problem_text stringlengths 51 114 | answer int64 -144 961k | sutra stringclasses 8
values | meaning stringclasses 8
values | topic stringclasses 2
values | difficulty stringclasses 3
values | latex_problem stringlengths 54 116 | params dict |
|---|---|---|---|---|---|---|---|
Solve the equation $(x + 4)(x + 5) = 0$ using Puranapuranabhyam Sutra (find one root). | -4 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Easy | Solve the equation $(x + 4)(x + 5) = 0$ using Puranapuranabhyam Sutra (find one root). | {
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Solve the equation $(x + 3)(x + 2) = 0$ using Puranapuranabhyam Sutra (find one root). | -3 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Easy | Solve the equation $(x + 3)(x + 2) = 0$ using Puranapuranabhyam Sutra (find one root). | {
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Solve the simultaneous equations: $x + y = 13$ and $x - y = 11$ using Sankalana-vyavakalanabhyam Sutra (find x). | 12 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Easy | Solve the simultaneous equations: $x + y = 13$ and $x - y = 11$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
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Solve for x: $(x + 3) / 8 = (x + 7) / 5$ using Anurupyena Sutra. | -13 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Easy | Solve for $x$: $\frac{x + 3}{8} = \frac{x + 7}{5}$ using Anurupyena Sutra. | {
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"c": 7,
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"d": 5,
"dividend": null,
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"num": null,
"num1": null,
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Solve the simultaneous equations: $x + y = 17$ and $x - y = 11$ using Sankalana-vyavakalanabhyam Sutra (find x). | 14 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Easy | Solve the simultaneous equations: $x + y = 17$ and $x - y = 11$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
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"base": null,
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"num": null,
"num1": null,
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"x_true": 14,
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Solve the simultaneous equations: $x + y = 49$ and $x - y = 33$ using Sankalana-vyavakalanabhyam Sutra (find x). | 41 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Medium | Solve the simultaneous equations: $x + y = 49$ and $x - y = 33$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
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"base": null,
"c": null,
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"num": null,
"num1": null,
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Find the square of 245 using the Ekadhikena Purvena Sutra. | 60,025 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Medium | Find the square of $245$ using Ekadhikena Purvena Sutra. | {
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"divisor": null,
"num": 245,
"num1": null,
"num2": null,
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Find the square of 65 using the Ekadhikena Purvena Sutra. | 4,225 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Easy | Find the square of $65$ using Ekadhikena Purvena Sutra. | {
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"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 65,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Divide 45926 by 1007 using the Paravartya Yojayet Sutra (find quotient). | 45 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $45926$ by $1007$ using Paravartya Yojayet Sutra (find quotient). | {
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"base": null,
"c": null,
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"dividend": 45926,
"divisor": 1007,
"num": null,
"num1": null,
"num2": null,
"val": null,
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Multiply 26 by 20 using the Urdhva-Tiryagbhyam Sutra. | 520 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Easy | Multiply $26 imes 20$ using Urdhva-Tiryagbhyam Sutra. | {
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"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 26,
"num2": 20,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 15)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | -15 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Hard | Solve the equation $(x + 15)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 15,
"b": 3,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Solve for x: $(x + 74) / 88 = (x + 75) / 59$ using Anurupyena Sutra. | -77 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Hard | Solve for $x$: $\frac{x + 74}{88} = \frac{x + 75}{59}$ using Anurupyena Sutra. | {
"a": 74,
"b": 88,
"base": null,
"c": 75,
"coeff_a": null,
"coeff_b": null,
"d": 59,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Divide 1551 by 103 using the Paravartya Yojayet Sutra (find quotient). | 15 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Medium | Divide $1551$ by $103$ using Paravartya Yojayet Sutra (find quotient). | {
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"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 1551,
"divisor": 103,
"num": null,
"num1": null,
"num2": null,
"val": null,
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} |
Solve for x: $(x + 16) / 14 = (x + 23) / 11$ using Anurupyena Sutra. | -48 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Medium | Solve for $x$: $\frac{x + 16}{14} = \frac{x + 23}{11}$ using Anurupyena Sutra. | {
"a": 16,
"b": 14,
"base": null,
"c": 23,
"coeff_a": null,
"coeff_b": null,
"d": 11,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Divide 22966 by 1008 using the Paravartya Yojayet Sutra (find quotient). | 22 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $22966$ by $1008$ using Paravartya Yojayet Sutra (find quotient). | {
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"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 22966,
