Home > Geometry calculators > Coordinate Geometry > Find the circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)
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Solution |
Find circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)
Solution:
Your problem `->` circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)
`A(4,1), B(-2,-3)` and `C(6,7)` form a triangle.
The center of a circle which passes through the three vertices of a triangle is called circum center.
Let P(x,y) be circum center
`:. PA=PB=PC`
`:. PA^2=PB^2=PC^2`
Now `PA^2=PB^2`
`(x-4)^2+(y-1)^2=(x+2)^2+(y+3)^2`
`(x^2-8x+16)+(y^2-2y+1)=(x^2+4x+4)+(y^2+6y+9)`
`-12x-8y=-4`
`3x+2y=1 ->(1)`
Now `PB^2=PC^2`
`(x+2)^2+(y+3)^2=(x-6)^2+(y-7)^2`
`(x^2+4x+4)+(y^2+6y+9)=(x^2-12x+36)+(y^2-14y+49)`
`16x+20y=72`
`4x+5y=18 ->(2)`
The point of intersection of the lines can be obtainted by solving the given equations.
`3x+2y=1`
and `4x+5y=18`
`3x+2y=1 ->(1)`
`4x+5y=18 ->(2)`
equation`(1) xx 5 =>15x+10y=5`
equation`(2) xx 2 =>8x+10y=36`
Substracting `=>7x=-31`
`=>x=-31/7`
Putting `x=-31/7 ` in equation `(1)`, we have
`3(-31/7)+2y=1`
`=>2y=1+(93/7)`
`=>2y=(7+93)/7`
`=>2y=100/7`
`=>y=50/7`
`:. x=-31/7" and "y=50/7`
`:. (-4.43,7.14)` is the intersection point of the given two lines.
`:. P(-4.43,7.14)` is circum center.
Solution provided by AtoZmath.com
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Mixed data - median {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 313. Grouped data - mode {{10,11,12,13,14},{3,12,18,12,3}} | | 314. Grouped data - mode {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 315. Grouped data - mode {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 316. Grouped data - mode {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 317. Mixed data - mode {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 318. Mixed data - mode {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 319. Grouped data - Variance {{10,11,12,13,14},{3,12,18,12,3}} | | 320. Grouped data - Variance {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 321. Grouped data - Variance {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 322. Grouped data - Variance {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 323. Mixed data - Variance {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 324. Mixed data - Variance {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 325. Grouped data - Standard deviation {{10,11,12,13,14},{3,12,18,12,3}} | | 326. Grouped data - Standard deviation {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 327. Grouped data - Standard deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 328. Grouped data - Standard deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 329. Mixed data - Standard deviation {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 330. Mixed data - Standard deviation {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 331. Grouped data - Population Variance {{10,11,12,13,14},{3,12,18,12,3}} | | 332. Grouped data - Population Variance {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 333. Grouped data - Population Variance {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 334. Grouped data - Population Variance {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 335. Mixed data - Population Variance {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 336. Mixed data - Population Variance {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 337. Grouped data - Population Standard Deviation {{10,11,12,13,14},{3,12,18,12,3}} | | 338. Grouped data - Population Standard Deviation {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 339. Grouped data - Population Standard Deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 340. Grouped data - Population Standard Deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 341. Mixed data - Population Standard Deviation {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 342. Mixed data - Population Standard Deviation {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 343. Grouped data - Sample Variance {{10,11,12,13,14},{3,12,18,12,3}} | | 344. Grouped data - Sample Variance {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 345. Grouped data - Sample Variance {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 346. Grouped data - Sample Variance {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 347. Mixed data - Sample Variance {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 348. Mixed data - Sample Variance {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 349. Grouped data - Sample Standard Deviation {{10,11,12,13,14},{3,12,18,12,3}} | | 350. Grouped data - Sample Standard Deviation {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 351. Grouped data - Sample Standard Deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 352. Grouped data - Sample Standard Deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 353. Mixed data - Sample Standard Deviation {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} | | 354. Mixed data - Sample Standard Deviation {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} | | 355. Grouped data - 1 quartiles of {{10,11,12,13,14},{3,12,18,12,3}} | | 356. Grouped data - 1 quartiles of {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 357. Grouped data - 1 quartiles of {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 358. Grouped data - 1 quartiles of {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 359. Grouped data - 4 deciles of {{10,11,12,13,14},{3,12,18,12,3}} | | 360. Grouped data - 4 deciles