If x^2 + 1/x^2 = 51, find x - 1/x.

The number that exceeds 16% of itself by 42 is:

There are 2 teachers and 5 doctors in a room. What is the probability that no two teachers sit together?

A bag contains 3 red, 6 white, and 7 black balls. Two balls are drawn at random. What is the probability that both are black?

 On 5th December 1993, Nirmala and Raju celebrated their anniversary on Sunday. What will be the day of their anniversary in 1997 ? 

 A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: 

 
Find the speed of the boat in still water, if a boat covers a certain distance upstream in 2 hours, while it comes back in 1`1/2` hours. If the speed of the stream be 3 kmph. 

Mother made a Gulab Jamun in a sphere of radius 6 cm, but she felt it was too big. She then converted the Gulab Jamun into smaller spheres of radius 2 cm. How many small Gulab Jamun spheres were formed?

Sam bought a sharpener, erasers, and pencils. The cost of each eraser is Rs 3, each sharpener is Rs 2, and each pencil is Rs 5. He spent Rs 34 in total and bought at least one of each item. The maximum number of erasers he could have bought is:

An institute has two batches. The second batch has 4/5 as many students as the first batch. The students are making invitations for a function. If each student in the second batch makes 3/4 as many invitations as each student in the first batch, what fraction of all the invitations does the first batch make?