"divisor": 1008,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Multiply 959 by 577 using the Urdhva-Tiryagbhyam Sutra. | 553,343 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Hard | Multiply $959 imes 577$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 959,
"num2": 577,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $3(x + 6) = 6(x + 6)$ using Shunyam Saamyasamuccaye. | -6 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Easy | Solve for $x$: $3(x + 6) = 6(x + 6)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 3,
"coeff_b": 6,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 6,
"x_true": null,
"y_true": null
} |
Multiply 85 by 86 using the Nikhilam Sutra (Base 100). | 7,310 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Medium | Multiply $85 imes 86$ using Nikhilam Sutra (Base $100$). | {
"a": null,
"b": null,
"base": 100,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 85,
"num2": 86,
"val": null,
"x_true": null,
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} |
Solve for x: $5(x + 5) = 3(x + 5)$ using Shunyam Saamyasamuccaye. | -5 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Hard | Solve for $x$: $5(x + 5) = 3(x + 5)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 5,
"coeff_b": 3,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 5,
"x_true": null,
"y_true": null
} |
Divide 44691 by 1007 using the Paravartya Yojayet Sutra (find quotient). | 44 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $44691$ by $1007$ using Paravartya Yojayet Sutra (find quotient). | {
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"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 44691,
"divisor": 1007,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Solve for x: $9(x + 3) = 7(x + 3)$ using Shunyam Saamyasamuccaye. | -3 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Medium | Solve for $x$: $9(x + 3) = 7(x + 3)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 9,
"coeff_b": 7,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 3,
"x_true": null,
"y_true": null
} |
Divide 97 by 11 using the Paravartya Yojayet Sutra (find quotient). | 8 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Easy | Divide $97$ by $11$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 97,
"divisor": 11,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 773 by 716 using the Urdhva-Tiryagbhyam Sutra. | 553,468 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Hard | Multiply $773 imes 716$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 773,
"num2": 716,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 1316 by 103 using the Paravartya Yojayet Sutra (find quotient). | 12 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Medium | Divide $1316$ by $103$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 1316,
"divisor": 103,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
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} |
Divide 45640 by 1004 using the Paravartya Yojayet Sutra (find quotient). | 45 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $45640$ by $1004$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 45640,
"divisor": 1004,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 90 by 86 using the Nikhilam Sutra (Base 100). | 7,740 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Medium | Multiply $90 imes 86$ using Nikhilam Sutra (Base $100$). | {
"a": null,
"b": null,
"base": 100,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 90,
"num2": 86,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 24899 by 1008 using the Paravartya Yojayet Sutra (find quotient). | 24 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $24899$ by $1008$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 24899,
"divisor": 1008,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 267 by 204 using the Urdhva-Tiryagbhyam Sutra. | 54,468 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Hard | Multiply $267 imes 204$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 267,
"num2": 204,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 27 by 22 using the Urdhva-Tiryagbhyam Sutra. | 594 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Easy | Multiply $27 imes 22$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 27,
"num2": 22,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 29) / 15 = (x + 11) / 20$ using Anurupyena Sutra. | -83 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Medium | Solve for $x$: $\frac{x + 29}{15} = \frac{x + 11}{20}$ using Anurupyena Sutra. | {
"a": 29,
"b": 15,
"base": null,
"c": 11,
"coeff_a": null,
"coeff_b": null,
"d": 20,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the simultaneous equations: $x + y = 140$ and $x - y = 102$ using Sankalana-vyavakalanabhyam Sutra (find x). | 121 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Hard | Solve the simultaneous equations: $x + y = 140$ and $x - y = 102$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
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"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": 121,
"y_true": 19
} |
Solve the equation $(x + 12)(x + 10) = 0$ using Puranapuranabhyam Sutra (find one root). | -12 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Hard | Solve the equation $(x + 12)(x + 10) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 12,
"b": 10,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 34154 by 1002 using the Paravartya Yojayet Sutra (find quotient). | 34 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $34154$ by $1002$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 34154,
"divisor": 1002,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 23 by 27 using the Urdhva-Tiryagbhyam Sutra. | 621 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Easy | Multiply $23 imes 27$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 23,