of {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 361. Grouped data - 4 deciles of {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 362. Grouped data - 4 deciles of {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 363. Grouped data - 15 percentiles of {{10,11,12,13,14},{3,12,18,12,3}} | | 364. Grouped data - 15 percentiles of {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 365. Grouped data - 15 percentiles of {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 366. Grouped data - 15 percentiles of {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 367. Grouped data - skewness {{61,64,67,70,73},{5,18,42,27,8}} | | 368. Grouped data - skewness {{61,5},{64,18},{67,42},{70,27},{73,8}} | | 369. Grouped data - skewness {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 370. Grouped data - skewness {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} | | 371. Grouped data - kurtosis {{61,64,67,70,73},{5,18,42,27,8}} | | 372. Grouped data - kurtosis {{61,5},{64,18},{67,42},{70,27},{73,8}} | | 373. Grouped data - kurtosis {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 374. Grouped data - kurtosis {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} | | 375. Grouped data - Sample skewness {{61,64,67,70,73},{5,18,42,27,8}} | | 376. Grouped data - Sample skewness {{61,5},{64,18},{67,42},{70,27},{73,8}} | | 377. Grouped data - Sample skewness {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 378. Grouped data - Sample skewness {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} | | 379. Grouped data - Sample kurtosis {{61,64,67,70,73},{5,18,42,27,8}} | | 380. Grouped data - Sample kurtosis {{61,5},{64,18},{67,42},{70,27},{73,8}} | | 381. Grouped data - Sample kurtosis {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 382. Grouped data - Sample kurtosis {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} | | 383. Grouped data - Population skewness {{61,64,67,70,73},{5,18,42,27,8}} | | 384. Grouped data - Population skewness {{61,5},{64,18},{67,42},{70,27},{73,8}} | | 385. Grouped data - Population skewness {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 386. Grouped data - Population skewness {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} | | 387. Grouped data - Population kurtosis {{61,64,67,70,73},{5,18,42,27,8}} | | 388. Grouped data - Population kurtosis {{61,5},{64,18},{67,42},{70,27},{73,8}} | | 389. Grouped data - Population kurtosis {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 390. Grouped data - Population kurtosis {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} | | 391. Grouped data - quartile deviation {{10,11,12,13,14},{3,12,18,12,3}} | | 392. Grouped data - quartile deviation {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 393. Grouped data - quartile deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 394. Grouped data - quartile deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 395. Grouped data - coefficient of quartile deviation {{10,11,12,13,14},{3,12,18,12,3}} | | 396. Grouped data - coefficient of quartile deviation {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 397. Grouped data - coefficient of quartile deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 398. Grouped data - coefficient of quartile deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 399. Statistics Graph - histogram {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 400. Statistics Graph - histogram {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 401. Statistics Graph - frequency polygon {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 402. Statistics Graph - frequency polygon {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 403. Statistics Graph - frequency curve {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 404. Statistics Graph - frequency curve {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 405. Statistics Graph - less than type cumulative frequency curve {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 406. Statistics Graph - less than type cumulative frequency curve{{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 407. Statistics Graph - more than type cumulative frequency curve {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 408. Statistics Graph - more than type cumulative frequency curve {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 409. Ungrouped data - missing frequency, {18,14,15,19,15,a,12,15,16},mean=16 | | 410. Ungrouped data - missing frequency, {-9,-4,a,5,8,11},median=2 | | 411. Grouped data - missing frequency, {{5-10,10-15,15-20,20-25,25-30,30-35},{11,20,35,20,a,6}},mean=18.1 | | 412. Grouped data - missing frequency, {{40-59,60-79,80-99,100-119,120-139},{50,?,500,?,50}},median=87.50,N=1000 | | 413. Combined Mean, N1=40,X1=10,SD1=1,N2=60,X2=15,SD2=2 | | 414. Combined Standard deviation, N1=40,X1=10,SD1=1,N2=60,X2=15,SD2=2 | | 415. Combined Mean, Combined Standard deviation, N1=40,X1=10,SD1=1,N2=60,X2=15,SD2=2 | | 416. Ungrouped data - mean deviation {85,96,76,108,85,80,100,85,70,95} | | 417. Grouped data - mean deviation {{10,11,12,13,14},{3,12,18,12,3}} | | 418. Ungrouped data - mean deviation about mean {85,96,76,108,85,80,100,85,70,95} | | 419. Grouped data - mean deviation about mean {{10,11,12,13,14},{3,12,18,12,3}} | | 420. Grouped data - mean deviation about mean {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 421. Ungrouped data - mean deviation about median {85,96,76,108,85,80,100,85,70,95} | | 422. Grouped data - mean deviation about median {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 