Explore topic-wise InterviewSolutions in Current Affairs.

Focal length of a lens depends on the refractive index of the glass from which it is made, and on the curvature of its two surfaces.

Zinc chloride ZnCl₂ combines with NH₃, released from NH₄Cl present in the cell to form the complex salt [Zn(NH₃)₂ Cl₂]. Otherwise the pressure developed due to released NH₃ would crack the seal of the cell.

Zn:

(i) Zincite - ZnO

(ii) Zinc blend - ZnS

The correct option is (D).

Geometrical length is the whole length of the magnet along measuring the length, why the magnetic length is the length between the two posted is North Pole and South Pole, 

And one thing is remember to you that magnetic length is 0. 85 times of the geometrical length of any magnet.

Al:

(i) Bauxite - Al₂O₃.2H₂O

(ii) Cyrollite - Na₃AlF₆

The electrical work of electrical energy produced is equal to the product of e.m.f. of the cell (E_cell).

W (electrical) = -E_cell x q

The negative sign indicates that work is done by the system on the surrounding. If n is the number of is the number of moles of electrons transferred in the redox reaction of the cell, then the quantity of electric charge that follows these the external circuit is given by the equation.

ρ = nF  ∴ W electrical = -nFE_cell

We know that ΔG = -W non-expansion

As in this case the non-expansion work done is electrical work done. Therefore,

ΔG = W electrical = -nFE_cell

For comparing different cells, standard cell potentials (E°_cell) are used. The corresponding free energy charge is called standard free energy (ΔG°). Thus we can write ΔG° = -nFE°_cell

Hg:

(i) Cinnarbar - HgS

(ii) silenide - HgSe

For the construction representation of galvanic cell generally a vertical line is drawn between metal and electrolyte and two vertical lines are written or drawn between two electrolytes (which are connected with a slat bridge.)

(i) Cu(s) |Cu²⁺_(aq.)||Ag⁺_(aq.)| Ag (s)

(ii) Zn(s)|Zn²⁺_(aq.)||Cu²⁺_(aq)| Cu (s)

Mg:

(i) Carnalite - KCl.MgCl₂.6H₂O

(ii) Magnesite - MgCO₃

Au:

(i) Calaverite - AuTe

(ii) Sylaverite - AuAgTe₂

Mn:

(i) Pyrolusite - MnO₂

(ii) Braunite - Mn₂O₃

Ca:

(i) Calcite - CaCO₃

(ii) Dolamite - CaCO₃.MgCO₃

Fe:

(i) Hemaetite - Fe₃O₄

(ii) Magnetite - Fe₃O₄

Ag:

(i) Silver glance - Ag₂S

(ii) Horn Silver - AgCl

Fuel cell: Fuel cell is galvanic cell which converts directly heart energy obtained from combustion of fuels in cell into electrical energy. Gases like hydrogen, methane, etc. are used in fuel cells. The most successful fuel cell is hydrogen-oxygen fuel cell.

The reaction taking place in hydrogen-oxygen fuel cell-

At cathode: O₂ (g) + 2H₂O (l) + 4e^- → 4OH^- (aq)

At anode: 2H₂O (g) + 4OH^- (aq.) → 4H₂O (l) + 4e^-1

Net reaction: 2H₂ (g) + O₂ (g) → 2H₂O (l)

The correct option is C) Total internal reflection.

It shines due to total internal reflection (TIR) the speed of light is faster inside the air bubble than in water. Thus the light gets reflected away from the bubble around the outside.

The correct option is A) -10 cm.

Power of lens =1/F 

Total power p = 15 + 5 = -10 D 

P = 1/f 

F= -10 cm

Electrochemical equivalent:-

∴ Z = m/It

If m = 1 kg, I = 1 A and t = 1 s then Z = 1

So, the electrochemical equivalent will be unit of any matter. If the current 1 A is floated up to 1s. 1 kg matter is stored or freed.

Two main parts of hind-brain are — Medulla and Cerebellum. Their functions are: 

Medulla : Involuntary actions such as blood pressure, salivation and vomiting. 

Cerebellum : It is responsible for precision of voluntary actions and maintaining the posture and balance of the body.

Vertical component of velocity at that point is zero.

(i) Vertical component of velocity,

(ii) Time of flight.

for maximum horizontal range, θ = 45º,

Velocity at highest point = Horizontal component of velocity = ucos 45º\(=\frac{u}{\sqrt2}\)

As R = \(\frac{u^2\,sin\,2\theta}{g}\) , i.e., R ∝ u²

When u is the doubled, the horizontal range becomes four times of the original horizontal range.

Four times the initial horizontal range.

Since R α \(v_0^2\), doubling the initial speed will increase the range by a factor of 2² = 4 times.

If two forces acting at a point are represented both in magnitude and direction by the two adjacent sides of a parallelogram then their resultant is represented by the diagonal of the parallelogram drawn from the same point.

The vector addition holds for two vectors of same nature i.e.,vectors representing physical quantities of same dimensions.

Since, commutation law of addition is valid for any angle between two vector, therefore, the angle between the two vectors can have any value.

(B) is the correct answer. Let sin^–1 (.6) = θ, i.e., sin θ = .6

Now sin (2θ) = 2 sinθ cosθ = 2 (.6) (.8) = .96.

The British also tried to win back people’s loyalty. Rewards were announced for loyal landholders. The loyal landlords were allowed to enjoy their traditional rights over the land. The rebels were told that if they submitted to the British, they would remain safe and their claims and rights would not be denied. But there was a condition that they had not killed any white people.

