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Iron is a metallic minerals.

Gujarat is the largest production of groundnut.

Stress \(\sigma\) = \(\cfrac{force F}{area A}\) = \(\cfrac{20\times10^3}{80\times10^{-6}}\) 

= 250 x 10⁶ pa = 250 Mpa

Solar is a non-renewable source of energy.

Rice is a kharif crops.

Stress \(\sigma\) = \(\cfrac{forcce F}{area A}\) hence, cross-sectional area, A = \(\cfrac{forcce F}{stress\,\sigma}\)

= \(\cfrac{1\times10^3}{7.8\times10^6}\) = 128.2 x 10^-6 m²

Circular area = \(\pi\)r² = 128.2 x 10^-6 m²

from which, r² = \(\cfrac{128.2 \times10^{-6}}{\pi}\) and radius r = \(\sqrt{\cfrac{128.2 \times10^{-6}}{\pi}}\)

= 6.388 10^-3 m = 6.388 mm

and diameter d = 2 x r = 2 x 6.388 = 12.78 mm

Stress \(\sigma\) = \(\cfrac{forcce F}{area A}\) = \(\cfrac{10\times10^3}{12\times12\times10^{-6}}\) = 69.44 x 10⁶ pa = 69.44 mpa

Hajipur is the headquarter of the East Central Railways.

Stress \(\sigma\) = \(\cfrac{forcce F}{area A}\) = hence, force = stress x area = stress \(\pi\)r²

= 120 x 10⁶ x \(\pi\) \(\left(\cfrac{5\times10^{-3}}{2}\right)^2\)

= 2356 N or 2.356 kN

Asia continent has the highest population growth.

Stress \(\sigma\) = \(\cfrac{forcce F}{area A}\) = hence, cross-sectional area, A = \(\cfrac{forcce F}{stress\,\sigma}\)

= \(\cfrac{400}{120\times10^6}\) = 3.333 x 10^-6 m²

Circular area = \(\pi\)r² = 3.3333 x 10^-6 m²

from which, r² = \(\cfrac{3.3333 \times10^{-6}}\pi\) and radius r = \(\sqrt{\cfrac{3.3333 \times10^{-6}}\pi}\)

= 1.030 x 10^-3 m = 1.030 mm

diameter d = 2 x r = 2 x 1.030 = 2.06 mm

Important cotton production area is Daccan.

Crop cultivation, Animal husbandry and Fishing activities are included in agriculture.

Tea crops are grown on mountain slopes.

Sikkim states has the lowest population in India.

Partisan means a person who is strongly committed to a party.

Area of tube end (annulus) = \(\pi\) \(\left(\cfrac{D^2}{4}-\cfrac{d^2}{4}\right)\)

= \(\pi\) \(\left(\cfrac{(60\times10^{-3})^2}{4}-\cfrac{(40\times10^{-3})^2}{4}\right)\)

= 1.5708 x 10^-3 mm²

Stress \(\sigma\) = \(\cfrac{force F}{area A}\) = \(\cfrac{60\times10^3}{1.5708\times10^{-3}}\)

= 38.20 x 10⁶ pa = 38.2 Mpa

Correct option (d) B and D

Delhi is Administrative city.

Recognized political parties stand for Parties recognized by the Election Commission with all the privileges and facilities.

In a biological context, arboreal is a term used to associate with trees, any mammal/animal which lives on trees are arboreal.

• Examples of arboreal animals are squirrels, koalas, primates, sloths, spider monkeys, leopards, chameleons, geckos, bats, tree frogs, snakes, birds, lizards, and tree snails.
• Many animals have sharp claws which help them to hut their prey. Their claws also help to climb up the trees, where they live. Tiger is one such example.

Some other keywords are:

• Terrestrial refers to things related to land or the planet Earth. Terrestrial may also refer to Terrestrial animal, an animal that lives on land as opposed to living in water, or sometimes an animal that lives on or near the ground, as opposed to arboreal life (in trees).
• An amphibian is a vertebrate (an animal with a backbone). Amphibians are cold-blooded, which means that their body temperature changes with their surroundings. They spend part of their lives in water (breathing with gills) and part of their lives on land (breathing with lungs).
• Aquatic means relating to water, living in or near water, or taking place in water, does not include groundwater, as "aquatic" implies an environment where plants and animals live. Aquatic may also refer to Aquatic animals.