423. Grouped data - mean deviation about median {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 424. Ungrouped data - mean deviation about mode {85,96,76,108,85,80,100,85,70,95} | | 425. Grouped data - mean deviation about mode {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 426. Grouped data - mean deviation about mode {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 427. Correlation Coefficient {{10,11,12,13,14},{3,12,18,12,3}} | | 428. Correlation Coefficient {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 429. Correlation Coefficient {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 430. Correlation Coefficient {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 431. Bivariate grouped data - Correlation Coefficient {{50-55,55-60,60-65,65-70},{90-100,100-110,110-120,120-130},{{4,7,5,2},{6,10,7,4},{6,12,10,7},{3,8,6,3}}} | | 432. Rank Correlation Coefficient {{35,40,42,43,40,53,54,49,41,55},{102,101,97,98,38,101,97,92,95,95}} | | 433. Rank Correlation Coefficient {1,6,5,10,3,2,4,9,7,8},{3,5,8,4,7,10,2,1,6,9},{6,4,9,8,1,2,3,10,5,7} | | 434. Regression line {{10,11,12,13,14},{3,12,18,12,3}} | | 435. Regression line {{10,3},{11,12},{12,18},{13,12},{14,3}} | | 436. Regression line {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} | | 437. Regression line {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} | | 438. Bivariate grouped data - Regression line {{50-55,55-60,60-65,65-70},{90-100,100-110,110-120,120-130},{{4,7,5,2},{6,10,7,4},{6,12,10,7},{3,8,6,3}}} | | 439. Regression line xbar=39.5,ybar=47.5,SDx=10.8,SDy=15,r=0.42 | | 440. Regression line sum x=130, sum y=220, sum x^2=2288, sum y^2=8822, sum xy=3467, n=10 | | 441. Correlation Coefficient from regression lines 5y=9x-22,20x=9y+350 | | 442. Method of Least Squares - Fit a straight line {{1996,1997,1998,1999,2000},{40,50,62,58,60}} | | 443. Method of Least Squares - Fit second degree parabola equation {{1996,1997,1998,1999,2000},{40,50,62,58,60}} | | 444. Method of Least Squares - Fit cubic equation {{1996,1997,1998,1999,2000},{40,50,62,58,60}} | | 445. Method of Least Squares - Linear fit {{1996,1997,1998,1999,2000},{40,50,62,58,60}} | | 446. Method of Least Squares - Quadratic fit {{1996,1997,1998,1999,2000},{40,50,62,58,60}} | | 447. Probability - Coin Calculator | | 448. Probability - Dice Calculator | | 449. Probability - Cards Calculator | | 450. Probability - Balls Calculator | | 451. Graph - plot y=x^2 | | 452. Graph - plot x=y^2 | | 453. Graph - plot 3x-y>=3, 5x+4y=1 | | 454. Graph - plot x^3-6x^2+4x+12 | | 455. Graph - plot sin x + cos x | | 456. Graph - plot sin x,cos x,tan x | | 457. Graph - plot number line 2,3,5,7,11,13 | | 458. Graph - plot points on x axis 2,3,5,7,11,13 | | 459. Graph - plot points on y axis 2,3,5,7,11,13 | | 460. Graph - plot points (-1,2),(-3,4),(-5,6) | | 461. Graph - plot circle (x+1)^2+(y-1)^2<=10 Calculator | | 462. Graph - plot ellipse (x-2)^2/25+(y+1)^2/10=1 Calculator | | 463. Graph - plot parabola y=3(x+1)^2+1 Calculator | | 464. Graph - plot parabola x=3(y+1)^2+1 Calculator | | 465. Graph - plot hyperbola (x-2)^2/25-(y+1)^2/10>=5 Calculator | | 466. Graph - plot polar r=2+4*cos(t) Calculator | | 467. Coordinate geometry - distance (7,8),(1,0) | | 468. Coordinate geometry - slope (7,8),(1,0) | | 469. Coordinate geometry - midpoint (-2,3) and (5,4) | | 470. Coordinate geometry - trisection points (-2,3) and (5,4) | | 471. Coordinate geometry - angle between 5x+2y-11=0 and 3x-y+11=0 | | 472. Coordinate geometry - Reflection of A(0,0),B(2,2),C(0,4),D(-2,2) | | 473. Coordinate geometry - collinear A(4,1),B(-2,-3),C(6,7) | | 474. Coordinate geometry - collinear A(0,0),B(2,0),C(-4,0),D(-2,0) | | 475. Coordinate geometry - right angle triangle A(0,0),B(0,3),C(4,0) | | 476. Coordinate geometry - equilateral triangle A(2,5),B(8,5),C(5,10.196152) | | 477. Coordinate geometry - isosceles triangle A(2,2),B(-2,4),C(2,6) | | 478. Coordinate geometry - square A(0,0),B(2,2),C(0,4),D(-2,2) | | 479. Coordinate geometry - rectangle A(1,-1),B(-2,2),C(4,8),D(7,5) | | 480. Coordinate geometry - rhombus A(3,0),B(4,5),C(-1,4),D(-2,-1) | | 481. Coordinate geometry - parallelogram A(1,5),B(1,4),C(-1,3),D(-1,4) | | 482. Coordinate geometry - centroid of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7) | | 483. Coordinate geometry - circumcentre of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7) | | 484. Coordinate geometry - area of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7) | | 485. Coordinate geometry - Slope Intercept 7y-4x+9=0 | | 486. Coordinate geometry - Slope YIntercept 7y-4x+9=0 | | 487. Coordinate geometry - XIntercept YIntercept of 7y-4x+9=0 | | 488. Coordinate geometry - Slope XIntercept YIntercept of (3,-5),(-7,9) | | 489. Coordinate geometry - line through (5,4), slope=1/2 | | 490. Coordinate geometry - line (3,5),(6,4) | | 491. Coordinate geometry - line m=2 and YIntercept=3 | | 492. Coordinate geometry - line XIntercept=3 and YIntercept=-5 | | 493. Coordinate geometry - line through intersection point of 5x+2y-11=0, 3x-y+11=0, parallel to 4x-3y+2=0 | | 494. Coordinate geometry - line through intersection point of 5x+2y-11=0, 3x-y+11=0 and perpendicular to 4x-3y+2=0 | | 495. Coordinate geometry - line through intersection point of 2x+3y+4=0, 3x+6y-8=0 and slope=2 | | 496. Coordinate geometry - line through intersection point of 4x+5y+7=0, 3x-2y-12=0 and (3,1) | | 497. Coordinate geometry - line through (5,5) and parallel to 2x+3y+4=0 | | 498. Coordinate geometry - line through (5,5) and perpendicular to 2x+3y+4=0 | | 499. Matrix determinant - det [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 500. Matrix adjoint - adj [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 501. Matrix - adjugate [[1,2],[3,4]] | | 502. Matrix - transpose [[1,2],[3,4]] | | 503. Matrix - inverse [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 504. Matrix - minor [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 505. Matrix - cofactor [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 506. Matrix - trace [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 507. Matrix - Gauss Jordan Elimination inverse [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 508. Matrix - Cayley Hamilton inverse [[10,-9,-12],[7,-12,11],[-10,10,3]] | | 509. Matrix addition - [[1,2],[3,4]] + [[2,-1],[-1,2]] | | 510. Matrix subtraction - [[1,2],[3,4]] - [[2,-1],[-1,2]] | | 511. Matrix multiplication - [[1,2],[3,4]] * [[2,-1],[-1,2]] | | 512. Matrix power - [[1,2],[3,4]]^2 | | 513. Matrix addition - A=[[1,2],[3,4]], B=[[2,-1],[-1,2]], 2A+3B | | 514. Matrix power - A=[[1,2],[3,4]],A^3 | | 515. Matrix determinant - A=[[10,-9,-12],[7,-12,11],[-10,10,3]], |A^2| | | 516. Matrix adjoint - A=[[10,-9,-12],[7,-12,11],[-10,10,3]], adj(A) | | 517. Matrix inverse - A=[[10,-9,-12],[7,-12,11],[-10,10,3]], A^-1 | | 518. Matrix transpose - A=[[1,2],[3,4]], A' | | 519. Matrix - A = [[1,2],[3,4]], B = [[2,-1],[-1,2]], (A * B)' = B' * A' | | 520. Matrix - row reduction [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 521. Matrix - reduce [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 522. Matrix - rank [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 523. Matrix - characteristic polynomial [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 524. Matrix - eigenvalues [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 525. Matrix - eigenvectors [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 526. Matrix - triangular [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 527. Matrix - diagonal [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 528. Matrix - Jordan decomposition [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 529. Matrix - lu decomposition [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 530. Matrix - cholesky decomposition [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 531. Matrix - qr decomposition [[1,-1,4],[1,4,-2],[1,4,2],[1,-1,0]] | | 532. Matrix - qr decomposition house holder [[1,-1,4],[1,4,-2],[1,4,2],[1,-1,0]] | | 533. Matrix - pivots [[8,-6,2],[-6,7,-4],[2,-4,3]] | | 534. Singular Value Decomposition - SVD [[4,0],[3,-5]] | | 535. Is Row matrix [[1,2,5]] | | 536. Is Column matrix [[1],[2],[5]] | | 537. Is Square matrix [[1,2,3],[4,5,6],[7,8,9]] | | 538. Is Horizontal matrix [[1,2,3],[4,5,6]] | | 539. Is Vertical matrix [[1,2],[4,5],[7,8]] | | 540. Is Diagonal matrix [[1,0,0],[0,5,0],[0,0,9]] | | 541. Is Identity matrix [[1,0,0],[0,1,0],[0,0,1]] | | 542. Is Scalar matrix [[2,0,0],[0,2,0],[0,0,2]] | | 543. Is Null matrix [[0,0,0],[0,0,0],[0,0,0]] | | 544. Is lower triangle matrix [[1,0,0],[2,3,0],[4,5,6]] | | 545. Is upper triangle matrix [[1,2,3],[0,4,5],[0,0,6]] | | 546. Is Orothogonal matrix [[0,1],[1,0]] | | 547. Is Singular matrix [[1,1,1],[1,1,1],[1,1,1]] | | 548. Is Nonsingular matrix [[1,2,3],[4,5,6],[7,8,9]] | | 549. Is Symmetric matrix [[1,2,3],[2,5,6],[3,6,9]] | | 550. Is SkewSymmetric matrix [[0,2,3],[-2,0,6],[-3,-6,0]] | | 551. Is Nilpotent matrix [[1,2,3],[1,2,3],[-1,-2,-3]] | | 552. Is Involutary matrix [[-5,-8,0],[3,5,0],[1,2,-1]] | | 553. Is Idempotent matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]] | | 554. Is Periodic matrix [[1,-2,-6],[-3,2,9],[2,0,-3]] | | 555. Is Positive Definite matrix [[25,15,-5],[15,18,0],[-5,0,11]] | | 556. decide types of matrix - Is matrix [[-5,-8,0],[3,5,0],[1,2,-1]] | | 557. bisection method 2x^3-2x-5 | | 558. bisection method 2x^3-2x-5, a=1, b=4 | | 559. false position method 2x^3-2x-5 | | 560. false position method 2x^3-2x-5, a=1, b=4 | | 561. regula falsi method 2x^3-2x-5 | | 562. regula falsi method 2x^3-2x-5, a=1, b=4 | | 563. newton raphson method 2x^3-2x-5 | | 564. newton raphson method 2x^3-2x-5, x0=1 | | 565. newton raphson method 2x^3-2x-5, a=1, b=4 | | 566. iteration method 2x^3-2x-5 | | 567. iteration method 2x^3-2x-5, a=1, b=4 | | 568. secant method 2x^3-2x-5 | | 569. secant method 2x^3-2x-5, a=1, b=4 | | 570. Birge-Vieta method x^4-3x^3+3x^2-3x+2, p=0.5 | | 571. Numerical Differentiation, 2x^3-4x+1, [2,4], x=2.1, h=0.25 | | 572. Numerical Differentiation, 2x^3-4x+1, [2,4], x=3.5, N=4 | | 573. Numerical Differentiation, {{1.4,1.6,1.8,2.0,2.2},{4.0552,4.9530,6.0496,7.3891,9.0250}},x=1.4 | | 574. Numerical Differentiation, {{1.4,4.0552},{1.6,4.9530},{1.8,6.0496},{2.0,7.3891},{2.2,9.0250}},x=1.4 | | 575. Euler method y'=-2x-y, y(0)=1, xn=0.5, h=0.1 | | 576. Runge-Kutta method y'=-2x-y, y(0)=1, xn=0.5, h=0.1 | | 577. Runge-Kutta 2 method y'=-2x-y, y(0)=1, xn=0.5, h=0.1 | | 578. Runge-Kutta 3 method y'=-2x-y, y(0)=1, xn=0.5, h=0.1 | | 579. Runge-Kutta 4 method y'=-2x-y, y(0)=1, xn=0.5, h=0.1 | | 580. Adams bashforth predictor method y'=-2x-y, y(0)=1, x=5 | | 581. Milne's simpson predictor corrector method y'=-2x-y, y(0)=1, x=5 | | 582. Adams bashforth predictor method y'=(x+y)/2,{{0,0.5,1,1.5},{2,2.636,3.595,4.968}},x=2 | | 583. Adams bashforth predictor method y'=(x+y)/2,{{0,2},{0.5,2.636},{1,3.595},{1.5,4.968}},x=2 | | 584. Milne's simpson predictor corrector method y'=(x+y)/2,{{0,0.5,1,1.5},{2,2.636,3.595,4.968}},x=2 | | 585. Milne's simpson predictor corrector method y'=(x+y)/2,{{0,2},{0.5,2.636},{1,3.595},{1.5,4.968}},x=2 | | 