List of practice Questions

For the hyperbola \(H: x^2 – y^2 = 1\) and the ellipse \(E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b>0\),  let the 
(1) eccentricity of E be reciprocal of the eccentricity of H, and 
(2) the line \(y= \sqrt\frac{5}{2}  x+k\) be a common tangent of E and H. 
Then \(4(a^2 + b^2)\) is equal to _______.

Select the most appropriate preposition/word/group of words to fill in the blank to make the given sentence most meaningfully complete :
Do not waste time and energy in being jealous ______ your rival's success.

2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure. The temperature of the calorimeter rises from 298 K to 300 K. The enthalpy change during the combustion of coal is –x kJ mol^–1. The value of x is ______.(Nearest integer)
(Given : Heat capacity of bomb calorimeter is 20.0 kJ K^–1. Assume coal to be pure carbon)

Two satellites A and B, having masses in the ratio 4 : 3, are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is

When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is _____ J. [nearest integer] (Given : R = 8.3 J K^–1 mol^–1 and log 2 = 0.3010)

All whales are mammals. All creatures breathe. Some whales are creatures. Mickey Mouse is a whale. Examine the following statements :
I. Mickey Mouse breathes.
II. Mickey Mouse does not breathe.
III. Mickey Mouse is a creature.
IV. Mickey Mouse is not a creature.
V. Mickey Mouse is a mammal.
VI. Mickey Mouse is not a mammal.
Choose the most appropriate answer.

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C).
(Given: coefficient of linear thermal expansion of gold α_L = 1.4 × 10^–5 K^–1)

Let f : [0, 1] → R be a twice differentiable function in (0, 1) such that f(0) = 3 and f(1) = 5. 
If the line y = 2x + 3 intersects the graph of f at only two distinct points in (0, 1) then the least number of points x ∈ (0, 1) at which f”(x) = 0, is ___________.

Choose the grammatically correct option for each of the following sentences.

The market for extremely short period loan is called........

The 45th FIDE Chess Olympiad will beheld in. … …

Who is hosting the 2022 Commonwealth Games?

In which sport is the term'Love'used?

Choose among the following investment instruments which has high risk,high volatility and high return?

Which among the following sector is a priority sector as per RBl?

World Economic Outlook'is published by......

Open Network for Digital Commerce is a private non-profit Section 8 company established by the Department for Promotion of Industry and Internal Trade of Government of India to develop open e-commerce.Name the first company to join this network.

James Webb Space Telescope is named after James Edwin Webb who worked at NASA as........

Draft Red Herring Prospectus filed by a company which plans IPO with SEBI does not contain information related to

…………is a minimum percentage of deposits that a commercial bank has to maintain in the form of liquid cash,gold or other securities.

Name the first foreign country to adopt India's Unified Payment Interface

is the India's first home-grown Asset Management Platform where individuals can store digital assets.

Autoliv Inc;is a fortune 500 company which is setting up its manufacturing plant in Tamil Nadu at an investment of 100 crore.Name the headquarter of this company.