Question
Find the smallest positive integer n such that 6n + 5 is
divisible by 7.Solution
ATQ,
6n + 5 ≡ 0 mod7 → 6n ≡ 2 → n ≡ 2×6⁻¹ mod7 → 6⁻¹ ≡ 6 (since 6×6 ≡ 1 mod7) → n ≡ 12 ≡ 5 mod7 → n = 5.
If (a + b) = 7 and ab = 10, then find the value of (a 2 + b 2 ).
If a, b and c are integers such that a 2 + b 2 + c 2 = 228, a + b + c = 26 and b = c, then find the value of a?
If
= -2 then find if a2 + b2 + c2 = 2(3a -5b -6c)-70 , then a-b-c = ?
If (10 a³ + 4b³): (11a³ — 15b³) = 7:5, then (3a + 5b): (9a - 2b) = ?
If x = 15, find x5 - 16x4 + 16x3 - 16x2 + 16x - 16 = ?
- If (x 2 = 2x – 1), then find the value of [x³ + (x⁴/1)][1 - x³]
A shopkeeper marked his article 25% above its cost price and offered a discount of 30%. If cost price of the article is Rs. 560, then find profit or los...
If x2a = y2b =z2c ≠ 0 and x2 = yz, then the value of (ab + bc + ca) /bc is :
If (p + q) = 12 and pq = 32, then find the value of (p² + q²).