586. Numerical Interpolation - Forward, 2x^3-4x+1, [2,4], x=2.1, h=0.25 | | 587. Numerical Interpolation - Forward, 2x^3-4x+1, [2,4], x=2.1, N=4 | | 588. Numerical Interpolation - Backward, 2x^3-4x+1, [2,4], x=2.1, h=0.25 | | 589. Numerical Interpolation - Backward, 2x^3-4x+1, [2,4], x=2.1, N=4 | | 590. Numerical Interpolation - Divided Difference, 2x^3-4x+1, [2,4], x=2.1, h=0.25 | | 591. Numerical Interpolation - Divided Difference, 2x^3-4x+1, [2,4], x=2.1, N=4 | | 592. Numerical Interpolation - Langrange's Interpolation, 2x^3-4x+1, [2,4], x=2.1, h=0.25 | | 593. Numerical Interpolation - Langrange's Interpolation, 2x^3-4x+1, [2,4], x=2.1, N=4 | | 594. Numerical Interpolation - Forward, {{0,1,2,3},{1,0,1,10}},x=2.1 | | 595. Numerical Interpolation - Forward, {{0,1},{1,0},{2,1},{3,10}},x=2.1 | | 596. Numerical Interpolation - Backward, {{0,1,2,3},{1,0,1,10}},x=2.1 | | 597. Numerical Interpolation - Backward, {{0,1},{1,0},{2,1},{3,10}},x=2.1 | | 598. Numerical Interpolation - Divided Difference, {{0,1,2,3},{1,0,1,10}},x=2.1 | | 599. Numerical Interpolation - Divided Difference, {{0,1},{1,0},{2,1},{3,10}},x=2.1 | | 600. Numerical Interpolation - Langrange's Interpolation, {{0,1,2,3},{1,0,1,10}},x=2.1 | | 601. Numerical Interpolation - Langrange's Interpolation, {{0,1},{1,0},{2,1},{3,10}},x=2.1 | | 602. Simpson rule, 1/x, [1,2], h=0.25 | | 603. Simpson rule, 1/x, [1,2], N=5 | | 604. Trapezoidal rule, 1/x, [1,2], h=0.25 | | 605. Trapezoidal rule, 1/x, [1,2], N=5 | | 606. Trapezoidal Simpson rule, 1/x, [1,2], h=0.25 | | 607. Trapezoidal Simpson rule, 1/x, [1,2], N=5 | | 608. Simpson rule, {{0.0,0.1,0.2,0.3,0.4},{1.0000,0.9975,0.9900,0.9776,0.8604}} | | 609. Simpson rule, {{0.0,1.0000},{0.1,0.9975},{0.2,0.9900},{0.3,0.9776},{0.4,0.8604}} | | 610. Trapezoidal rule, {{0.0,0.1,0.2,0.3,0.4},{1.0000,0.9975,0.9900,0.9776,0.8604}} | | 611. Trapezoidal rule, {{0.0,1.0000},{0.1,0.9975},{0.2,0.9900},{0.3,0.9776},{0.4,0.8604}} | | 612. Trapezoidal Simpson rule, {{0.0,0.1,0.2,0.3,0.4},{1.0000,0.9975,0.9900,0.9776,0.8604}} | | 613. Trapezoidal Simpson rule, {{0.0,1.0000},{0.1,0.9975},{0.2,0.9900},{0.3,0.9776},{0.4,0.8604}} | | 614. 1's complement subtraction 10110-11101 | | 615. 2's complement subtraction 10110-11101 | | 616. 7's complement subtraction 342-614 | | 617. 8's complement subtraction 342-614 | | 618. 9's complement subtraction 670-831 | | 619. 10's complement subtraction 670-831 | | 620. 15's complement subtraction B06-C7C | | 621. 16's complement subtraction B06-C7C | | 622. 1's complement 11101 | | 623. 2's complement 11101 | | 624. 7's complement 614 | | 625. 8's complement 614 | | 626. 9's complement 831 | | 627. 10's complement 831 | | 628. 15's complement C7C | | 629. 16's complement C7C | | 630. Is Boolean Algebra D8 | | 631. Is Boolean Algebra D10 | | 632. truth table p or q | | 633. truth table p or (q and r)=(p or q) and (p or r) | | 634. logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r) | | 635. logical validity Hypothesis = p=>q;p and Conclusion = q | | 636. Game - Online Sudoku Creator and Solver | | 637. Game - Online Dots game | | 638. Game - 21 MatchStick Problem | | 639. Game - The Mind Reader Game | | 640. Game - Shift-It | | 641. Game - 2 Digit Number Guess | | 642. Game - Minesweeper | | 643. Game - Tic-Tac-Toe | | 644. Game - Chess With CPU | | 645. Game - Concentration | | 646. Game - Lights Out | | 647. Game - Three Glass Puzzle (MilkCane Problem) | | 648. Game - Peg | | 649. Game - Tower of Hanoi | | 650. Assignment problem (Using Hungarian method) | | 651. Travelling salesman problem using hungarian method | | 652. Travelling salesman problem using branch and bound (penalty) method | | 653. Travelling salesman problem using branch and bound method | | 654. Travelling salesman problem using nearest neighbor method | | 655. Crew assignment problem | | 656. Operation Research LPP - Simplex method | | 657. Operation Research LPP - BigM method | | 658. Operation Research LPP - Two-Phase method | | 659. Operation Research LPP - Graphical method | | 660. Operation Research LPP - Primal to dual conversion | | 661. Operation Research LPP - Dual Simplex method | | 662. Operation Research LPP - Integer Simplex method (Gomory's cutting plane method) | | 663. Operation Research LPP - Branch and Bound method | | 664. Operation Research LPP - 0-1 Integer programming problem | | 665. Transportation Problem - North-West corner method | | 666. Transportation Problem - Least cost method | | 667. Transportation Problem - Vogel's approximation method | | 668. Transportation Problem - Optimal solution using MODI method | | 669. Transportation Problem - Optimal solution using stepping stone method | | 670. PERT and CPM | | 671. Sequencing Problems | | 672. Replacement and Maintenance Models-1.1 | | 673. Replacement and Maintenance Models-1.2 | | 674. Replacement and Maintenance Models-1.3 | | 675. Replacement and Maintenance Models-2 | | 676. Replacement and Maintenance Models-3 | | 677. Game theory Saddle Point | | 678. Game theory Dominance method | | 679. Game theory Algebraic method | | 680. Game theory Calculus method | | 681. Game theory Arithmetic method | | 682. Game theory Matrix method | | 683. Game theory 2Xn Games | | 684. Game theory Graphical method | | 685. Game theory LPP method | | 686. Game theory Bimatrix method | | 687. Word Problems - Problem on Ages Calculator | | 688. Word Problems - Unitary Method Calculator | | 689. Simple Interest - Find the simple interest on Rs 730 for 184 days at 25/4 % per annum. | | 690. Simple Interest - Find the simple interest on Rs 4660 for 5 years at 