Practice Test

Q1) Let P = { 2,3,4,....,100} and Q = { 101,102,103,....200}. How many elements of Q are there such that they do not have any element of P as a factor ? Show Answer

Q2) What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8 ? Show Answer

Q3) A certain number in a certain base is 144. Which of the following is always true ?
I. Square root of the number written in the same base is 12.
II. If base is increased by 2, the number becomes 100. Show Answer

Q4) A rectangle is drawn such that none of its sides has length greater than 'a'. All lengths less than 'a' are equally likely. the chance that the rectangle has its diagonal greater than 'a' is ( in terms of %) Show Answer

Q5) If x is a real number, [x] is greatest integer less than or equal to x, then 3|x| +2 - [x] =0. Will the above equation have any real root ? Show Answer

Q6) A vessel has a milk solution in which milk and water are in the ratio 4 : 1. By addition of water to it, milk solution with milk and water in the ratio 4 : 3 was formed. On replacing 14 L of this solution with pure milk the ratio of milk and water changed to 5 : 3. What is the volume of the water added ? Show Answer

Q7) A, B and C can independently do a work in 15 days, 20 days and 30 days, respectively. They work together for some time after which C leaves. A total of Rs. 18000 is paid for the work and B gets Rs. 6000 more than C. For how many days did A work ? Show Answer

Q8) Find the complete set of values that satisfy the relations | |x| - 3| < 2 and || x| - 2| < 3. Show Answer

Q9) Letters of the word " ATTRACT" are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the three letters on a piece of paper and then replace the three cards. The exercise ends when all possible combinations of letters are exhausted. Then, he is asked to strike out all words in his list, which look the same when seen in a mirror. How many words is he left with ? Show Answer

Q10) When asked for his taxi number, the driver replied, " If you divide the number of my taxi by 2,3,4,5,6 each time you will find a remainder of one. But, if you divide it by 11, the remainder is zero. You will also not find any other driver with a taxi having a lower number who can say the same ". What is the taxi number ? Show Answer

Q11) A student is asked to form numbers between 3000 and 9000 with digits 2,3,5,7 and 9. If no digit is to be repeated, in how many ways can the student do so ? Show Answer

Q12) The side of an equilateral triangle is 10 cm long. by drawing parallel to all its sides, the distance between any two parallel lines being the same. The triangle is divided into smaller equilateral triangle, each of which has sides of length 1 cm. How many such small triangles are formed ? Show Answer