Crack RRB Group D 2026 ALGEBRA 02 + PYQ | Tamil - Part 50

[00:00:00]Hello friends, welcome to Chandra Gr x + 1 X X value.

[00:00:38]So X + 1 X + 1 X first a + 1 A 6 then find the value of a square + 1 by A square. Okay. A + 1.

[00:01:01]So a square + 1 square a + 1 square.

[00:01:19]So a + 1 a square a square a + 2 a 2 into a into 1 a + b square 1= 6 36 remaining a square + 1 by a square + 2 36. So a square + 1 square for exam purpose. So x + 1 x x + 1 x² + 1x² thenus value then x + 1 x - 3 a plus so x + 1 x a - 3 a + 1 x 4 + 1 x four Continuation.

[00:03:26]Right. Okay. Next. Kelvin.

[00:03:35]X² - 1 by X 4 Find X^ 6 - 1 by X - 1 by X so X - 1 by X X - 1 by X so - 1 X² - 1 by X1 4 x² x - 1x = four x^ 6 - 1x 6 by x - 1 x 3 - 1 x X - 1 by x - 1x - 1 = a + 3 a x - 1 x + 3 x^ 5 - 1 by x^ 5.

[00:05:26]So a + 3 aus a + 3 x + 3 into 4.

[00:05:47]So 4 cube + 3 into 4 4 cube 64 3 4 are 12. So 64 + 12 76.

[00:06:06]If x² + 1x square 47 then find the value of x + 1x.

[00:06:12]So x square + 1 x square 47uscus equus 2 47 a square 49 x + 1 x= 7 reverse okay x + 1<unk> 8 find the value of x - 1x so x + 1x 3<unk> 8 x - 1 by x.

[00:07:16]So x + 1 x - 1 x 3 - 4 x - 4 x - x + 1 + right square 3<unk> 8 square 9 into 8 uh 98 72 - 4 68.

[00:08:06]So roo<unk> 68 roo<unk> 68 4 into 17. So four cancel right X + 1 X power n x n - 1 by x.

[00:08:52]So x^ n roo<unk> over a power n sorry a power 2 - 4 x Right.

[00:09:22]square 123 x² + 1x² x + 1 x + 1 a square a - 23 square.

[00:09:52][snorts] So a square 125 square 125. So 25 x + 1 whichever is okay 1 square 12 square root 121 which is equivalent to 11 simple x =<unk> 10 + 3 value of x - 1 x + 3 x + 1 xq 1x right x - 1 x - 1 x - 1 x - 1 x - 1 x a + 3 x - 1 1x 1 of this 10 + 3<unk> 10 plus roo<unk> 9 cor Right.

[00:12:09]x already 10 + 3us 1x<unk> 10 - 3 so plus roo<unk> 10 - roo<unk> 10 cancel sorryus 3 + 3 6 - right. So x value roo<unk> 10 + 3 1 x value roo<unk> 10us 3 - roo<unk> 10 + 3. So plus roo<unk> 10 - 10 cancel. So 3 + 3 6 right. Right. So x - 1 by x.

[00:13:01]So a cube 6 cube + 3 a 3 3 into 6 6 cube 2 and 6 + 18.

[00:13:11]So 234 option number four right okay right okay six sum or product given find express and a unknown so A model. A machine produces two types of widgets. The number of widgets produced per day of type A is A and of type B is B. If a + b is 50, a + a square + b square is 1,300.

[00:14:04]Then find the product of number of widgets produced per day of the two types.

[00:14:20]A square + B square.

[00:14:27]Okay. A B [snorts] A + B 15 A square + B square,300 [snorts] A square B square A whole square for a square + b² + 2 a.

[00:15:06]So 50² = a square + b square + 2 a. So 50 square a 2 a 20032 600 so statementing Simple, right?

[00:15:55]Find the product of two numbers whose sum is 24 and whose difference is eight.

[00:16:09]X Y + Y 24 right answer. So 2x 2 2x = 24 + 8 32. So 16 first 16 y= 24 16 So 16 into 8 16 right of two numbers.

[00:17:40]who sums difference given a + c + b + C the whole square. A + B + C the whole square. Now A square + B square + C square + 2 into A B + B C + C A + B + C the whole square= A square + B square + C square + 2 into A + B C + C A + B + C the whole square A + B + C.