7/2 % per annum. | | 691. Simple Interest - The interest on a certain amount of money at 8 % per year for a period of 4 years is Rs 512 . Find the sum of money. | | 692. Simple Interest - Simple Interest on Rs 972 at 14 % per annum for a certain time is Rs 476.28 . Find the time ? | | 693. Simple Interest - Simple Interest on Rs 972 at a certain rate % per annum for 3.5 years is Rs 476.28 . Find the rate ? | | 694. Simple Interest - A sum of money lent at simple interest amounts to Rs 1008 in 2 years and to 1112 in 3 years Find the sum and the rate of interest. | | 695. Simple Interest - What sum of money lent out at simple interest at 9 % p.a. for 3/2 years will produce the same interest as Rs 2250 lent at 6 % p.a. for 5 years | | 696. Simple Interest - A man puts out Rs 500 for 4 years on simple interest and Rs 600 for 3 years The total interest he receives is Rs 190 . What is the rate percent per annum? | | 697. Simple Interest - A sum was put at simple interest at a certain rate for 2 years Had it been put at 3 % higher rate, it whould have fetched Rs 300 more. Find the sum. | | 698. Simple Interest - Divide Rs 16875 into two parts such that the interest at 7/2 % p.a. for 2 years on one part is equal to the other at 4 % p.a. for 5 years | | 699. Simple Interest - A shopkeeper borrowed Rs 20000 from two money lendeRs For one loan he paid 12 % and for the other 14 % per annum. After 1 year, he paid Rs 2560 as interest. How much did he borrow at each rate ? | | 700. Simple Interest - At what rate percent per annum will sum of money double in 8 years? | | 701. Simple Interest - Rajeev deposited money in the post office which is doubled in 20 years at a simple rate of interest. In how many years will the original sum triple itself ? | | 702. Compound Interest - Calculate Compound Interest and amount on Rs 4500 at 10 % per annum in 3 years | | 703. Compound Interest - Calculate Compound Interest and amount on Rs 625 for 2 years at 9 %, compounded half-yearly. | | 704. Compound Interest - Calculate Compound Interest on Rs 8000 for 9 months at 20 % per annum, compounded quartely . | | 705. Compound Interest - What sum of money becomes Rs 9261 in 3 years at 5 % per annum, compounded annually ? | | 706. Compound Interest - What will Rs 25000 amounts to in two years at Compound Interest if the rates for successive years be 4 % and 5 % per year. | | 707. Compound Interest - A sum of money amounts to Rs 6690 after 3 years and to Rs 10035 after 6 years on compound interest. Calculate the sum of money. | | 708. Compound Interest - A man borrows Rs 2500 at 5 % simple interest for 2 years He immediately lends this money at compound interest at the same rate for the same time. What is the additional amount he gets at the ends of the years correct to nearest rupee? | | 709. Compound Interest - The difference between the compound interest and the simple interest on a certain sum at 10 % per annum for 2 years is Rs 52 . Find the sum. | | 710. Compound Interest - If the compound interest on a certain sum for 3 years at 10 % per annum be Rs 331, what would be the simple interest ? | | 711. Compound Interest - A sum of money 2 times itself at compound interest in 15 years In how many years, it will become 8 times of itself ? | | 712. Percentage - What is 20 % of 80 . | | 713. Percentage - 42 is 3 % of what. | | 714. Percentage - What percent of 65 is 130 . | | 715. Percentage - A's annual income is increased/decreased from Rs 60000 to Rs 75000 . Find the percentage of increase in A's income. | | 716. Percentage - In a school of 225 boys, 15 were absent then what percent were present ? | | 717. Percentage - A earns 25 % more than B. By what percent does B earn less then A. | | 718. Percentage - A reduction of 20 % in the price of basmati rice would enable a man to buy 2 kg of rice more for Rs 250 . Find the reduced price per kg. | | 719. Percentage - The price of tea has gone up by 20 %. By how much percent should its consumption be reduced so as not to increase the expenditure? | | 720. Percentage - Find the selling price of an item, of which the printed price is Rs 25000 if the successive discounts given are 10 %, 8 % and 4 %. | | 721. Percentage - The successive discount of 10 % and 5 % are given on the purchased Computer. If the final price of the Computer is Rs 10260 , then find the printed price of the Computer. | | 722. Percentage - 130 is what percent of 65 . | | 723. Percentage - What is the percentage increase/decrease from 20 to 40 ? | | 724. Profit Loss Discount - Find selling price when cost price = Rs 50, Loss/Gain = 10 % . | | 725. Profit Loss Discount - Find cost price when selling price = 55 , Loss/Gain = 10 % | | 726. Profit Loss Discount - Find Loss/Gain % when cost price = 50 and selling price = 55 . | | 727. Profit Loss Discount - By selling an article for Rs 110 a man loses 12 %. For how much should he sell it to gain 8 %. | | 728. Profit Loss Discount - A man sells two houses for Rs 536850 each. On one he gains and on the other he loses 5 %. Find his gain or loss % on the whole transaction. | | 729. Profit Loss Discount - If selling price of 10 articles is the same as the cost price of 12 articles, find the gain %. | | 730. Profit Loss Discount - By selling 100 pencils, a shopkeeper gains the selling price of 20 pencils. Find the gain percent. | | 731. Profit Loss Discount - A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 grams for 1000 grams. Find the gain percent. | | 732. Profit Loss Discount - If the marked price of an article is Rs 380 and a discount of 5 % is given on it, what is the selling