"num2": 27,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 825 using the Ekadhikena Purvena Sutra. | 680,625 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Hard | Find the square of $825$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 825,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 9 by 8 using the Nikhilam Sutra (Base 10). | 72 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Easy | Multiply $9 imes 8$ using Nikhilam Sutra (Base $10$). | {
"a": null,
"b": null,
"base": 10,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 9,
"num2": 8,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 8 by 9 using the Nikhilam Sutra (Base 10). | 72 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Easy | Multiply $8 imes 9$ using Nikhilam Sutra (Base $10$). | {
"a": null,
"b": null,
"base": 10,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 8,
"num2": 9,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $3(x + 1) = 3(x + 1)$ using Shunyam Saamyasamuccaye. | -1 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Medium | Solve for $x$: $3(x + 1) = 3(x + 1)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 3,
"coeff_b": 3,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 1,
"x_true": null,
"y_true": null
} |
Multiply 7 by 8 using the Nikhilam Sutra (Base 10). | 56 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Easy | Multiply $7 imes 8$ using Nikhilam Sutra (Base $10$). | {
"a": null,
"b": null,
"base": 10,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 7,
"num2": 8,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 21573 by 1006 using the Paravartya Yojayet Sutra (find quotient). | 21 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $21573$ by $1006$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 21573,
"divisor": 1006,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 92) / 84 = (x + 42) / 31$ using Anurupyena Sutra. | -12 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Hard | Solve for $x$: $\frac{x + 92}{84} = \frac{x + 42}{31}$ using Anurupyena Sutra. | {
"a": 92,
"b": 84,
"base": null,
"c": 42,
"coeff_a": null,
"coeff_b": null,
"d": 31,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $10(x + 10) = 9(x + 10)$ using Shunyam Saamyasamuccaye. | -10 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Medium | Solve for $x$: $10(x + 10) = 9(x + 10)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 10,
"coeff_b": 9,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 10,
"x_true": null,
"y_true": null
} |
Multiply 18 by 11 using the Urdhva-Tiryagbhyam Sutra. | 198 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Easy | Multiply $18 imes 11$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 18,
"num2": 11,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 3)(x + 5) = 0$ using Puranapuranabhyam Sutra (find one root). | -3 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Easy | Solve the equation $(x + 3)(x + 5) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 3,
"b": 5,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 7 by 7 using the Nikhilam Sutra (Base 10). | 49 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Easy | Multiply $7 imes 7$ using Nikhilam Sutra (Base $10$). | {
"a": null,
"b": null,
"base": 10,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 7,
"num2": 7,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the simultaneous equations: $x + y = 101$ and $x - y = 69$ using Sankalana-vyavakalanabhyam Sutra (find x). | 85 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Hard | Solve the simultaneous equations: $x + y = 101$ and $x - y = 69$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": 85,
"y_true": 16
} |
Multiply 9 by 9 using the Nikhilam Sutra (Base 10). | 81 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Easy | Multiply $9 imes 9$ using Nikhilam Sutra (Base $10$). | {
"a": null,
"b": null,
"base": 10,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 9,
"num2": 9,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the simultaneous equations: $x + y = 9$ and $x - y = 1$ using Sankalana-vyavakalanabhyam Sutra (find x). | 5 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Easy | Solve the simultaneous equations: $x + y = 9$ and $x - y = 1$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": 5,
"y_true": 4
} |
Divide 1259 by 101 using the Paravartya Yojayet Sutra (find quotient). | 12 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Medium | Divide $1259$ by $101$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 1259,
"divisor": 101,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 88 by 90 using the Nikhilam Sutra (Base 100). | 7,920 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Medium | Multiply $88 imes 90$ using Nikhilam Sutra (Base $100$). | {
"a": null,
"b": null,
"base": 100,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 88,
"num2": 90,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 95 using the Ekadhikena Purvena Sutra. | 9,025 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Easy | Find the square of $95$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 95,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 35937 by 1005 using the Paravartya Yojayet Sutra (find quotient). | 35 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $35937$ by $1005$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 35937,
"divisor": 1005,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 962 by 990 using the Nikhilam Sutra (Base 1000). | 952,380 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Hard | Multiply $962 imes 990$ using Nikhilam Sutra (Base $1000$). | {
"a": null,
"b": null,
"base": 1000,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 962,
"num2": 990,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 11) / 23 = (x + 12) / 21$ using Anurupyena Sutra. | -22 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Medium | Solve for $x$: $\frac{x + 11}{23} = \frac{x + 12}{21}$ using Anurupyena Sutra. | {
"a": 11,
"b": 23,
"base": null,