[00:18:37]So 15 square = a square + b square + c square + 2 into a b + b c plus c 15 square 22 a b c a b c plus b c + c. So 1425 3us 142. So a plus b c plus c option number four.

[00:19:35]If 2x + 3 y = 8 4x² + 9 y = 32 8 x + 27 y + 27 y formula 8 x + 27 y number 27 number x A bul 2x X + a + b first. So 2x + 3 y a + b then a + bul a + b the whole square a square into a 2x b 3 y right so 2x x + 3 y a + b square. Sorry.

[00:21:28]Yes. 2x + 3.

[00:21:31]So 8 uh 2x + 3 y the whole square 8 square - 3 into 2 uh into 3 3 into 6 6 18 18 xy Okay.

[00:22:00]A square + b square= a square + b square + 2 a.

[00:22:09]So 2x + 3 y the whole square for 4x² + 9 y² + 2 3 6 6 12 12 x y a + a square + b square + 2 a b right 2 a + 3 8 square 4x + 9 X square + 12 X Y. So 8 square 64 64 32 32 32 12 X Y XY 32 by 12.

[00:23:04]So 8 into 64 8 square 64. So 64 minus 18 into 8 by 3.

[00:23:17]So 3 18 cancel 6. So 8 into 64 - 68 48 48 64 subract 64 48 subtract 16. So 8 into 16 again 128.

[00:23:33]Yeah. So a + a square for a square + b square + 2 a + a + b the whole squareus 3 So right a square + 24 find the value of 2. So, so I think you can solve this.

[00:24:39]A + B the whole square minus A minus B the whole square A square B square P= 4 A A 4 square plus a b square. So a minus b the whole square + 4 a right.

[00:25:21]So a b square a - 6. So 6 square + 4 into a 135.

[00:25:30]So 6 square 36 4 into 135 540. So 36 + 540 add 576 A square root square 24 right a + b 4 A B3 A.

[00:26:16]Okay.

[00:26:18]And then square b 21 a b.

[00:26:44]So obviously answer right.

[00:26:58]Okay.

[00:26:59]X - Y 3 X - Y square X - Y square X - Y square X X + Y into X - Y - Y already X + X + Y X + Y square. So X square X - Y X - Y X. So x + y the whole square x - y the whole square + 4 x y - y 3. So 3² + 4 into xy 4 into 18 72 72 + 9 81. So x + y square x + y x + y - y 3. So 9 3's are 27.

[00:28:33]here. Right.

[00:28:42]X + 3 +<unk> 22 Y 3 -<unk>2 X + Y square X + Y X + Y square X + Y 32 3 - 22 the number 32 + 3 -<unk>2 so x 3 + 3 x + y <unk>22 into 3 -<unk>22 So a square b square. So a square 3 into 3 3² 9 roo<unk>2 into roo<unk> 22 22. So - 22. So 9 - 22 -3 x + y + y square. So x² + y² = x² + y square x + y x + y the whole square simple.

[00:30:22]So x + y square 6² - 2 into x y -3. So 6 square 36 - 2 into -3 + 26. So 36 + 26 62 option 62.

[00:30:48]This is the correct answer.

[00:30:52]Right.

[00:30:56]Add the KV. The product of two numbers is 96 and the sum is 20. Find the value of the square of the difference. So the product of two numbers.

[00:31:25]So first 96 + yul.

[00:31:44]So 126 12 + 8 20 square x - y 12 - 8 the whole square 12 - 8 square right linear equations and word problems. So the number is 18 more than it's 34. Find the number is 18 more than it 34. number then it's 3/4 by 3 sorry 3x 3x Okay. 3x4.

[00:33:40]So 3x 4 x + 18.

[00:33:54]So 3x + 18 = 3x + 42x 3x4 Four parts four parts.

[00:34:59]Right.

[00:35:01]Number doubled and increased by seven becomes 29. Find the number 2 +al.

[00:35:19]So 2x so 29 22 by 2 simple equation statement a student thinks of a twodigit number that the digits add up to 15 and the greater digit is three more than the smaller What is the product of two digits?

[00:36:05]So 2 18.

