A family went to a restaurant for dinner. The bill of ₹3000 was handed, which was not inclusive of the 4% Goods and Service Tax (GST). The final bill amount would be?

Option 1) ₹3120

Option 2) ₹3300

Option 3) ₹3395

Option 4) ₹3595

Four points given by position vectors (2 \vec{a} + 3 \vec{b} - \vec{c}, \vec{a} - 2 \vec{b} + 3 \vec{c}, 3 \vec{a} + 4 \vec{b} - 2 \vec{c}) and (\vec{a} - 6 \vec{b} + 6 \vec{c}) are coplanar, where (\vec{a}, \vec{b}) and (\vec{c}) are non-coplanar vectors.
A) True
B) False

If f(x) = (x - a)(x - b), then if a and b are the zeros of the polynomial f(x), f(a) = f(b).

1. True

2. False

Give the structures and IUPAC names of monohydric phenols with the molecular formula C₇H₈O.

Find the value of the given expression

[ \left(x^{3}+2x^{2}+3x\right) \div 2x ]

A ( \frac{1}{2}\left(x^{2}+2x+3\right) )

B ( \frac{1}{2} )

C ( \left(x^{2}+2x+3\right) )

D 1

You have budgeted $66 a month to spend on yoga classes. Your yoga studio charges $22 per month membership fee, plus $5 per class attended. Find the possible number of classes you can attend each month.

A. 8
B. 7
C. 6
D. 9

A force of 20 N acts on a body of mass 4 kg for 5 seconds when it is initially at rest. Calculate the velocity acquired by the body and the change in momentum of the body.

(-8) x (3) = ____
Option 1) -24
Option 2) 24
Option 3) 26
Option 4) -26

Find the coefficient of c in the product of (c + 8)(c - 7).

Option 1) 1
Option 2) -1
Option 3) 2
Option 4) -2

The process in which excess water comes out in the form of vapor through leaves is called transpiration.
Option 1) transpiration
Option 2) photosynthesis
Option 3) respiration
Option 4) digestion

Passage

Those who try to keep up with discussions on current affairs in the newspaper and on television may be forgiven if they conclude that caste is India’s destiny. If there is one thing the experts in the media who comment on political matters have in common, it is their preoccupation with caste and the part it plays in electoral politics. Many are now coming to believe that, despite the undeniable demographic, technological, and economic changes taking place in the country, the division into castes and communities remains the ineluctable and ineradicable feature of Indian society. They also believe that to ignore those divisions or to draw attention to other divisions such as those of income, education, and occupation is to turn our backs on the ground reality. The more radical among them add that ignoring those realities amounts to an evasion of the political responsibility of redistributing the benefits and burdens of society in a more just and equitable manner. Does nothing change in India? A great many things have, in fact, changed in the last 60 years, both in our political perceptions and in social reality. The leaders of the nationalist movement who successfully fought for India’s freedom from colonial rule believed that India may have been a society of castes and communities in the past but would become a nation of citizens with the adoption of a new republican constitution. They were too optimistic. The Constitution did create rights for the citizen, but it did not eradicate caste from the hearts and minds of the citizens it created. For many Indians, and perhaps the majority, the habits of the heart are still the habits of a hierarchical society.

“What does the author imply by ‘the habits of the heart are still the habits of a hierarchical society’?”

Those who stay informed about current events through newspapers and television might be forgiven if they conclude that caste is indeed India’s fate. If there is one thing that experts who discuss political matters in the media have in common, it is their fixation on caste and its role in electoral politics. Many have now come to believe that despite the undeniable demographic, technological, and economic changes occurring in the country, the division based on caste and community remains an inevitable and irredeemable characteristic of Indian society. They also believe that ignoring these divisions or drawing attention to other divisions, such as those based on income, education, and profession, signifies turning away from the core reality. Some of the more radical among them add that ignoring these realities amounts to evading the political responsibility of justly and equitably redistributing the benefits and burdens of society. Does nothing change in India? In fact, many things have changed significantly in our political consciousness and social realities over the last sixty years. The leaders of the nationalist movement, who successfully fought for India’s freedom from colonial rule, believed that while India may have been a society of castes and communities in the past, it would become a nation of citizens with the adoption of a new democratic constitution. They were overly optimistic. The constitution did indeed create rights for citizens, but it did not eliminate caste from the minds and hearts of the citizens it established. For many Indians, or perhaps most, the habits of the heart remain those of a stratified society.

“What does the author mean by saying, ‘the habits of the heart are still the habits of a hierarchical society’?”

Option 1: Income and occupation-based hierarchy has come to dominate the hearts of Indians.
Option 2: The Indians continue to believe and behave according to castes and communities.
Option 3: Caste continues to play its role in the minds of the politicians.
Option 4: Caste shall remain India’s destiny.

Consider a piston cylinder arrangement with a spring at its natural length. Due to heat transfer, the gas expands until the piston hits the stop. The mass of the piston is 10 kg and the area is 78 cm². The initial and final specific internal energies are 214 kJ/kg and 337 kJ/kg. Then, find the correct options. (K = 10000 N/m; g = 9.8 m/s²; x = 5 cm)

A. Initial pressure of gas is 112.5 kPa.
B. Work done by gas on the piston is approximately 56.5 J.
C. Work done by gas on the piston is 100 J.
D. Heat transfer for 0.5 g of gas is 118 J.

An air chamber of volume V has a neck of cross-sectional area a into which a light ball of mass m can move without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air is B, the time period of the resulting oscillation of the ball is given by:

(A) ( T = 2 \pi \sqrt{\frac{B a^{2}}{m V}} )
(B) ( T = 2 \pi \sqrt{\frac{B V}{m a^{2}}} )
(C) ( T = 2 \pi \sqrt{\frac{m B}{V a^{2}}} )
(D) ( T = 2 \pi \sqrt{\frac{m V}{B a^{2}}} )

The species in which the N atom is in a state of sp hybridization is:
(A) NO₂⁻
(B) NO₃⁻
(C) NO₂
(D) NO₂⁺

Which of the following is the common test for protein?
Option 1) Pink colour
Option 2) Blue-black colour
Option 3) Violet colour
Option 4) Red colour

Teflon is
A (\left[\mathrm{CF}_{2}-\mathrm{CF}_{2}\right]_{n})
B (\left[\mathrm{CF}_{2}-\mathrm{CCl}_{2}\right]_{n})
C (\left[\mathrm{CBr}_{2}-\mathrm{CBr}_{2}\right]_{n})
D (\mathrm{CF}_{2} \mathrm{Cl}_{2})

Be and Al exhibit many properties which are similar. But the two elements differ in:

Option 1) exhibiting amphoteric nature of oxides

Option 2) forming polymeric hydrides

Option 3) forming covalent halides

Option 4) exhibiting maximum covalence in compounds

Intermediaries which carry disease-causing microorganisms from one person to another are called vectors.

1. True
2. False

Magnetic force fields are produced due to:

Option 1) Moving charges

Option 2) Moving and stationary charges

Option 3) Stationary charges

Option 4) None of these

Tribal lands remain highly militarised in the North Eastern region of India.
Option 1) Northern
Option 2) North Eastern
Option 3) Southern
Option 4) South Western