Step 1: Understanding the 86th Constitutional Amendment Act, 2002:
The 86th Amendment to the Constitution of India, enacted in 2002, was a landmark amendment focusing on the right to education. It introduced significant changes to the Fundamental Rights, Directive Principles of State Policy, and Fundamental Duties.
Step 2: Analyzing the Changes Introduced:
It inserted Article 21-A into the Constitution, making the Right to Education a Fundamental Right for children between the ages of 6 and 14 years.
It modified the Directive Principle in Article 45 to direct the state to provide early childhood care and education for all children until they complete the age of six years.
It added a new Fundamental Duty under Article 51-A(k). This new duty states: "It shall be the duty of every citizen of India who is a parent or guardian to provide opportunities for education to his child or, as the case may be, ward between the age of six and fourteen years."
Step 3: Evaluating the Options:
Option (A) and (B) are not listed as Fundamental Duties.
Option (C) directly corresponds to the new Fundamental Duty added by the 86th Amendment under Article 51-A(k).
Option (D) is a Fundamental Duty under Article 51-A(a), but it was part of the original set of duties, not added by the 86th Amendment.
Step 4: Final Answer:
The Fundamental Duty inserted by the 86th Amendment is the responsibility of parents/guardians to provide opportunities for education to a child between the ages of 6-14.
Match List-I with List-II
List-I (Statement) | List-II (Article) |
---|---|
(A) Equal pay for equal work for man and woman | (I) Article 43 |
(B) Just and human condition for work and maternity relief | (II) Article 47 |
(C) Living wage and decent standard of life of labour | (III) Article 39(d) |
(D) High level of nutrition and standard of living and improving public health | (IV) Article 42 |
Choose the correct answer from the options given below:
Match List-I with List-II for the index of refraction for yellow light of sodium (589 nm)
LIST-I (Materials) | LIST-II (Refractive Indices) | ||
---|---|---|---|
A. | Ice | I. | 1.309 |
B. | Rock salt (NaCl) | II. | 1.460 |
C. | CCl₄ | III. | 1.544 |
D. | Diamond | IV. | 2.417 |
Choose the correct answer from the options given below:
Match the LIST-I with LIST-II
LIST-I | LIST-II | ||
---|---|---|---|
A. | Compton Effect | IV. | Scattering |
B. | Colors in thin film | II. | Interference |
C. | Double Refraction | III. | Polarization |
D. | Bragg's Equation | I. | Diffraction |
Choose the correct answer from the options given below:
Match List-I with List-II on the basis of two simple harmonic signals of the same frequency and various phase differences interacting with each other:
LIST-I (Lissajous Figure) | LIST-II (Phase Difference) | ||
---|---|---|---|
A. | Right handed elliptically polarized vibrations | I. | Phase difference = \( \frac{\pi}{4} \) |
B. | Left handed elliptically polarized vibrations | II. | Phase difference = \( \frac{3\pi}{4} \) |
C. | Circularly polarized vibrations | III. | No phase difference |
D. | Linearly polarized vibrations | IV. | Phase difference = \( \frac{\pi}{2} \) |
Choose the correct answer from the options given below:
For Particular Integral, Match the LIST-I with LIST-II
LIST-I | LIST-II | ||
---|---|---|---|
A. | \( \frac{1}{(D-1)} x^2 \) | I. | \( xe^x \) |
B. | \( \frac{1}{D^2+D+1} \cos x \) | II. | \( \sin x \) |
C. | \( \frac{1}{(D-1)^2} e^x \) | III. | \( \frac{x^2 e^x}{2} \) |
D. | \( \frac{1}{D^3-3D^2+4D-2} e^x \) | IV. | \( -(x^2 + 2x + 2) \) |
(Note: List-I Item A is assumed to be \( \frac{1}{D-1} x^2 \) based on the options)
If \( x = r\cos\theta, y = r\sin\theta \) then Match the LIST-I with LIST-II
LIST-I | LIST-II | ||
---|---|---|---|
A. | \( \frac{\partial r}{\partial x} \) | I. | \( \frac{1}{r} \) |
B. | \( \frac{\partial r}{\partial y} \) | II. | \( \frac{y}{r} \) |
C. | \( \frac{\partial(x,y)}{\partial(r,\theta)} \) | III. | \( \frac{x}{r} \) |
D. | \( \frac{\partial(r,\theta)}{\partial(x,y)} \) | IV. | \( r \) |
(Note: There is a typo in the question; it should be \( y = r \sin\theta \))