1. Orthocentre of the triangle with vertices (0,0), (3,4), and (4,0) is

a. 3, 5/4

b. 3,12

c. 3, 3/4

d. 3,9

2. The number of integral piont (integral point means both the coordinates should be integers) that lie exactly in the interior of the triangle with vertices (0,0), (0,21) and (21,0) si

a. 133

b. 233

c. 190

d. 105

3. Which of the following expressions are meaningful

(u,v and w are vectors)

a. u.(v×w)

b. (u.v).w

c. (u.v)w

d. u×(v.w)

4. An n digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only three digits 2,5, and 7. The smallest value of n for which this is possible is

a. 6

b. 7

c. 8

d. 9

5. In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. the number of news papers is

a. at least 30

b. at most 20

c. exactly 25

d. none of the above.

Problems 1 and 2 are from Jee 2003

Problems 3 to 5 are from Jee 1998

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