PROGRESSIONS-PART-II-(E)-03-Assignment

239. nth term of the series will be (a) (b) (c) (d) 240. If denotes the nth term of the series then t50 is (a) (b) (c) (d) 241. First term of the 11th group in the following groups (1), (2, 3, 4), (5, 6, 7, 8, 9), ..... is (a) 89 (b) 97 (c) 101 (d) 123 242. The sum of the series upto n terms is (a) (b) (c) (d) None of these 243. Sum of n terms of series will be (a) (b) (c) (d) 244. If |a|<1 and |b|<1, then the sum of the series is (a) (b) (c) (d) 245. term of the series + .......will be (a) (b) (c) (d) 246. The nth term of series will be (a) (b) (c) (d) 247. If then is (a) 1 (b) – 1 (c) 0 (d) – 2 248. The number 111.......1 (91 times) is a (a) Even number (b) Prime number (c) Not prime (d) None of these 249. The difference between an integer and its cube is divisible by (a) 4 (b) 6 (c) 9 (d) None of these 250. In the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8,......, where n consecutive terms have the value n , the 1025th term is (a) 29 (b) 210 (c) 211 (d) 28 251. Observe that . Then n3 as a similar series is (a) (b) (c) (d) None of these 252. The sum of the series 3 . 6 + 4 . 7 + 5 . 8 +....... upto (n – 2) terms (a) (b) (c) (d) None of these 253. The sum of the series upto n terms, will be (a) (b) (c) (d) 254. The sum to n terms of the series is (a) (b) (c) (d) 255. (a) 2481 (b) 2483 (c) 2485 (d) 2487 256. The sum to terms of is (a) (b) (c) (d) 257. (a) (b) (c) (d) None of these 258. Sum of the squares of first n natural numbers exceeds their sum by 330, then n= (a) 8 (b) 10 (c) 15 (d) 20 259. equals (a) (b) (c) (d) 260. The sum to n terms of the infinite series is (a) (b) (c) (d) None of these 261. The sum of all the products of the first n natural numbers taken two at a time is (a) (b) (c) (d) None of these 262. The sum of the series 1. 3. 5 + 2. 5. 8 +3. 7. 11+.....up to 'n' terms is (a) (b) (c) (d) 263. The sum of first n terms of the given series is when n is even. When n is odd, the sum will be (a) (b) (c) (d) None of these 264. The value of is (a) (b) (c) (d) 265. The sum of the series to n terms is (a) (b) (c) (d) None of these 266. For any odd integer , (a) (b) (c) (d) 267. The sum of the infinite terms of the sequence is (a) (b) (c) (d) 268. The sum of the infinite series is (a) (b) (c) (d) 269. If in a series , then is equal to (a) (b) (c) (d) None of these 270. is equal to (a) 0 (b) (c) (d) None of these 271. For all positive integral values of n, the value of is (a) (b) (c) (d) 272. The sum of terms of (a) (b) (c) (d) 273. The sum of terms of is (a) (b) (c) (d) 274. The sum equals [] (a) (b) (c) (d) 275. Sum of the terms of the series (a) (b) (c) (d) 276. The sum of the series is (a) 1 (b) 0 (c) (d) 4 277. (a) Is divisible by 5 (b) Is an odd integer divisible by 5 (c) Is an even integer which is not divisible by 5 (d) Is an odd integer which is not divisible by 5 278. The sum of all numbers between 100 and 10,000 which are of form is equal to (a) 55216 (b) 53261 (c) 51261 (d) 53216 279. The cubes of the natural numbers are grouped as then sum of the numbers in the nth group is (a) (b) (c) (d) None of these 280. The value of the expression is (a) (b) (c) (d) None of these 281. If ....up to then equals to (a) (b) (c) (d) None of these 282. The value of is (a) (b) (c) (d) None of these 283. Let . Then is equal to (a) ,for all (b) , when n is odd (c) , when n is even (d) None of these 284. The sum to n terms of the series is (a) (b) (c) (d) None of these 285. If a and b are two different positive real numbers, then which of the following relations is true (a) (b) (c) (d) None of these 286. If a, b, c are in A.P. as well as in G.P., then (a) (b) (c) (d) 287. If three numbers be in G.P., then their logarithms will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 288. If the arithmetic, geometric and harmonic means between two distinct positive real numbers be A, G and H respectively, then the relation between them (a) (b) (c) (d) 289. If the