"c": 12,
"coeff_a": null,
"coeff_b": null,
"d": 21,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 30042 by 1009 using the Paravartya Yojayet Sutra (find quotient). | 29 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $30042$ by $1009$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 30042,
"divisor": 1009,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 44435 by 1008 using the Paravartya Yojayet Sutra (find quotient). | 44 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Hard | Divide $44435$ by $1008$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 44435,
"divisor": 1008,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 11)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | -11 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Hard | Solve the equation $(x + 11)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 11,
"b": 3,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Divide 103 by 11 using the Paravartya Yojayet Sutra (find quotient). | 9 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Easy | Divide $103$ by $11$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 103,
"divisor": 11,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 3)(x + 4) = 0$ using Puranapuranabhyam Sutra (find one root). | -3 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Easy | Solve the equation $(x + 3)(x + 4) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 3,
"b": 4,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $5(x + 5) = 7(x + 5)$ using Shunyam Saamyasamuccaye. | -5 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Hard | Solve for $x$: $5(x + 5) = 7(x + 5)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 5,
"coeff_b": 7,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 5,
"x_true": null,
"y_true": null
} |
Divide 57 by 11 using the Paravartya Yojayet Sutra (find quotient). | 5 | Paravartya Yojayet | Transpose and Apply. Useful for division where the divisor is slightly greater than a power of 10. | Arithmetic | Easy | Divide $57$ by $11$ using Paravartya Yojayet Sutra (find quotient). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": 57,
"divisor": 11,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 7) / 3 = (x + 6) / 4$ using Anurupyena Sutra. | -10 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Easy | Solve for $x$: $\frac{x + 7}{3} = \frac{x + 6}{4}$ using Anurupyena Sutra. | {
"a": 7,
"b": 3,
"base": null,
"c": 6,
"coeff_a": null,
"coeff_b": null,
"d": 4,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 85 using the Ekadhikena Purvena Sutra. | 7,225 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Easy | Find the square of $85$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 85,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 5)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | -5 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Easy | Solve the equation $(x + 5)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 5,
"b": 3,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 795 using the Ekadhikena Purvena Sutra. | 632,025 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Hard | Find the square of $795$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 795,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $3(x + 6) = 4(x + 6)$ using Shunyam Saamyasamuccaye. | -6 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Easy | Solve for $x$: $3(x + 6) = 4(x + 6)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 3,
"coeff_b": 4,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 6,
"x_true": null,
"y_true": null
} |
Multiply 293 by 386 using the Urdhva-Tiryagbhyam Sutra. | 113,098 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Hard | Multiply $293 imes 386$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 293,
"num2": 386,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 36 by 80 using the Urdhva-Tiryagbhyam Sutra. | 2,880 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Medium | Multiply $36 imes 80$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 36,
"num2": 80,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 485 using the Ekadhikena Purvena Sutra. | 235,225 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Medium | Find the square of $485$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 485,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 82) / 62 = (x + 59) / 85$ using Anurupyena Sutra. | -144 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Hard | Solve for $x$: $\frac{x + 82}{62} = \frac{x + 59}{85}$ using Anurupyena Sutra. | {
"a": 82,
"b": 62,
"base": null,
"c": 59,
"coeff_a": null,
"coeff_b": null,
"d": 85,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 23) / 12 = (x + 17) / 27$ using Anurupyena Sutra. | -27 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Medium | Solve for $x$: $\frac{x + 23}{12} = \frac{x + 17}{27}$ using Anurupyena Sutra. | {
"a": 23,
"b": 12,
"base": null,
"c": 17,
"coeff_a": null,
"coeff_b": null,
"d": 27,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 78 by 70 using the Urdhva-Tiryagbhyam Sutra. | 5,460 | Urdhva-Tiryagbhyam | Vertically and Crosswise. A general method applicable to all cases of multiplication. | Arithmetic | Medium | Multiply $78 imes 70$ using Urdhva-Tiryagbhyam Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 78,
"num2": 70,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the simultaneous equations: $x + y = 45$ and $x - y = 25$ using Sankalana-vyavakalanabhyam Sutra (find x). | 35 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Medium | Solve the simultaneous equations: $x + y = 45$ and $x - y = 25$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": 35,
"y_true": 10
} |
Solve for x: $9(x + 7) = 9(x + 7)$ using Shunyam Saamyasamuccaye. | -7 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Hard | Solve for $x$: $9(x + 7) = 9(x + 7)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 9,
"coeff_b": 9,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 7,
