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📚Explanationto👆👆 Question7️⃣ ✅️What smallest number should be subtracted from 9805 so that it is divisible by 8? a) 6 b) 7 c) 5 d) 8 Answer: (c) 5 📝📝📝📝📝📝📝📝📝📝📝📝📝 ✅Solution: On dividing 9805 by 8, the remainder is 5. So, 5 is the smallest number which should be subtracted from 9805 to make it divisible by 8.

✅Explanation to Question ️6️⃣👆👆 👉Which of the following number is divisible by 9? a) 56785 b) 45678 c) 65889 d) 67578 Answer: (c) 65889 📝📝📝📝📝📝📝📝📝📝📝📝📝 ✅Solution: A number is divisible by 9 if the sum of its digits is divisible by 9. 📝The Sum of the digits of the given numbers are: 6+7+5+7+8= 33 5+6+7+8+5= 31 6+5+8+8+9= 36 4+5+6+7+8= 30 📝The sum of the digits of the number 65889 is 36, which is divisible by 9, so the correct answer is 65889. ============================ ✅Help us reach students who may need this channel 📌Join, Share 👇 https://t.me/tutorialpointeth

✅Question 5️⃣👆👆The sum of odd numbers upto 240 is - a) 11400 b) 12400 c) 13400 d) 14400 📚Answer: (d) 14400 📝SOLUTION: Number of odd numbers up to 240 = 240/2 = 120 starting with 1, and 1, 3, 5, 7, …, 239. This an arithmetic sequence with first term A1=1, and common difference d=2. The sum of the nth terms is given by: S(n)=n[2A1 =(n-1)d]/2 =n[2+2n-2]/2 =n^2 Therefore, the sum of first n odd numbers = n^2 n = 120 Required sum = 120^2 = 14400

✅️Question️4️⃣👆👆Which of the following is the unit digit in the product of 853 x 452 x 226 x 1346? a) 2 b) 5 c) 6 d) 7 Answer: (c) 6 📝📝📝📝📝📝📝 📚Explanation: Pick up the unit digit of each number and multiply them; 3 in 853 2 in 452 6 in 226 6 in 1346 Therefore 👉3 x 6 x 2 x 6 = 216 (consider the unit digit in the product) So, the unit digit in the product of 853 * 1346 * 452 * 226 is 6.

✅3) What will be the value of x3 + y3 + z3, if x + y + z = 0? a) 3xyz b) 2xyz c) xyz d) xyz(xy + yz + zx) 🔴Answer: (a) 3xyz 🟢Solution🔴 It is given that x + y + z = 0 On cubing both sides, we will get (x + y + z)^3 = 0 (x + y + z)^3 =x^3+y^3+z^3+6xyz+x^2(3y+3z)+y^2(3x+3z)+z^2(3x+3y) ……(*) since x+y+z=0 equation (*) reduces to x^3 + y^3 + z^3 - 3xyz = 0 So, the value of x^3+y^3+z^3 is equal to 3xyz🟢

✅Explanations to Question 2️⃣Above👆2) Between any two numbers, there are - a) Two rational numbers b) No rational number c) Infinite rational numbers d) None of the above 🔴Answer:(c) Infinite rational numbers 🟢Find a rational number between 2/5 and 3/6. For this add the two numbers and divide the result by 2 as follows. (2/5 + 3/6)/2 Taking LCM = [(12 + 15)/30]/2 By further calculation = (27/30)/2 So we get = 9/10 × 1/2 = 9/20, and it is between 2/5 and 3/6 By the same method we can find rational numbers between 2/5 and 9/12, and 9/12 and 3/6. This process can continue indefinitely.