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Correct option is (C) x + y = 36

The cost of a mango is Rs x and cost of a banana is Rs y. Then, the cost of a mango and a banana is Rs (x+y). But given that the cost of a mango and a banana is Rs 36.

\(\therefore\) x+y = 36

C) x + y = 36

Correct option is (D) 8x + 6y – 1 = 0

\(\frac{x}{3}+\frac{y}{4}=\frac{1}{24}\)

\(\Rightarrow\) \(\frac{4x+3y}{12}=\frac{1}{24}\)

\(\Rightarrow\) 2 (4x+3y) = 1

\(\Rightarrow\) 8x + 6y - 1 = 0

D) 8x + 6y – 1 = 0

Correct option is (A) linear

An equation of the form ax+by+c = 0 is called a linear equation.

Correct option is  A) linear

16a² - \(\frac{25}{4a^2}\)    \(\because\) (a² - b²) = (a - b)(a + b)

(4a)² - \((\frac{5}{2a})^2\) = \((4a-\frac{5}{2a})({4a+\frac5{2a}})\)

Given x = 8 is the root of 12x + 7 = 11.

Now, substituting x = 8 in place of ‘x’ in the given equation, we get

= 12(8) + 7 =11

= 4 + 7 = 11

= 11 = 11

Since, LHS = RHS

Hence, x = 8 is the root of 12x + 7 = 11.

 x + 2y = \(\frac{3}{2}\)

⇒ 2x + 4y = 3 …(i)

 2x + y = \(\frac{3}{2}\)

⇒ 4x + 2y = 3 …(ii)

Multiplying eq2 by 2 and subtracting from eq1

2x + 4y – 8x – 4y = 3 – 6

⇒ - 6x = - 3

⇒ x = 1/2

Thus,

2 × 1/2 + 4y = 3

⇒ y = 1/2

The correct option is B) Facsimile telegraphy.

Fax stands for facsimile. It is an electronic copy of any sort of document which is sent on a telephone no. which is connected to a printer.

It is the kinetic energy gained by an electron when it is accelerated through a potential difference of 1 volt. 

1 eV = 1.6 x 10^-19 J 

1 MeV = 1.6 x 10^-13 J

(b) Violet

E = \(\frac{hc}{λ}\)  Photon in violet region has least λ and hence highest energy.

The correct option is C) 10²⁰

Since E = hv 

Where E = Energy 

h = Planck’s constant and v = frequency. 

Given; 

E = 6.62 J 

v = 10¹⁴ Hz 

Let the no. of photons be x. 

=) E = (x) x (hv) 

=) 6.62 = (x) x (6.62 x 10^-34 Js) x 10¹⁴ 

=) 6.62/6.62 = (x) x (10^-20) 

=) 1 = (x) x (1)/ 10²⁰ 

=) 1020 = x.

E = nhv, where hv is the energy of a photon in a radiation of frequency v and n is the number of photons in the radiation.

∴ n = \(\cfrac E{hv}\) = \(\cfrac{(6.63)}{(6.63\times10^{-34})(10^{14})}\) = 10²⁰

B. Lack of patriotism in Indian soldiers.

D. Wagher women

A. On 4^th June, 1857

Tatya Tope, the strong and brave commander undertook the leadership of Nanasaheb Peshwa’s army.

Jagirdar Kunwarsingh of Jagdishpur undertook the leadership of the revolt in Bihar.

Garbad Das Patel, the headman of Anand in Kheda district collected 2000 volunteers of the Koli and Nayakada communities and undertook the leadership of the revolt in Kheda district.

Though Jagirdar Kunwar singh of Jagdishpur was 70 years of age he fought bravely against the British. He v even chopped off the arm which had been shot during battle. Kunwar singh attained martyrdom due to the grievous injuries he sustained in the battle in April, 1858.

Radius of cannon ball = 14 cm

Volume of cannon ball = 4/3 πr³ = 4/3 π(14)³

Radius of Cone = 35/2 cm

Volume of Cone = 1/3 πr² h = 1/3 π(35/2)² h

Let h be the height of the cone.