So, we may say that arboreal animals, sharp claws, trees are interlinked and correctly matched.

A national symbol is some specific considering and manifesting itself as a national community. The national animal tiger symbolizes power, the national flower lotus symbolizes purity, the national tree banyan symbolizes immortality, the national bird, the peacock symbolizes elegance, and the national fruit mango symbolizes the tropical climate of India.

National Symbols of India

The minimum population density necessary for a settlement to be designated as urban settlement is 400 persons per sq. km.  

(c) Blizzard – Siberian Plains. A blizzard is a severe snowstorm caused by strong sustained winds of at least 56 km/h (35 mph) and lasting for a prolonged period of time – typically three hours or more. 

Chinook – Prairie Plains. Chinook winds blows in the interior west of North America, where the Canadian Prairies and Great Plains meet various mountain ranges, although the original usage is in reference to wet, warm coastal winds in the Pacific Northwest of the United States of America. 

Bora – Green land. Cold and usually dry katabatic winds, like the Bora, result from the downslope gravity flow of cold, dense air. Katabatic flows slumping down from uplands or mountains may be funneled and strengthened by the landscape and are then known as mountain gap wind. 

Khamsin – Egypt. Khamsin can be triggered by depressions that move eastwards along the southern parts of the Mediterranean or along the North African coast from February to June. In Egypt, khamsin usually arrives in April but occasionally occurs between March to May, carrying great quantities of sand and dust from the deserts, with a speed up to 140 kilometres per hour, and a rise of temperatures as much as 20°C in two hours.

(a) A. Kuroshio current – warm Pacific current 

B. Peru current – cold current in Pacific ocean 

C. Labrador current – cold current in Atlantic ocean 

D. Florida current – Warm current in Atlantic ocean

Kota is fertilizer plants is not in the public sector.

(a) The holes in the plates become oval shaped and joints become loose 

Crushing strength of plate/rivet crushing failure of the plate/rivet. This type of failure occurs when the compressive stress between the shank of the rivet and the plate exceeds the yield stress in compression. The failure results in elongating the rivet hole in the plate and loosening of the joint.

Gujarat is drought prone region.

Tamilnadu state has longer period of sugarcane crushing.

(c) Former USSR

Naharkatiya oilfields are located in Assam.

(a) The Niger river is the principal river of western Africa, extending about 4,180 km. Its drainage basin is 2,117,700 km2 in area. Its source is in the Guinea Highlands in southeastern Guinea. The Orange river, Gariep river, Groote river or Senqu river is the longest river in South Africa. It rises in the Drakensberg mountains in Lesotho, flowing westwards through South Africa to the Atlantic Ocean.

Equation of parabola y² = 8x compare with the standard form

y² = 4ax ∴ 4a = 8 ∴ a = 2 

∴ focus = (a,0) = (2,0) 

Equation of directrix : x = -a. 

x = -2 or [x + 2 = 0] 

Latus rectum = 4a = 8.

x = x/3, a = 9y, n = 10, r = 5 

n = 10 (even) there is only one middle term is (n/2 + 1) = (10/2 + 1) = 6^th term 

General term T_r+1 = ⁿC_r x^n-r a^r ⇒ T_s+1 = ¹⁰C₅ (x/3)^{10 - 5}(9y)⁵ 

T₆ = ¹⁰C₅ (x/3)⁵ g5 y5 ⇒ T6 = 10C5 . x⁵/3⁵ × 9⁵ y⁵ = ¹⁰C₅ (xy)5 × (3¹⁰/3⁵)

T₆ = [¹⁰C₅ (xy)⁵ 3⁵] is the middle term.

 Answer is : (c)

Number of electric field lines entering the surface is equal to the field lines leaving the surface.

The centre of the circle = (5,0). 

The equation y² = 20x ⇒ y² = 4ax ⇒ a = 5 

directrix is x = -5, LR = 20.