price ? | | 733. Profit Loss Discount - If 12 % is allowed as discount on a radio and its selling price is Rs 836 , what is its marked price ? | | 734. Profit Loss Discount - A cycle dealer marks his goods 25 % above his cost price and allows a discount of 8 % on it. Find his gain percent. | | 735. Profit Loss Discount - Successive discounts of 20 % and 10 % equivalent to a single discount of how many percent? | | 736. Profit Loss Discount - If a commission of 10 % is given on the list price, the gain is 20 %. Find the gain percent, if the commission is increased to 20 %. | | 737. Profit Loss Discount - If the manufacturer gives 20 % commission to the dealer on the printed price and if the dealer sells the item at the printed price, what is the percentage of his profit ? | | 738. Profit Loss Discount - A dealer gets 25 % commission on the printed price of an item. If he gives 10 % discount to the customer on printed price, find his prifit in percentage. | | 739. Profit Loss Discount - The printed price of a saree is Rs 900 . A cloth-mearchant purchases it at 15 % commission. He spends Rs 35 for roll-polish and then sells the saree at the printed price. What is the prifit of the merchant in percentage ? | | 740. Profit Loss Discount - A carpenter made a table which cost him Rs 1500 . He decided the price so that he would get 20 % profit. He gave 8 % commission on the decided price while selling. Find the sales price of the table and the profit of the carpenter. | | 741. Profit Loss Discount - The printed price of a book is Rs 720 . After giving 10 % discount to the customer on the printed price, the book-seller gets 20 % profit. Find the purchase price for the book-seller. | | 742. Profit Loss Discount - If 20 % discount is given on the decided price which is decided by addition of 20 % profit on the purchase price, then will there be profit or loss? What is the percentage? | | 743. Profit Loss Discount - A watch manufacturing company decided the price with 25 % profit on the cost price. By selling a watch with 8 % discount on th printed price, the company has a profit of Rs 300 . Find the cost-price of a watch. | | 744. Profit Loss Discount - If the sales price of 12 pens is fixed as the original price of 15 pens, then what percentage of profit is earned in the deal ? | | 745. Statistics Wording Problem - The mean of 10 observations is 12.5 . While calculating the mean one observation was by mistake taken as -8 instead of +8 . Find the correct mean. | | 746. Statistics Wording Problem - The mean of 10 observations is 35 . While calculating the mean two observations were by mistake taken as 35 instead of 25 and 30 instead of 45 . Find the correct mean. | | 747. Statistics Wording Problem - The mean of 15 observations is 16.4 . If we remove one observation from it then the mean of remaining observations is 17 , then find out the removed observation ? | | 748. Statistics Wording Problem - The sum of 15 observation is 343 . If we remove two observation 18 and 26 , then find out the mean of remaining observations. | | 749. Statistics Wording Problem - The mean of 5 observations is 20 . If we add one new observation then the new mean of the observations is 25 . So find out new added observation. | | 750. Statistics Wording Problem - The mean of observation is 10 . If we add 2 and then multiply or divide by 3 in each observation, then find the new mean ? | | 751. HCF LCM - The HCF of two numbers is 14 and their LCM is 11592 . If one of the numbers is 504 , find the other? | | 752. HCF LCM - Find the largest number which can exactly divide 513,783,1107 . | | 753. HCF LCM - Find the smallest number exactly divisible by 12,15,20,27 . | | 754. HCF LCM - Find the least number which when divided by 6,7, 8, 9,12 leaves the same remainder 2 in each case. | | 755. HCF LCM - Find the largest number which divides 77 , 147 , 252 to leave the same remainder in each case. | | 756. HCF LCM - Greatest number which can divide 1354 , 1806 , 2762 leaving the same remainder 10 in each case. | | 757. HCF LCM - The greatest number that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder. | | 758. HCF LCM - The greatest number that will divide 290 , 460 , 552 leaving respectively 4 , 5 , 6 as remainder. | | 759. HCF LCM - The product of HCF and LCM of 18 and 16 is | | 760. HCF LCM - LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600 . If one number is 280 , then find the other number ? | | 761. HCF LCM - Find the least number which is exactly divided by 28,36,45 when we add 19 to it | | 762. Installment - A briefcase is available for Rs 800 cash or for Rs 500 cash down payment and Rs 320 to be paid after 6 months. Find the rate of interest charged under the installment plan. | | 763. Installment - A bicycle is sold for Rs 1800 cash or for Rs 600 cash down payment followed by 2 monthly installmnets of Rs 610 each. Compute the rate of the interest charged under the installment scheme. | | 764. Installment - A washing machine is available at Rs 6400 cash or for Rs 1400 cash down payment and 5 monthly installments of Rs 1030 each. Calculate the rate of interest charged under the instalment plan. | | 765. Installment - A computer is sold by a company for Rs 19200 cash or for Rs 4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12 % per annum, find each installment. | | 766. Installment - A State Government announces sale of flats of Rs 555000 cash or Rs 42750 cash down payment and 3 equal Yearly installments. The Government also charges a nominal interest at the rate of 8 % per annum copuounded as installment plan in this