From statement:

Volume of cannon ball = Volume of Cone

⇨ 4/3 π (14)³ 

= 1/3 π(35/2)² h

h = 35.84

Therefore, height of the cone is 35.84 cm.

S = {1,2,3,4,5,6}

Let A = event of even number on dice

= {2,4,6}

and B = even number greater than 2

= {4,6}

A ∩ B = {4,6}

Similarly, n(A ∩ B) = 2

n(s) = n(A) = 3

∴ P(B/A) = n(A ∩ B)/n(A) = 2/3

Given equations, 

3x - 4y + 5z = 0 ...(i) 

2x - y - 2z = 0 ...(ii)

According to formula, a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0 is perpendicular if, 

a₁a₂ + b₁b₂ + c₁c₂ = 0

Here, a₁ = 3, b₁ = -4, c₁ = 5

a₂ = 2, b₂ = -1, c₂ = -2 

then a₁a₂ + b₁b₂ + c₁c₂ 

= 3 x 2 + (-4) x (-1) + 5 x (-2)

= 6 + 4 - 10 = 10 - 10 = 0

Hence, eq. (i) and (ii) is perpendicular.

Given the equation

6x - 3y + 2z + 9 = 0

∴ Its parallel equation

6x - 3y + 2z + d = 0

Given that equation passes from origin to 5 cm

∴ 5 = (6(0) - 3(0) + 2(0) + d)/√(6² + 3² + 2²)

d = 5√(36 + 9 + 4)

d = 5√49

d = 5 x 7 = 35

∴ 6x - 3y + 2z + 35 = 0

Correct option is  B) 3x

C) Circumference

Correct option is  A) Perimeter

Given, cos^–1α + cos^–1β + cos^–1γ = 3π … (1)

Principal value of cos^-1 x is [0, π]

So, maximum value which cos^-1 x can have is π.

So, if (1) is correct then all the three terms i.e,

cos^–1α, cos^–1β, cos^–1γ should be equal to π

So, cos^–1α = π

cos^–1β = π

cos^–1γ = π

So, α = β = γ = -1

So, α(β + γ) + β (γ + α) + γ (α + β)

= (-1)(-1-1) + (-1)(-1-1) + (-1)(-1-1)

= 3(-1)(-2)

= 6

There are three ways of heat transmission namely, 

(1) Conduction (2) Convection (3) Radiation

RBCs are destroyed in the spleen.

Here, n = 10; x = weekly growth (in cm) of plant

Mean of growth of plant:
x̄ = \(\frac{Σx}{n}\)
= \(\frac{1.0+3.2+1.4+1.9+2.4+1.6+1.4+2.1+1.3+1.5}{10}\)
= \(\frac{17.8}{10}\)
= 1.78 cm

(i) Bleaching powder-CaOCl₂  

(ii) Ca(OH)2 + CI₂→ CaOCI₂+ H₂O

(iii) Two uses other than disinfection are :

(a) Paper industries (b) Chemical Industries.

Communication through words may be easy but for effective communication emphasis has to be given on the choice of diction. In fact, the impact of any communication depends on the choice of diction. A set of words may convey almost the same meaning but out of these words only a particular word will convey the meaning effectively.

(b) Exhaustible

Wood coal, Hard coal, Dung cakes, Agricultural wastes. Kerosene, diesel, petrol, gasoline, alcohol. Gobar gas, water gas (H₂ + CO) Producer gas (N₂ + CO), Natural gas, Liquefied petroleum gas (LPG) etc. are the fuel used in daily life.

Complete combustion: When sufficient amount of oxygen is supplied to a burning substance, then it bums with blue flame, it is called complete combustion.

Example: combustion of LPG (liquefied Petroleum Gas).

Incomplete combustion: When any combustion substance do not get sufficient amount of oxygen supply, then it bums with yellow flame. It is called incomplete combustion.

Example: Burning of wood that causes air pollution.

Mata Sulakliani, wife of Guru Nanak Dev Ji, belonged to Batala (District Gurdaspur). Guru Nanak Dev Ji had two sons named Baba Sri Chand and Baba Lakhmi Das.