As sin function is dimensionless and wt- kx is dimensionless now difference of two quantity ( wt) and ( kx) is dimensionless therefore 

wt= M⁰L⁰T⁰ 

=>w* time(T¹) = M⁰L⁰T⁰ 

=>w= M⁰L⁰T⁰ / T¹

= M⁰L⁰T^-1 

also kx= M0L0T0 

=>k* distance(L¹) 

= M⁰L⁰T⁰ 

=>k= M⁰L⁰T⁰ /L¹

=M⁰L^-1T⁰  

We have 

a_m = a + (m – 1)d = n, …… (1) 

and a_n = a + (n – 1)d = m …….. (2) 

Solving (1) and (2), we get 

(m, n) d = n – m, or d = -1, 

and a = n + m – 1 ……. (3) 

Therefore a_p = a + (p – 1)d ……. (4) 

= n + m – 1 + (p – 1) (-1)

= n + m – p 

Hence, the p^th term is n + m – p.

The coordinate will be : (3, 6), (3, -6)

Explanation:

As we know that coordinates of the focus of parabola with equation y²=4ax are (a,0).

The focal distance of this parabola is 2a.

Here, y² = 12x when we compare it to y² = 4ax then
4a = 12 
a = 3
we can say the points lie on point of intersection of latus rectum and the parabola, so we put x = 3
we get y² = 36 
y = ±6

so coordinates are (3, 6), (3, -6)

Fibres: A long fine continuous thread or filament

Correct option:

(B) a^x log a

Correct option:

(A) parallel 

Let y = x + (1/x)

∴ dy/dx = 1 - (1/x²)

or, dy/dx = ((x² - 1)/x²)

For maximum or minimum value of y, dy/dx = 0

∴ ((1 - x²)/x²) = 0 

= 1 - x² = 0

x = 1,-1

Again, d²y/dx² = 2/x³

At, x = 1, d²y/dx² = 2 > 0

So, y has minimum value at x = 1

and minimum value of y = x + (1/x) = 1 + (1/1) = 2

and at, x = -1,

d²y/dx² = 2/(-1)³ = -2 < 0

So, y has maximum value at x = -1 

and maximum value of y = -1 + (1/-1) = -2

So, minimum value of given function is greater than maximum value.

option b is the correct answer........

first find general tern of (1+x)ⁿ 

T_r+1 = ⁿC_r x^r

Tp= T_(p-1)+1 = ⁿCp-1 x^p-1

Cofficient of pth term = P

 ⁿCp-1 = P

T_p+1= T_(p)+1 = ⁿCp x^p

Cofficient of (P+1)th term = q

ⁿCp= q

P+q = ⁿCp-1 + ⁿCp

       =ⁿ⁺¹Cp

Let us assume that √2 is rational i.e.. the gives statement is false. 

∴ √2 = 1/2 ≠ 0 a and b have no conunon factor. 

Squaring ∴ 2 = a²/b² ⇒ [a² = 2b²] ⇒ 2 divides a 

Again put a = 2C(C ∈ Z) ⇒ ∴ (2c)² = 2b² 

∴ 4c² = 2b² or [b² = 2c²]² divide b 

i.e., 2 divides both a and b hence our assumption is i.e.. a and b does flot have common contradict out statement √2 is rational is false. 

∴ √2 is irrational.

If possible Let √2 is rational 

∴ √2 = p/q, p, q ∈ z, q ≠ 0 

We assume that p and q do not have any common factor 

p = √2q ⇒ p = 2q² 

p² is a multiple of 2 ⇒ ∴ p is a multiple of 2 

∴ p = 2k, k ∈ z ⇒ p² = 4k 

2q² = 4k² ⇒ q² = 2k² 

q² = 2k² 

q² is a multiple of 2 ⇒ ∴ q is a multiple of z 

∴ p and q are both multiple of 2 and hence has a common factor z which is a contradiction 

∴ our assumption is wron 

∴ √2 is irrational 

Spindle moulder machine are commonly used to trim and shape wood to make it ideal for various uses such as in shutters, windows, frames, doors, etc.

These tools also allow tenoning for window assemblage, that is, a milling process used to join side jambs to head jambs in window frames and frames in general.

These are ‘secondary processing’ tools, which work on solid wood and are not used on timber that is to be cut to measure, but on wood that is to be finished, milled and subsequently worked.

The guard's main purpose is to provide pressure on the workpiece to hold it very firmly onto the table and horizontally against the fence. Compared to its smaller cousin, the router table, a spindle moulder is able to produce work with a much larger profile such as a crown moulding.