welfare scheme. | | 767. Installment - A man borrows money from a finance company and has to pay it back in 2 equal Half Yearly installments of Rs 4945 each. If the interest is charged by the finance company at the rate of 15 % per annum compounded as installment plan, find the principal and t | | 768. Installment - A TV set is available for Rs 19650 cash payment or for Rs 3100 cash down payment and 3 equal Yearly installments. If the shopkeeper charges interest at the rate of 10 % per annum compounded as installment plan, calculate the amount of each installment. | | 769. Installment - Ram borrowed a sum of money and returned it in 3 equal Quarterly installments of Rs 17576 each. Find the sum borrowed, if the rate of interest charged was 16 % per annum compounded as installment plan. Find also the total interest charged. | | 770. Arithmetic Progression - For given arithemetic progression series 7,3,-1,-5,-9 ,... find 10 th term and addition of first 10 th terms. | | 771. Arithmetic Progression - For arithemetic progression f( 5 ) = 56 , f( 8 ) = 86 then find f( 10 ) and S( 10 ). | | 772. Arithmetic Progression - For arithemetic progression f( 5 ) = 25 , f( 11 ) = 49 , then find n such that f(n) = 105 . | | 773. Arithmetic Progression - For arithemetic progression S( 33 ) = 198 , then find f( 17 ). | | 774. Arithmetic Progression - For arithemetic progression f( 17 ) = 6 , then find S( 33 ). | | 775. Arithmetic Progression - For arithemetic progression f( 7 ) = 13 , S( 14 ) = 203 , then find f( 10 ) and S( 8 ). | | 776. Arithmetic Progression - For arithemetic progression addition of 3 terms is 27 and their multiplication is 648 , then that numbers | | 777. Arithmetic Progression - For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of first 41 terms. | | 778. Arithmetic Progression - For arithmetic progression Sm = n and Sn = m then prove that Sm+n = -(m - n) | | 779. Arithmetic Progression - For arithmetic progression Sm = n and Sn = m then prove that Sm-n = (m - n)(1 + 2n / m) | | 780. Arithmetic Progression - Find the sum of all natural numbers between 100 to 200 and which are divisible by 4 . | | 781. Arithmetic Progression - Find the sum of all natural numbers between 100 to 200 and which are not divisible by 4 . | | 782. Arithmetic Progression - For arithemetic progression addition of three terms is 15 and addition of their squres is 83 , then find that numbers | | 783. Arithmetic Progression - If S1, S2, S3 are sum of n, 2n, 3n terms of arithmetic progression series then prove that S3 = 3(S2 - S1) | | 784. Arithmetic Progression - If Sn is sum of n even terms of arithmetic progression series and Sn' is sum of n odd terms of arithmetic progression series then prove that Sn = (1 + 1/n) Sn' | | 785. Arithmetic Progression - For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273 , then find that numbers | | 786. Arithmetic Progression - For arithemetic progression of four terms, addition of end terms is 14 and multiplication of middle two terms is 45 , then find that numbers | | 787. Arithmetic Progression - For arithemetic progression, addition of four terms is 4 and addition of multiplication of end terms and multiplication of middle terms is -38 , then find that numbers | | 788. Geometric Progression - For given geometric progression series 3,6,12,24,48 ,... find 10 th term and addition of first 10 th terms. | | 789. Geometric Progression - For given geometric progression series 3,6,12,24,48 ,... then find n such that S(n) = 3069 . | | 790. Geometric Progression - For given geometric progression series 3,6,12,24,48 ,... then find n such that f(n) = 1536 . | | 791. Geometric Progression - For geometric progression f( 1 ) = 2 , f( 4 ) = 54 then find f( 3 ) and S( 3 ). | | 792. Geometric Progression - For geometric progression f( 1 ) = 2 , f( 4 ) = 54 , then find n such that f(n) = 18 . | | 793. Geometric Progression - For geometric progression addition of 3 terms is 26 and their multiplication is 216 , then that numbers | | 794. Geometric Progression - For geometric progression multiplication of 5 terms is 1 and 5 th term is 81 times then the 1 th term. | | 795. Geometric Progression - Arithmetic mean of two number is 13 and geometric mean is 12 , then find that numbers | | 796. Geometric Progression - Two numbers are in the ratio 9 : 16 and difference of arithmetic mean and geometric mean is 1 , then find that numbers | | 797. Geometric Progression - Find 6 arithmetic mean between 3 and 24 . | | 798. Geometric Progression - Find 3 geometric mean between 1 and 256 . | | 799. Geometric Progression - Prove that 1 + (1 + 2) + (1 + 2 + 3) + ... n terms = n/6 (n + 1) (n + 2) | | 800. Geometric Progression - Prove that 1 * (2^2 - 3^2) + 2 * (3^2 - 4^2) + 3 * (4^2 - 5^2) + ... n terms = n/6 (n + 1) (4n + 11) | | 801. Geometric Progression - 1 + x^4 + 3^2 + 4 + x^6 + 6^2 + 7 + x^8 + 9^2 + ... 3n terms | | 802. Geometric Progression - 1 + (1 + 3) + (1 + 3 + 5) + ... n terms | | 803. Geometric Progression - Prove that for all n belongs to N, 1^2 * n + 2^2 * (n - 1) + 3^2 * (n - 2) + ... + n^2 * 1 = n/12 (n + 1)^2 (n + 2) | | 804. Geometric Progression - Prove that 1 * 2^2 + 3 * 5^2 + 5 * 8^2 + ... n terms = n/2 (9n^3 + 4n^2 - 4n - 1) | | 805. Geometric Progression - Prove that 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ... n terms = n/12 (n + 1)^2 (n + 2) | | 806. Geometric Progression - Prove that 2 + 5 + 10 + 17 + ... n terms = n/6 (2n^2 + 3n + 7) | | 807. Geometric Progression - Prove that sum [ sum (2n -3) ] = n/6 (n + 1)(2n - 5) |
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