) (6t², 8t)

Point of intersection of the tangents at t₁ and t₂ to 

y² = 4ax is [at₁t₂, a(t₁ + t₂)] 

Here, t₁ = t, t₂ = 3t, 

a = \(\frac{8}{4}\) = 2 

So a t₁t₂ = 2(t) (3t) = 6t² 

a(t₁ + t₂) = 2(t + 3t) = 8t 

∴ Point = (6t², 8t²)

(b) In snow lands

Correct option is: (A) Increases

Gay-Lussac's law states that at constant volume The pressure of a fixed amount of a gas is directly proportional to the temperature.

P ∝ T at constant volume.

Thus, pressure increases if the temperature is increased at a constant volume.

Correct option is (A) Increases

Correct option is: (B) 0.46

PM = \(\rho\)RT 

At same temperature and pressure

\(\frac {PM_{NH3}}{PM_{HCl}} = \frac {\rho_{NH3}RT}{\rho_{HCl}RT}\)

= \(\frac {\rho_{NH3}}{\rho_{HCl}} = \frac {17}{36.5} \) 

= \(\frac {\rho_{NH3}}{\rho_{HCl}} \) 

= 0.46

Correct option is (B) 0.46

Correct option is: (C) increases from V to 1.2V

Using Charles's law

V ∝ T, at constant pressure

\(\frac {V_1}{T_1} = \frac {V_2}{T_2} \)

\(\frac {V_f}{T_f} = \frac {V_i}{T_i} \)

\(V_f\) = \(\frac {360\, Vi}{300}\) 

 \(V_f\) = 1.2 Vi

Hence, at constant pressure, on heating ideal gas from 300k to 360k, its volume increases from V to 1.2 V

(C) increases from V to 1.2V

Ideal gas equation is obtained by combining three gas laws, namely, Boyle’s law, Charles’ law and Avogadro law. Mathematically, it is given as:

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

(ii) Adding salt to water

(iv) Decreasing the temperature of water

Sodium metal is highly reactive and combines with air forming sodium oxide. 

(i) Exceptionally small size of its atom

(ii) Its high polarising power

(i) Beryllium is not readily attacked by acids because of the presence of an oxide film on the surface of the metal.

(ii) Beryllium sulphate is readily soluble in water as the greater hydration enthalpy of Be²⁺ overcomes the lattice enthalpy factor.

a. an oxide film

1. According to Newton’s first law, for a body to achieve uniform velocity, the net force acting on it should be zero. 

2. In real life, a body in motion is constantly being acted upon by resistive or opposing force like friction, in the direction opposite to that of the motion. 

3. To overcome these opposing forces, an additional external force is required. Thus, the net force is not maintained at zero, making it hard to achieve uniform velocity.

MF < MCl < MI, lesser the difference in electronegativity, more will be covalent character.

1. Force due to tension in string: Electromagnetic (EM) force, reaction force, non-conservative force. 

2. Normal force: Electromagnetic (EM) force, non-conservative force. Reaction force 

3. Frictional force: Electromagnetic (EM) force, reaction force, non-conservative force. 

4. Resistive force offered by air or water for objects moving through it: Electromagnetic (EM) force, non-conservative force.

K, Rb and Cs are more reactive therefore, they form superoxide in preference to oxides and peroxides K⁺ ,Rb⁺ and Cs⁺ ions are large cations and superoxide ion O₂^- , is also large. Larger cations stabilize larger anions, therefore, they form superoxide.

 (I) 2 Na(s) + 2 H₂O------> 2NaOH + H₂ 

 (II) Na₂O₂ is formed 

2 Na + O₂ ------> Na₂O₂ 

 (iii) H₂O₂ is formed 

 Na₂O₂ + 2 H₂O------> 2 NaOH + H₂O₂

Li₂CO₃ is a salt of a weak acid (CO₂) and a weak base (LiOH). Since the weak base cannot attract CO₂ Strongly, therefore, Li₂CO₃ decomposes at a lower temperature.On the other hand ,NaOH is a Much stronger base than LiOH and hence can attract CO₂ more strongly.

Sodium hydroxide is obtained by electrolysis of an aq.solution of NaCl in castner kellner cell using Mercury cathode and carbon anode .Sodium metal which is discharged at cathode combines with Mercury to form sodium amalgam.Cl₂ is evolved at anode. The sodium amalgam thus obtained is treated with water to form sodium hydroxide and hydrogen gas.

The oxidation state of K in KO₂ - is +1. It has 1 unpaired electron in π*2p MO. Therefore it is Paramagnetic.

2 KO₂ + 2H₂O ------> 2 KOH + H₂O₂ + O₂

Correct option is A) wages

1. Positive

2. Hydroxyl

3. Salt

4. neutralization.

Real and virtual.

Convex Lens, Scale, Piece of paper, Sunrays. 

(OR) 

Convex Lens, V-Stand, Candle, Match box, Screen, Scale.

a) The object should be kept in less than 20 cm (i.e. less than focal length). 

b) In order to get enlarged real image, object should be kept between 20 cm to 40 cm in front of lens. 

c) In order to get image of same size object should be kept at a distance of 40 cm from the lens.

d) In order to get diminished image the object should be kept beyond 40 cm from the lens.

Correct option is B) Velocity

Correct option is C) Acceleration

If a graph is in curved shape, then it is curved line graph.

slope of the straight line graph = \(\frac{Change \,in \,y\,-\,coordinates}{Change\,in\,x\,-\,coordinates}=\frac{\Delta y}{\Delta x}\)

Hooke’s Law: Elongation of the spring is proportional to mass. The graph of extension and mass is a straight line graph and it indicates the relationship of direct proportional between extension and mass.

The elongation of the spring is proportional to the applied mass within the elastic limit of the spring.

x - axis scale = \(\frac{Range}{Number \,of\,grids\,on\,X\,-\,axis}\)

1. The 13 colonies of North America were dissatisfied with the rule of the master country, England. True. 

2. The French society was divided into three classes, each enjoying similar rights and privileges. False. 

3. The French Revolution began with the storming of Bastille in 1789. True. 

4. A new constitution was framed by the French Assembly in 1785. False. 

5. The French Revolution led to rise of nationalism in Europe. True. 

6. India was greatly inspired by both the American and French Revolutions. True.

The common people of France were greatly inspired by the revolutionary writings of the famous French Philosophers like Rousseau, Montesquieu and Voltaire. They attacked the church and the nobility in their writings. Rousseau wrote that subjects have the right to overthrow a king who does not rule according to the general will. They propagated the ideas of liberty, fraternity and equality.

1. By the middle of the 18th century eleven British colonies had been established along the east coast of North America. False. 

Correct : By the middle of the 18th century 13 British colonies had been established along the east coast of North America. 

2. The American colonists were rigid and conservative. False. 

Correct: The American colonists were simple and liberal. 

3. The American revolutionaries were greatly impressed by the ideas of European philosophers. True. 

4. George Washington was the first elected President of the United States of America. True. 

5. The French Revolution laid the foundation of a democratic government. True.

By the mid-18th century 13 British colonies had been established on the east coast of North America.

Correct Answer is: (a)

You will see that as the speed of oscillation of the pendulum slowly decreases, the second pendulum which was initially stationary, begins to swing. Thus, one pendulum transfers its energy to the other.

Its kinetic energy would be, (b) 100π²

(d) at first greater than mg, and later becomes equal to mg.