"x_true": null,
"y_true": null
} |
Solve for x: $4(x + 3) = 9(x + 3)$ using Shunyam Saamyasamuccaye. | -3 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Medium | Solve for $x$: $4(x + 3) = 9(x + 3)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 4,
"coeff_b": 9,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 3,
"x_true": null,
"y_true": null
} |
Solve the simultaneous equations: $x + y = 17$ and $x - y = 13$ using Sankalana-vyavakalanabhyam Sutra (find x). | 15 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Easy | Solve the simultaneous equations: $x + y = 17$ and $x - y = 13$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": 15,
"y_true": 2
} |
Multiply 94 by 87 using the Nikhilam Sutra (Base 100). | 8,178 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Medium | Multiply $94 imes 87$ using Nikhilam Sutra (Base $100$). | {
"a": null,
"b": null,
"base": 100,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 94,
"num2": 87,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 1) / 9 = (x + 4) / 3$ using Anurupyena Sutra. | -5 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Easy | Solve for $x$: $\frac{x + 1}{9} = \frac{x + 4}{3}$ using Anurupyena Sutra. | {
"a": 1,
"b": 9,
"base": null,
"c": 4,
"coeff_a": null,
"coeff_b": null,
"d": 3,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $6(x + 9) = 2(x + 9)$ using Shunyam Saamyasamuccaye. | -9 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Medium | Solve for $x$: $6(x + 9) = 2(x + 9)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 6,
"coeff_b": 2,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 9,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 8)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | -8 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Medium | Solve the equation $(x + 8)(x + 3) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 8,
"b": 3,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 985 by 956 using the Nikhilam Sutra (Base 1000). | 941,660 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Hard | Multiply $985 imes 956$ using Nikhilam Sutra (Base $1000$). | {
"a": null,
"b": null,
"base": 1000,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 985,
"num2": 956,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 505 using the Ekadhikena Purvena Sutra. | 255,025 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Hard | Find the square of $505$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 505,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Find the square of 55 using the Ekadhikena Purvena Sutra. | 3,025 | Ekadhikena Purvena | By one more than the previous one. Useful for multiplication of numbers whose last digits add up to 10 or 100, and for squaring numbers ending in 5. | Arithmetic | Easy | Find the square of $55$ using Ekadhikena Purvena Sutra. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": 55,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 4) / 2 = (x + 8) / 6$ using Anurupyena Sutra. | -2 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Easy | Solve for $x$: $\frac{x + 4}{2} = \frac{x + 8}{6}$ using Anurupyena Sutra. | {
"a": 4,
"b": 2,
"base": null,
"c": 8,
"coeff_a": null,
"coeff_b": null,
"d": 6,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $(x + 16) / 10 = (x + 20) / 28$ using Anurupyena Sutra. | -13 | Anurupyena | Proportionately. Useful for solving equations and finding ratios. | Algebra | Medium | Solve for $x$: $\frac{x + 16}{10} = \frac{x + 20}{28}$ using Anurupyena Sutra. | {
"a": 16,
"b": 10,
"base": null,
"c": 20,
"coeff_a": null,
"coeff_b": null,
"d": 28,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Multiply 991 by 970 using the Nikhilam Sutra (Base 1000). | 961,270 | Nikhilam Navatashcaramam Dashatah | All from nine and the last from ten. Useful for subtraction from powers of 10 and multiplication of numbers close to base 10. | Arithmetic | Hard | Multiply $991 imes 970$ using Nikhilam Sutra (Base $1000$). | {
"a": null,
"b": null,
"base": 1000,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": 991,
"num2": 970,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the simultaneous equations: $x + y = 30$ and $x - y = 10$ using Sankalana-vyavakalanabhyam Sutra (find x). | 20 | Sankalana-vyavakalanabhyam | By addition and by subtraction. Useful for solving simultaneous linear equations or problems involving sums and differences. | Algebra | Medium | Solve the simultaneous equations: $x + y = 30$ and $x - y = 10$ using Sankalana-vyavakalanabhyam Sutra (find $x$). | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": 20,
"y_true": 10
} |
Solve the equation $(x + 10)(x + 5) = 0$ using Puranapuranabhyam Sutra (find one root). | -10 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Medium | Solve the equation $(x + 10)(x + 5) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 10,
"b": 5,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve the equation $(x + 8)(x + 4) = 0$ using Puranapuranabhyam Sutra (find one root). | -8 | Puranapuranabhyam | By the completion or non-completion. Useful in specific cases of solving equations. | Algebra | Medium | Solve the equation $(x + 8)(x + 4) = 0$ using Puranapuranabhyam Sutra (find one root). | {
"a": 8,
"b": 4,
"base": null,
"c": null,
"coeff_a": null,
"coeff_b": null,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": null,
"x_true": null,
"y_true": null
} |
Solve for x: $6(x + 10) = 4(x + 10)$ using Shunyam Saamyasamuccaye. | -10 | Shunyam Saamyasamuccaye | When the sum is the same, that sum is zero. Useful for solving certain linear equations. | Algebra | Hard | Solve for $x$: $6(x + 10) = 4(x + 10)$ using Shunyam Saamyasamuccaye. | {
"a": null,
"b": null,
"base": null,
"c": null,
"coeff_a": 6,
"coeff_b": 4,
"d": null,
"dividend": null,
"divisor": null,
"num": null,
"num1": null,
"num2": null,
"val": 10,
"x_true": null,
"y_true": null
} |
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