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Describe the three lists of Federalism provided by the Drafting Committee in the Constituent Assembly.
Concept: A Tumultuous Time
Read the source given below carefully and answer the questions that follow:
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"We are not going just to copy" This is what Jawahar Lal Nehru said in his famous speech of 13 December, 1946: We say that it is our firm and solemn resolve to have an independent sovereign republic. India is bound to be sovereign, it is bound to be independent and it is bound to be a republic ... Now, some friends have raised the question: "Why have you not put in the word 'democratic' here?" Well, I told them that it is conceivable, of course, that a republic may not be democratic but the whole of our past is witness to this fact that we stand for democratic institutions. Obviously we are aiming at democracy and nothing less than a democracy. What form of democracy, what shape it might take is another matter. The democracies of the present day, many of them in Europe and elsewhere, have played a great part in the world's progress. Yet it may be doubtful if those democracies may not have to change their shape somewhat before long if they have to remain completely democratic. We are not going just to copy, I hope, a certain democratic procedure or an institution of a so-called democratic country. We may improve upon it. In any event whatever system of government we may establish here must fit in with the temper of our people and be acceptable to them. We stand for democracy. It will be for this House to determine what shape to give to that democracy, the fullest democracy. |
- Define the term sovereignty.
- Which constitutions of the countries were referred by the Constitution Assembly?
- How is democracy explained in this source?
Concept: The Vision of the Constitution
Who among the following demanded justice for women, not reserved seats or separate electorates in the Constituent Assembly?
Concept: Defining Rights
Who among the following in the Constituent Assembly proposed 'horizontal tricolour National flag of saffron, white and green in equal proportion'?
Concept: A Tumultuous Time
Explain the arguments given in favour of strong Centre in the Constituent Assembly.
Concept: The Powers of the State
Match the following:
| Column-I (Leaders) |
Column-II - (Role in the Constituent Assembly) |
||
| A. | Jawaharlal Nehru | i. | President of the Constituent Assembly |
| B. | B.R. Ambedkar | ii. | Constitutional Advisor |
| C. | Rajendra Prasad | iii. | Chairman of the Drafting Committee |
| D. | B.N. Rau | iv. | Worked on the 'Objective Resolution' |
Concept: A Tumultuous Time
Consider the given statements regarding Constituent Assembly and select the correct from the following options:
- Motilal Nehru moved resolution of National flag in the Constituent Assembly.
- G.B. Pant was the Legal Advisor.
- Sardar Patel was the Constitutional Advisor.
- K.M. Munshi was called as Frontier Gandhi.
Concept: A Tumultuous Time
"One of the topics most vigorously debated in the Constituent Assembly was the respective rights of the Central and State governments." Analyse the statement with supporting arguments.
Concept: The Powers of the State
Let A = {1, 2, 3,......, 9} and R be the relation in A × A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)].
Concept: Types of Relations
Let f : N→N be a function defined as f(x)=`9x^2`+6x−5. Show that f : N→S, where S is the range of f, is invertible. Find the inverse of f and hence find `f^-1`(43) and` f^−1`(163).
Concept: Inverse of a Function
Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.
Concept: Types of Relations
If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.
Concept: Types of Relations
If the function f : R → R be given by f[x] = x2 + 2 and g : R → R be given by `g(x)=x/(x−1)` , x≠1, find fog and gof and hence find fog (2) and gof (−3).
Concept: Inverse of a Function
If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3`, show that fof (x) = x for all `x ≠ 2/3`. Also, find the inverse of f.
Concept: Types of Relations
The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at ______.
Concept: Types of Functions
Read the following passage:
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An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. |
Based on the above information, answer the following questions:
- How many relations are possible from B to G? (1)
- Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
- Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
OR
A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)
Concept: Types of Relations
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
Concept: Properties of Inverse Trigonometric Functions
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
Concept: Properties of Inverse Trigonometric Functions
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Concept: Inverse Trigonometric Functions (Simplification and Examples)
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Concept: Properties of Inverse Trigonometric Functions
