Search Previous Year Questions

The correct answer is A region of calm climate.

• The sun shines almost vertically on the equator throughout the year ans as a result the air gets warm and rises over the equatorial region and produce equatorial low pressure.
• This belt extends from equator to 10º N and 10º S latitudes.
• Due to excessive heating horizontal movement of air is absent here and only convectional currents are there.
• Therefore this belt is called doldrums (the zone of calm) due to virtual absence of surface winds.
• These are the regions of convergence because the winds flowing from sub tropical high pressure belts converge here. This belt is also known as Inter Tropical Convergence Zone (ITCZ).

The correct answer is Specific Gravity.

Given:

x/y + y/x = 1

Formula Used:

(a³ + b³) = (a + b)(a² + b² - ab)

Calculation:

x/y + y/x = 1

(x² + y²)/xy = 1

⇒ x² + y² = xy

⇒ x² + y² - xy = 0

Multiply by (x + y) both the side we get, 

⇒ (x + y)(x² - xy + y²) = 0(x + y) 

⇒ x³ + y³ = 0

∴ x³ + y³ = 0

Calculation:

**Using

Assumption:

**

Let (x + a)/(b + c) = -1 , (x + b)/(a + c) = -1 , (x + c)/(a + b) = -1

(x + a)/(b + c) + (x + b)/(a + c) + (x + c)/(a + b) = -1 + (-1) + (-1) = - 3

If (x + a)/(b + c) = - 1, then x + a = - b - c or x = - (a + b + c)

Similarly, (x + b)/(a + c) = -1

(x + b) = -a - c or x = - (a + b + c)

Similarly, (x + c)/(a + b) = - 1

(x + c) = -a - b or x = - (a + b + c)

We assumed (x + a)/(b + c) = -1 , (x + b)/(a + c) = -1 , (x + c)/(a + b) = -1 and we got each value x equal in all three conditions.

∴ Assumption is correct and x = -(a + b + c)

Given:

Ratio of male and female members of a club = 5 ∶ 6

After 22 female left, New ratio = 6 ∶ 5

Calculation:

Let the number of male be 5x and female be 6x

Number of female left = 22

According to question,

5x/(6x - 22) = 6/5

⇒ 36x = 25x + 132

⇒ 11x = 132 or x = 12

Male members = 5x = 60

∴ The number of male members is 60.

Inital ratio of Male to female = (5 ∶ 6) × 6 = 30 ∶ 36

After 22 female left, New ratio Male to female = (6 ∶ 5) × 5 = 30 ∶ 25

Only females left, value of male must remain same so, New ratio = 30 ∶ 25

36 - 25 = 11 unit = number of females left = 22 or 1 unit = 22/11 = 2

Number of male = 30 unit = 30 × 2 = 60

∴ The number of male members is 60.

• The correct answer is option 3 i.e. Total internal reflection of light.

Explanation:

• On hot summer days, the air near the ground becomes hotter than the air at higher levels.

• The refractive index of air increases with its density. Hotter air is less dense and has a smaller refractive index than cooler air. If the air currents are small, that is, the air is still, the optical density at different layers of air increases with height.

• As a result, light from a tall object such as a tree passes through a medium whose refractive index decreases towards the ground.

• Thus, a ray of light from such an object successively bends away from the normal and undergoes total internal reflection, if the angle of incidence for the air near the ground exceeds the critical angle.

• To a distant observer, the light appears to be coming from somewhere below the ground and naturally assumes that light is being reflected from the ground, say, by a pool of water near the tall object such inverted images of distant tall objects cause an optical illusion to the observer. This phenomenon is called a mirage.

• This type of mirage is especially common in hot deserts.

• Some of you might have noticed that while moving in a bus or a car during a hot summer day, a distant patch of road, especially on a highway, appears to be wet. But, you do not find any evidence of wetness when you reach that spot. This is also due to mirage.

Confusion Points

• Students are usually confused about whether mirage is the phenomenon of refraction or total internal reflection.
• It is a case of total internal reflection.

Calculation:

(x – 1)² + (y – 4)² = 0

(x – 1)² = - (y – 4)² = 0 

Put x – 1 = 0 and y – 4 = 0 

x = 1 and y = 4

As only above value can make the equation zero 

∴ x³ + y³ = 1 + 64 = 65

The correct answer is Germanium.

• The seed of the development of modern solid-state semiconductor electronics goes back to the 1930s when it was realized that some solid-state semiconductors and their junctions offer the possibility of controlling the number and the direction of flow of charge carriers through them.
• Simple excitations like light, heat, or small applied voltage can change the number of mobile charges in a semiconductor.
• Note that the supply and flow of charge carriers in the semiconductor devices are within the solid itself, while in the earlier vacuum tubes/valves, the mobile electrons were obtained from a heated cathode and they were made to flow in an evacuated space or vacuum.
• No external heating or large evacuated space is required by the semiconductor devices.
• They are small in size, consume low power, operate at low voltages, and have a long life and high reliability.
• Even the Cathode Ray Tubes (CRT) used in television and computer monitors which work on the principle of vacuum tubes are being replaced by Liquid Crystal Display (LCD) monitors with supporting solid-state electronics.
• Much before the full implications of the semiconductor devices were formally understood, a naturally occurring crystal of galena (lead sulphide, PBS) with a metal point contact attached to it was used as a detector of radio waves.
• On the basis of the relative values of electrical conductivity (σ) or resistivity ( ρ = 1/σ ), the solids are broadly classified as:

1. Metals: They possess very low resistivity (or high conductivity). ρ ~ 10^–2 – 10^–8 Ωm; σ ~ 10² – 10⁸ Sm^–1
2. Semiconductors: They have resistivity or conductivity intermediate to metals and insulators. ρ ~ 10^–5 – 10⁶ Ωm; σ ~ 10⁵ – 10^–6 Sm^–1
3. Insulators: They have high resistivity (or low conductivity). ρ ~ 10¹¹ – 10¹⁹ Ωm; σ ~ 10^–11 – 10^–19 Sm^–1

• The values of ρ and σ have given above are indicative of the magnitude and could well go outside the ranges as well.
• Relative values of the resistivity are not the only criteria for distinguishing metals, insulators and semiconductors from each other. There are some other differences too.
• Semiconductors could be:

1. Elemental semiconductors: Si and Ge
2. Compound semiconductors: Examples are:

• Inorganic: CdS, GaAs, CdSe, InP, etc.
• Organic: anthracene, doped phthalocyanines, etc.
• Organic polymers: polypyrrole, polyaniline, polythiophene, etc.
• Most of the currently available semiconductor devices are based on elemental semiconductors Silicon (Si) or Germanium (Ge) and compound inorganic semiconductors.
• Some semiconductor devices are junction diodes (a 2-electrode device) and bipolar junction transistor (a 3-electrode device).
• However, after 1990, a few semiconductor devices using organic semiconductors and semiconducting polymers have been developed signaling the birth of a futuristic technology of polymer-electronics and molecular-electronics.

Calculation:

Diagonal of square = √2a

If Diagonal increased by 10% then sides also increased by 10%

a' = a + 0.1a = 1.1a

(a')² = (1.1a)² = 1.21a²

Change in area = 1.21a² - a² = 0.21a²

∴ Change in area = 21%

The correct answer is option 2 i.e. Granite.