It was rumoured that the new cartridges were coated with the fat of cows and pigs. This hurt the sentiments of both the Hindus and the Muslims.

x - y + z = 4

x - 2y + 3z = 9

2x + y + 3z = 1

Subtracting eq2 and eq3

⇒ x + 3y = 0

⇒ x = -3y

Substituting in eq1

⇒ -3y – y + z = 4

⇒ z = 4 + 4y

Substituting in eq2

⇒ -3y – 2y + 12 + 12y = 1

⇒ 7y = -11 ⇒ y = - 11/7

Thus,

x = 33/7

And z = 4 – 44/7 = - 16/7

23x - 29y = 98

29x - 23y = 110

Adding both equation

⇒ 52x – 52y = 208

⇒ x – y = 4 ----- (1)

Subtracting both equation

⇒ -6x - 6y = -12

⇒ x + y = 12 ----- (2)

(1) + (2)

⇒ 2x = 16

⇒ x = 8

Thus,

y = 4

The given equations are: 

23x - 29y = 98 …..(i) 

29x - 23y = 110 ……(ii) 

Adding (i) and (ii), we get: 

52x – 52y = 208 

⇒x – y = 4 ……(iii)

Subtracting (i) from (ii), we get: 

6x + 6y = 12

⇒x + y = 2 ……(iv) 

Now, adding equation (iii) and (iv), we get: 

2x = 6 

⇒x = 3 

On substituting x = 3 in (iv), we have: 

3 + y = 2 

⇒y = 2 – 3 = -1 

Hence, x = 3 and y = -1.

The quarterly (3 months) fee = Rs. 540

∴ The fee for 1 month = Rs. 540/3 = Rs. 180

Thus, the fee for 7 months = Rs. (180 × 7) = Rs. 1260

Let the number of votes cast for the candidates be 5x and 7x.

According to question,

7x = 20734

x = 20734/7

x = 2962

∴ Number of votes received by opponent candidate = 5 × 2962 = 14810

The correct answer is 30°

Rotation of earth in 24 hours = 360°

∴ Rotation of earth in 1 hour = 360°/24 = 15°

∴ Rotation of earth in 2 hours = 2 × 15° = 30°

Shivangi will consume 2 × 15 tablets i.e., 30 tablets in 15 days.

Cost of 10 tablets = Rs. 17

∴ Cost of 1 tablet  = Rs. 17/10

Thus, the cost of 30 tablets = Rs. 17/10 x 30 = Rs. 51

Since A and B are square matrices of same order. 

(A + B)(A - B) = A² –AB + BA – B

Since A and B are square matrices of same order. 

(A + B)² = (A+ B)(A + B) 

= A² + AB + BA+ B²

Given A and B are symmetric matrices 

A’ = A --- 1 

B’ = B ---- 2 

Now (AB – BA)’ = (AB)’ – (BA)’ 

= B’A’ – A’B’ 

[∵(AB) ’ = B’A’ ] 

= BA – AB [Using 1 and 2] 

∴(AB – BA)’ = - (AB - BA) 

AB-BA is a skew symmetric matrix.

Since A and B are square matrices of same order. 

(A - B)² = (A- B)(A - B) 

= A² - AB - BA+ B²

\(2​​​​\begin{pmatrix}3 & 4 \\5 & x \\\end{pmatrix}\) + \(​​​​\begin{pmatrix}1 & y \\0 & 1 \\\end{pmatrix}\) = \(​​​​\begin{pmatrix}7 & 0 \\10 & 5 \\\end{pmatrix}\)

To solve this problem we will use the comparison that is we will use that all the elements of L.H.S are equal to R.H.S .

= \(​​​​\begin{pmatrix}6 & 8 \\10 & 2x \\\end{pmatrix}\) + \(​​​​\begin{pmatrix}1 & y \\0 & 1 \\\end{pmatrix}\)

= \(​​​​\begin{pmatrix}7 &8+ y \\10 & 2x+1 \\\end{pmatrix}\)

Comparing with R.H.S 

8 + y = 0 

y = - 8 

2x + 1 = 5 

2x = 4 

x = 2

Correct answer is\(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\)

\(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\) + 2A = \(​​​​\begin{pmatrix} 5 & 6 \\ -7 & 10 \\ \end{pmatrix}\)

⇒ 2A = \(​​​​\begin{pmatrix} 5 & 6 \\ -7 & 10 \\ \end{pmatrix}\) - \(​​​​\begin{pmatrix} 3 & -2 \\ 5 & 6 \\ \end{pmatrix}\)

⇒ 2A = \(​​​​\begin{pmatrix} 2 & 8 \\ -12 & 4 \\ \end{pmatrix}\)

Dividing the matrix by 2 

A = \(​​​​\begin{pmatrix} 1 & 4 \\ -6 & 2 \\ \end{pmatrix}\)

By comparing L.H.S and R.H.S 

x - y = -1 -------- i 

2x – y = 0 -------- ii 

2x+ z = 5 --------- iii 

3z + w =13 ------- iv 

Using i in equation ii 

x = -1 + y 

ii becomes, -2 + 2y –y = 0 

y = 2 

x = 1 

Putting x in iii 

2 + z =5 

z = 3 

Putting z in iv 

9 + w = 13 

w = 4

When a given matrix is singular then the given matrix determinant is 0. 

|A| = 0

Given, A = \(​​​​\begin{pmatrix}3-2x & x+1 \\2 & 4 \\\end{pmatrix}\)

|A|

4(3 - 2x) – 2(x+1) = 0 

12 – 8x -2x -2 = 0 

10 -10x = 0 

10x = 0 

x = 1

When a plane through the centre of a sphere cuts it into two equal parts, then each part is called a hemisphere.

The solid enclosed between two concentric spheres.