Exams

List of fundamental duties of the citizens of India in Article 51A of the Indian Constitution :

1. to abide by the constitution and respect its ideal and institutions;

2. to cherish and follow the noble ideals which inspired our national struggle for freedom;

3. to uphold and protect the sovereignty, unity and integrity of India;

4. to defend the country and render national service when called upon to do so;

5. to promote harmony and the spirit of common brotherhood amongst all the people of India   transcending religious, linguistic and regional diversities, to renounce practices derogatory to the   dignity of women;

6. to value and preserve the rich heritage of our composite culture;

7. to protect and improve the natural environment including forests, lakes, rivers, and wild-life       and to have compassion for living creatures;

8. to develop the scientific temper, humanism and the spirit of inquiry and reform;

9. to safeguard public property and to abjure violence;

10. to strive towards excellence in all spheres of individual and collective activity

11. 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.

Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=> x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by

Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r

Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400

q = 1/3 (p + r) => 3q = p + r

Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300

r = 1200 - (p + q) => r = Rs.500.