Exams

Observe that in each column, square of sum of digits in the first row = Respective second row elements.

In the same way, square of sum of digits in the second row = Respective third row elements.

=> 6+42=102=100

=> 4+92=132=169

=> 8+12=92=81.

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.

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.