arithmetic, geometric and harmonic means between two positive real numbers be and H, then (a) (b) (c) (d) 290. If a, b, c are in A.P. then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 291. The geometric mean of two numbers is 6 and their arithmetic mean is 6.5. The numbers are (a) (3, 12) (b) (4, 9) (c) (2, 18) (d) (7, 6) 292. In the four numbers first three are in G.P. and last three in A.P. whose common difference is 6. If the first and last numbers are same, then first will be (a) 2 (b) 4 (c) 6 (d) 8 293. If are the two A.M.'s between two numbers a and b and be two G.M.'s between same two numbers, then (a) (b) (c) (d) 294. If the A.M. and H.M. of two numbers is 27 and 12 respectively, then G.M. of the two numbers will be (a) 9 (b) 18 (c) 24 (d) 36 295. The A.M., H.M. and G.M. between two numbers are and 12, but necessarily in this order. Then H.M., G.M. and A.M. respectively are (a) (b) (c) (d) 296. If G.M. =18 and A.M.=27, then H.M. is (a) (b) (c) 12 (d) 297. If sum of A.M. and H.M. between two numbers is 25 and their G.M. is 12, then sum of numbers is (a) 9 (b) 18 (c) 32 (d) 18 or 32 298. If then a, b, c, d are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 299. The numbers 1,4, 16 can be three terms (not necessarily consecutive) of (a) No A.P. (b) Only one G.P. (c) Infinite number of A.P’s. (d) Infinite numbers of G.P’s. 300. In a G.P. of alternately positive and negative terms, any terms is the A.M. of the next two terms . Then the common ratio is (a) – 1 (b) – 3 (c) – 2 (d) 301. If a, b, c are in A.P., then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 302. The A.M. of two given positive numbers is 2. If the larger number is increased by 1, the G.M. of the numbers becomes equal to the A.M. of the given numbers. Then the H.M. of the given numbers is (a) (b) (c) (d) None of these 303. If pth , qth, rth and sth terms of an A.P. be in G.P., then will be in (a) G.P. (b) A.P. (c) H.P. (d) None of these 304. If a, b, c are the positive integers, then is (a) (b) (c) (d) None of these 305. If a, b, c are in A.P., then shall be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 306. If a, b, c, d and p are different real numbers such that then a, b, c, d are in (a) A.P. (b) G.P. (c) H.P. (d) 307. If the first and terms of an A.P., G.P. and H.P. are equal and their nth terms are respectively a, b and c, then (a) (b) (c) (d) (a) and (c) both 308. If the and terms of an A.P. are in G.P. and m, n, r in H.P., then the value of the ratio of the common difference to the terms of the A.P. is (a) (b) (c) (d) 309. Given and a, b, c, d are in G.P., then x, y, z, u are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 310. If a, b, c are in G.P. and and are in A.P., then a, b, c are the length of the sides of a triangle which is (a) Acute angled (b) Obtuse angled (c) Right angled (d) Equilateral 311. If a, b, c are in A.P., b, c, d are in G.P. and c, d, e are in H.P., then a, c, e are in (a) No particular order (b) A.P. (c) G.P. (d) H.P. 312. If a, b, c are in A.P. and are in H.P., then (a) (b) (c) (d) None of these 313. The harmonic mean of two numbers is 4 and the arithmetic and geometric means satisfy the relation the numbers are (a) 6, 3 (b) 5, 4 (c) 5, ¬– 2.5 (d) – 3, 1 314. In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third numbers, the series becomes A.P., then the greatest number is (a) 8 (b) 4 (c) 24 (d) 16 315. If a, b, c are in G.P. and x, y are the arithmetic means between a, b and b, c respectively, then is equal to (a) 0 (b) 1 (c) 2 (d) 316. If a, b, c are in A.P. and a, b, d in G.P., then a, a – b, d – c will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 317. If x, 1, z are in A.P. and x, 2, z are in G.P., then x, 4, z will be in (a) A.P. (b) G.P. (c) H.P. (d) None of these 318. if are in A.P.; while if are in H.P., then the value of a will be (a) 1 (b) 2 (c) 3 (d) 9 319. If 9 A.M.'s and H.M.'s are inserted between the 2 and 3 and if the harmonic mean H is corresponding