At Sultanpur Lodhi, Guru Nanak Dev Ji worked as Bhandari (the store accountant) in a Lodhi Khana (government storehouse) of Subedar Daulat Khan Lodhi.

Guru Nanak Dev Ji gave the message that ‘No one is a Hindu or Muslim’. These were the first words, which Guru Nanak Dev Ji uttered after attaining enlightenment. The meaning of his message was that all the Hindus and Muslims were equal. It also meant that Hindus and Muslims had forgotten the real message of their respective religions.

Guru Nanak Dev Ji visited the following places during his first Udasi :

1. Guru Sahib went from Sultanpur Lodhi to Sayyidpur where Guru Sahib made Bhai Lalo his follower.
2. Then Guru Sahib visited Talumba, Kurukshetra and Panipat. Guru Sahib gave the message of doing the right deeds to the people of those areas.
3. From Panipat, Guru Sahib reached Haridwar via Delhi. Guru Sahib preached against superstitions at those places.
4. Then Guru Sahib visited Kedarnath, Badrinath,’ Gorakhmatta, Benaras, Patna, Hajipur, Dhubri, Kamrup (Assam) Shillong, Dacca, Jaganath Puri and a number of places in South India. Finally, Guru Sahib came back from Pakpattan to Sultanpur Lodhi via Dipalpur.

Rainwater flows into river and is stored in reservoirs on dams. These are at height and therefore, their water has potential energy.

Our body gets energy from the food we eat.

(1) The preparation of dilute sulphuric acid falls in the category of extreme exothermic process.

(2) During the preparation of dilute sulphuric acid. large amount of water is taken in a glass container which is surrounded by ice. Cool it for twenty minutes, Now small quantity of conc. H₂SO₄ is added slowly with stirring. Therefore, only a small amount of heat is liberated at a time. In this way dilute sulphuric acid is prepared.

(3) On the other hand, in the process of dilution or conc. sulphuric acid with water, very large amount of heat is liberated. As a result, water gets evaported instantaneously, if it is poured in to conc. H₂SO₄ which may cause an accident.

Penicillium: Penicillium is a genus of ascomycetous fungi of major importance in the natural environment as well as food and drug production. Members of the genus produce penicillin, a molecule that is used as an antibiotic, which kills or stops the growth of certain kinds of bacteria inside the body.

Lactobacilli Plus: Gram-positive facultative anaerobic or microaerophilic rod-shaped bacteria. Most of its members convert lactose and other sugars to lactic acid.

(a) When an atom gains one or more electrons an anion is formed. During the change of an atom into an anion the one or more electrons are added to the valence shell of the atom. The nuclear charge remains the same. An increase in the number of electrons in the valence shell reduces the effective nuclear charge due to greater mutual shielding by the electrons. As a result, electron cloud expands, i.e., the ionic radius increases.

(b) A cation is formed when one or more electrons are lost by an atom. The cation formed is always smaller than the size of the parent atom. This may be due to the following reasons.

(i) Disappearance of the valence shell:- In certain cases, the loss of electrons leads to a complete disappearance of the valence shell. Removal of the outermost shell decreases the size.

(ii) Increase of effective nuclear charge:- In a cation, the number of electrons is less than in the corresponding atom. The total nuclear charge remains the same. This increases the effective nuclear charge. As a result, the electrons are attracted towards the nucleus more strongly, thereby leading to a decrease in its size.

Fluorine is the most electronegative element and is given a value of 4.0 (Pauling scale). Therefore, N (Electronegativity = 3) is less electronegative than fluorine.

Glorious Revolution : The Revolution of 1688 in England happened without shedding a drop of blood. This transformation, therefore, is known as “Glorious” or ‘Bloodless Revolution”.

Devine right: The rights that are provided by Gods are called Divine Rights.

(a) the tiger which was brought to fulfil Mrs. Packletide’s desire is referred to as the herd-robber.

(b) the herd-robber was suffering from the infirmities of age. It was feared that he would die before the shooting took place.

(c) venerable means old and respectable.

(d) Restless.