Condition for n² − 1 to Be Divisible by 8 Video Explanation Watch the video below for a clear explanation: Solution Question: n² − 1 is divisible by 8, if n is: (a) an integer    (b) a natural number    (c) an odd integer    (d) an even integer Step 1: Factorise the Expression […]

General Form of an Odd Integer Video Explanation Watch the video below for a clear explanation: Solution Question: For some integer q, every odd integer is of the form: (a) q    (b) q + 1    (c) 2q    (d) 2q + 1 Key Concept An odd integer is an integer that is not

General Form of an Even Integer Video Explanation Watch the video below for a clear explanation: Solution Question: For some integer m, every even integer is of the form: (a) m    (b) m + 1    (c) 2m    (d) 2m + 1 Key Concept An even integer is any integer that is divisible

Remainder When the Square of a Prime Number Greater Than 3 Is Divided by 6 Video Explanation Watch the video below for a clear explanation: Solution Question: The remainder when the square of any prime number greater than 3 is divided by 6, is: (a) 1    (b) 3    (c) 2    (d) 4

Find the Product of Two Numbers Using Given HCF and LCM Conditions Video Explanation Watch the video below for a clear explanation: Solution Question: If the sum of the LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, find the product of the two numbers. (a) 203400

When LCM and HCF of Two Rational Numbers Are Equal Video Explanation Watch the video below for a clear explanation: Solution Question: The LCM and HCF of two rational numbers are equal. Then the numbers must be: (a) prime    (b) co-prime    (c) composite    (d) equal Important Property For any two rational numbers

Units Digit of 6n − 5n for Any Natural Number n Video Explanation Watch the video below for a clear explanation: Solution Question: If n is any natural number, then 6n − 5n always ends with: (a) 1    (b) 3    (c) 5    (d) 7 Step 1: Observe the Units Digit Pattern The

Divisibility of 92n − 42n for Natural Number n Video Explanation Watch the video below for a clear explanation: Solution Question: If n is a natural number, then 92n − 42n is always divisible by: (a) 5    (b) 13    (c) both 5 and 13    (d) None of these Step 1: Rewrite the

Smallest Rational Number to Be Multiplied with 1/3 for One Decimal Place Video Explanation Watch the video below for a clear explanation: Solution Question: The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal. Step 1: Requirement for One Decimal Place A decimal that

Smallest Number to Be Multiplied with √27 to Get a Rational Number Video Explanation Watch the video below for a clear explanation: Solution Question: The smallest number by which √27 should be multiplied so as to get a rational number is: (a) √27    (b) 3√3    (c) √3    (d) 3 Step 1: Simplify