[00:36:45]So x 15 6 add 15 15. So 9 + 6 uh 9 + sorry 9 + 6 15 9 - 6 Okay 54 right a twodigit number is 7.75 times the sum of its digits if digits are reversed the number decreases by 55 Four. What is the original number?

[00:37:39]Okay.

[00:37:41]twodigit number.

[00:37:49]For examp 1 2 3 4 5 6 7 8 Number system.

[00:38:31]So 70 + 1 7 into 10 + 1 7 into 10 + [snorts] 5 31 5 into 100 + 3 into x y 51. So concept 10 x + y 10 x + y fraction 75 / 100.

[00:39:40]So cancel 4 into 25 uh 3 into 25 1 into 25. So 31.

[00:39:49]So 31x4 fraction fraction 31 by4 31x4 Simp y 10 x + y right 10 x + 4 into 10 40 40x + 4 y = 31 31x + 31 y.

[00:40:47]So 40x 31 x 31 y 4 y 27 y right 10 x + y 10 y + x y + 10 x + y - y x + x - 10 x = 54 - 54. So 9 y - 9x = - 54 9 x - 9 y = 54 into 3 27 y.

[00:42:47]So 27 y - 9 y = 54. So 27 y - 9 y 18 y 18 y 54 y 3. So y 3 into 3 9 y 3. So original number 10 x + y original number. So 10 into x 9 + 3 10 into 3 + 9.

[00:43:20]So 93 number 10 y + x, right?

[00:43:42]Okay.

[00:43:43]If 9 is subtracted from the numerator of a fraction, it becomes 2x 9. And if 12 is added to the denominator, it becomes 1x 3. What is the sum of the numerator and denominator of the original fraction?

[00:43:59]foreign.

[00:44:11]Okay.

[00:44:14]Y X 2 by 9 right 1 by 3 1 by three. So multiply 9 into x 9 into 9 81 2 9 x = 2 y + 81. Right.

[00:45:30]3x y + 12.

[00:45:38]So 3x 9 y + 36 right 2 y + 81 3 y + 36= So 2 y 3 y sub y 81 - 36 subract 45 So y So first equation 9 3x = y + 12. So 45 + 12 57 57 / 3 19. So x + y 19 + 45.

[00:46:42]So total on the uh 64 right okay the product of two consecutive odd numbers is 16,383 which is the smaller one two consecutive odd numbers.

[00:47:26]First one odd number three odd number five. So consecutive odd numbers 1 3 3 5 odd numbers 123 number 12. So three last 15. So last option then 127 number 129. So 97 9 3 are 9 sevens are 63. So possibility 125 125 number 127. So five.

[00:48:33]So five. So possibility then 9 [clears throat] 129 odd number 131. So answer. So 127 is your answer. Okay.

[00:48:55]Simple.

[00:49:03]Okay. The sum of digits of a two-digit number is five. If nine is added to this number, the digits inter change their places. Find the number.

[00:49:24]x 10 x + y.

[00:49:30]Okay.

[00:49:38]Then 10 x.

[00:49:53]So 10 y + x y + x y + 9 y - 9 y x - 9 y - 9 x + y x + y right [snorts] 9 x + 9 y 9 into 5 45 Okay = 45 - 9 36 So x + y 2 y 3 10 x + y 10 into 2 20 + 3 23. So 10 x + y 10 y. Okay. Right.

[00:51:32][snorts] Topic: Simultaneous equations.

[00:52:06]Cost of two balls and three bats.

[00:52:15]The cost of two balls and three bats is 84. Cost of three balls and one bat is 63. What is the cost of five balls and three bats?

[00:52:27]for superarket 2b.

[00:52:49]B. So 3 A plus 1 B.

[00:53:20]So 33 3 9 9 a + 3 into b 3 b equal to uh 63 into 189 right 3b = 84us So - 3 - 3 cancel 9 a - 2 2 a 7 a 189 - 84.

[00:53:54]So 33 into 15 63 cost of five balls and three beds.

[00:54:31]B 3 into B.

[00:54:35]So 5 into 15 + 3 into 18 5 into 15 75 75 + 3 into 18 54. So total 129 righte friends.

[00:55:38]I'll uh try to answer them as soon as possible. Okay. Thank you for watching.

[00:55:42]Uh, keep learning until the next one.

[00:55:44]See you in the next one.