[amp_mcq option1=”5″ option2=”7″ option3=”8″ option4=”None of the above” correct=”option4″]
number theory
2. How many numbers from 1 to 100 are there each of which is not only exactly divisible by 4 but also has 4 as its digit ?
[amp_mcq option1=”7″ option2=”8″ option3=”18″ option4=”25″ correct=”option1″]
3. A prime number between 10 and 40 remains unchanged if its digits are reversed. The square of such a number is
[amp_mcq option1=”12″ option2=”484″ option3=”1089″ option4=”None of the above” correct=”option4″]
4. The sum of squares of three natural numbers is 138 and sum of their products taken two at a time is What is the sum of these numbers?
[amp_mcq option1=”10″ option2=”20″ option3=”30″ option4=”None of the above ” correct=”option4″]
5. How many numbers are there from 3 to 100 which are divisible by 4 and either unit digit or tenth digit or both include 4 ?
[amp_mcq option1=”10″ option2=”11″ option3=”19″ option4=”less than 10 ” correct=”option2″]
6. The last number, which must be added to 7912 to make it a perfect square, is
[amp_mcq option1=”8″ option2=”9″ option3=”12″ option4=”16″ correct=”option1″]
Detailed SolutionThe last number, which must be added to 7912 to make it a perfect square, is
7. Suppose x, y, z are three positive integers such that x < yz and xyz = Which one of the following values of S yields more than one solution to the equation x+y+z=S?
[amp_mcq option1=”13″ option2=”4″ option3=”15″ option4=”16″ correct=”option2″]
8. If 2028 is the product of two natural number shaving two digits each and 13 is their highest common factor, then the numbers are
[amp_mcq option1=”26, 78″ option2=”13, 156″ option3=”36, 68″ option4=”39,52″ correct=”option1″]
9. The smallest number which when increased by 10, is completely divisible by 12, 15, 18, 20 and 24, is:
[amp_mcq option1=”230″ option2=”250″ option3=”290″ option4=”350″ correct=”option2″]