27. In how many ways can the letters of the word 'LEADER' be arranged?

Ans : 360


Explanation :

The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

Required number of ways =	6!	= 360.
	(1!)(2!)(1!)(1!)(1!)

26. If a - b = 3 and a^2 + b^2 = 29, find the value of ab.

Ans :10

Explanation:
2ab = (a² + b²) - (a - b)²
   = 29 - 9 = 20
   ab = 10.

25. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

Answer: 63

Explanation:

Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) =		7 x 6	x 3		= 63.
		2 x 1

24. Find the output.

void main()
{
int i=3, *j, k;
j = &i;
printf("%d\n", i**j*i+*j);
}

Answer: 
30

23. A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope?

Solution: 

Add all sides 25+11+31 to get rope length rope length =67,rope is made in to as square. So side of square is 67/4=16.75 and so area is 16.75*16.75=280.5625.
Ans : 280.5625

22. If DDMUQZM is coded as CENTRAL then RBDJK can be coded as _____

Ans : QCEIL

21. Four different integers are in increasing AP such that one number is equal to sum of the squares of the other three numbers.

Ans : 1,0,1,2

20. Rs 1,050 are divided among P, Q and R. The share of P is 2/5 of the combined share of Q and R. P gets ?

Ans : Rs 300

19. A train 130 metres long and travelling at 45 km/hr can cross a bridge in 30 seconds. Find the length of the bridge.

Answer:

245 m.  

Explanation:

Speed =		45 x	5	m/sec	=		25	m/sec.
			18				2

Time = 30 sec.

Let the length of bridge be x metres.

Then,	130 + x	=	25
	30		2

 2(130 + x) = 750

 x = 245 m.

18. Pointing to a lady a person said, "The son of her only brother is the brother of my wife." How is the lady related to the person?

Answer:

Sister of father-in-law 

Explanation:

Brother of person's wife → brother-in-law of the person. Hence, the son of lady's brother is brother-in-law of the person.

Therefore, the brother of the lady is the father-in-law of the person. Hence, the lady is the sister of the person's father-in-law.