to arithmetic mean A, then (a) 1 (b) 3 (c) 5 (d) 6 320. If the pth, qth and rth term of a G.P. and H.P. are a, b, c, then (a) – 1 (b) 0 (c) 1 (d) Does not exist 321. If the product of three terms of G.P. is 512. If 8 added to first and 6 added to second term, so that number may be in A.P., then the numbers are (a) 2, 4, 8, (b) 4, 8, 16 (c) 3, 6, 12 (d) None of these 322. If the ratio of H.M. and G.M. between two numbers a and b is then ratio of the two numbers will be (a) (b) (c) (d) 323. If the A.M. and G.M. of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be (a) (b) (c) (d) 324. Let be in A.P. and be in H.P. If and then is (a) 2 (b) 3 (c) 5 (d) 6 325. If are in A.P., then (a) a, b, c are in A.P. (b) are in A.P. (c) a, b, c are in G.P. (d) a, b, c are in H.P. 326. If and be two A.M’s, G.M’s and H.M’s between two numbers respectively, then equals (a) 1 (b) 0 (c) 2 (d) 3 327. If are in G.P., (a) A.P. (b) H.P. (c) G.P. (d) None of these 328. If p, q, r are in one geometric progression and a, b, c in another geometric progression, then are in (a) A.P. (b) H.P. (c) G.P. (d) None of these 329. If first three terms of sequence are in geometric series and last three terms are in harmonic series, then the value of and will be (a) (b) (c) (a) and (b) both are true (d) None of these 330. If are in G.P., then are in (a) A. P. (b) G. P. (c) H. P. (d) None of these 331. If and are two geometric means and A the arithmetic mean inserted between two numbers, then the value of is (a) (b) A (c) 2 A (d) None of these 332. If are in H.P., then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 333. If a, b, c are in A.P., then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 334. The sum of three decreasing numbers in A.P. is 27. If are added to them respectively, the resulting series is in G.P. The numbers are (a) 5, 9, 13 (b) 15, 9, 3 (c) 13, 9, 5 (d) 17, 9, 1 335. If in the equation the sum of roots is equal to sum of square of their reciprocals, then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 336. If a, b, c are in A.P., then are in (a) A.P. (b) G.P. only when (c) G.P. if (d) G.P. for all 337. If are in H.P., then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 338. The common difference of an A.P. whose first term is unity and whose second, tenth and thirty fourth terms are in G.P., is (a) (b) (c) (d) 339. The sum of three consecutive terms in a geometric progression is 14. If 1 is added to the first and the second terms and 1 is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is (a) 1 (b) 2 (c) 4 (d) 8 340. are arithmetic mean, geometric mean and harmonic mean between two positive numbers x and y respectively. Then identify the correct statement among the following (a) h is the harmonic mean between a and g (b) No such relation exists between a, g and h (c) g is the geometric mean between a and h (d) a is the arithmetic mean between g and h 341. Let the positive numbers a, b, c, d be in A.P., then abc, abd, acd, bcd are (a) Not in A.P./G.P./H.P. (b) In A.P. (c) In G.P. (d) In H.P. 342. If and are in H.P., then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 343. If A and G are arithmetic and geometric means and , then (a) (b) (c) (d) 344. If A is the A.M. of the roots of the equation and is the G.M. of the roots of the equation then (a) (b) (c) (d) None of these 345. If are three unequal numbers such that are in A.P. and b – a, c – b, a are in G.P., then a : b : c is (a) 1 : 2 : 3 (b) 2: 3 : 1 (c) 1 : 3 : 2 (d) 3 : 2 : 1 346. If are in A.P. and are in H.P., then (a) (b) (c) are in G.P. (d) are in G.P. 347. Let be any positive real numbers, then which of the following statement is not true (a) (b) (c) (d) 348. If are positive real numbers whose product is a fixed number c, then the minimum value of is (a) (b) (c) (d) 349. Suppose are in A.P. and are in G.P. If a < b < c and , then the value of a is (a) (b) (c) (d) 350. Two sequences and are defined by then (a) is an A.P., is a G.P. (b) and