number of theory test questions

Question 1 - Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 (n+m) and (n+m+1) ar..

Scientific Notation - Notation of large number in terms of exponential form, 10 raised to required value. It is also a standart notation representation as " p x 10 q ". where 'p' and 'q' are any integer..

Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..

Question: Define an even number. Answer: A number which is divisible by 2 is called an even number..

Question: Define an odd number. Answer: A number when divided by 2 gives remainder 1 is called an odd number..

Question: When a rational number can be expressed as terminating decimal? Answer: A rational number can be expressed as terminating decimal, when the factors of its denominator are in the form 2 n x 5 ..

Question: If the first term of an AP is 11, the common difference is 3 and the last term is 98, find the number of terms. Answer: 98 = 11 + (n - 1)3 98 - 11 + 3 = 3n 3n = 90 n = 30 Hence the number of terms = 30..

Question: Four numbers are in AP. Sum of the first three is 21 and sum of last three is 30. Find the numbers. Answer: Let the numbers a - 3d, a - d, a + d, a + 3d be in AP. ..

Question: For the given sequence, suggest possible next three terms and find the general term. -3, 1, 5,---- Answer: First term = -3, Common difference = 1-(-3) = 4 = 5 - 1 Next three terms are 5 + 4 = 9, 9 + 4 = 13, 13 + 4 = 17 General term is = a + (n - 1)d = -3 + (n - 1)4 =..

Question: Find four numbers in AP whose sum is 26. Sum of the products of the extremes and the middle terms is 62. Answer: Let (a - 3d), (a - d), (a + d), (a + 3d) be the four numbers in AP The numbers are ..