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Working of institution

Which of the following statements about the judiciary is false?
a Every law passed by the Parliament needs approval of the SupremeCourt
b Judiciary can strike down a law if it goes against the spirit of the Constitution
c Judiciary is independent of the Executive
d Any citizen can approach the courts if her rights are violated

Working of institution

Who among the following is a part of the political executive?
a District Collector
b Secretary of the Ministry of Home Affairs
c Home Minister
d Director General of Police

Working of institution

If you are elected as the President of India which of the following decision can you take on your own?
a Select the person you like as Prime Minister.
b Dismiss a Prime Minister who has a majority in Lok Sabha.
c Ask for reconsideration of a bill passed by both the Houses.
d Nominate the leaders of your choice to the Council of Ministers.

Conic Sections

Write the equation of a parabola with vertex at the origin and axis along the x-axis. Identify its focus and directrix.

Complex Numbers

Find the modulus and argument of the complex number 3 minus 4i.

Principle of Mathematical Induction

Prove by mathematical induction that the sum of the first n odd numbers is equal to n squared.

Trigonometry

• Prove that the value of sin squared theta plus cos squared theta equals 1.

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Sets and Relations

Let A be the set of all natural numbers less than 10, and B be the set of all even natural numbers less than 10. Find A union B and A intersection B.

Probability Distributions

1. Define a binomial distribution. What is the probability of obtaining exactly 2 heads in 5 flips of a fair coin?

Differential Equations

• Solve the differential equation dy/dx = 3y.

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