are both G.P. (c) and are both A.P. (d) is a G.P., is neither A.P. nor G.P. 351. If = 0 and then a, b, c are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 352. If x, y, z are in G.P. and are in A.P., then (a) or (b) (c) but their common value is not necessarily zero (d) 353. If in a progression etc., bears a constant ratio with then the terms of the progression are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 354. If then are in (a) A.P. (b) G.P. (c) H.P. (d) None of these 355. If are in A.P., are in G.P. and are in H.P., where a, b are positive, then the equation has its roots (a) Real and unequal (b) Real and equal (c) Imaginary (d) None of these 356. If a, x, b, are in A.P., a, y, b are in G.P. and a, z, b are in H.P. such that and then (a) (b) (c) (d) None of these 357. If a, b, c are in G.P. and a, p, q in A.P. such that are in G.P. then the common difference of the A.P. is (a) (b) (c) (d) 358. If x, y, z are positive then the minimum value of is (a) 3 (b) 1 (c) 9 (d) 16 359. a, b, c are three positive numbers and has the greatest value Then (a) (b) (c) (d) None of these 360. If and the minimum value of is , then the is (a) 2 (b) 1 (c) 6 (d) 3 361. If x, y, z are three real numbers of the same sign then the value of lies in the interval (a) (b) (c) (d) 362. The sum of the products of the ten numbers taking two at a time is (a) 165 (b) – 55 (c) 55 (d) None of these 363. Let be squares such that for each the length of a side of equals the length of a diagonal of If the length of a side of is 10 cm, then for which of the following values of n is the area of less then 1 sq cm (a) 7 (b) 8 (c) 9 (d) 10 364. Jairam purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual installment of Rs. 1000 with 10% per annum interest. How much money is to be paid by Jairam (a) Rs. 21555 (b) Rs. 20475 (c) Rs. 20500 (d) Rs. 20700 365. The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is (a) 2489 (b) 4735 (c) 2317 (d) 2632 366. The product of positive numbers is unity. Their sum is [MP PET 2000] (a) A positive integer (b) Equal to (c) Divisible by (d) Never less than 367. If are positive real numbers such that then satisfies the relation (a) (b) (c) (d) 368. The sum of all positive divisors of 960 is (a) 3048 (b) 3087 (c) 3047 (d) 2180 369. is greater than (a) (b) (c) (d) 370. If the altitudes of a triangle are in A.P., then the sides of the triangle are in (a) A.P. (b) H.P. (c) G.P. (d) Arithmetico-geometric progression 371. A boy goes to school from his home at a speed of x km/hour and comes back at a speed of y km/hour, then the average speed is given by (a) A.M. (b) G.M. (c) H.M. (d) None of these 372. A monkey while trying to reach the top of a pole height 12 metres takes every time a jump of 2 metres but slips 1 metre while holding the pole. The number of jumps required to reach the top of the pole, is (a) 6 (b) 10 (c) 11 (d) 12 373. Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two balls and so on. If 669 more balls are added then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of the triangle did. The initial number of balls is (a) 1600 (b) 1500 (c) 1540 (d) 1690 374. If a, b and c are three positive real numbers, then the minimum value of the expression is (a) 1 (b) 2 (c) 3 (d) 6 375. If and then the minimum value of equals to (a) 50 (b) (c) (d) 376. If a, b and c are positive real numbers, then least value of is (a) 9 (b) 3 (c) 10/3 (d) None of these 377. In the value of 100 ! the number of zeros at the end is (a) 11 (b) 22 (c) 23 (d) 24 378. If then the value of is (a) 1/3 (b) 3 (c) 1/2 (d) 2 379. Let where[x] denotes the integral part of x. Then the value of is (a) 50 (b) 51 (c) 1 (d) None of these 380. are n points on the parabola in the first quadrant. If where are in G.P. and then is equal to (a) (b) (c) (d) 381. The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is and the total surface area is The length of the longest edge is (a) 12 cm (b) 6 cm (c) 18 cm (d) 3 cm 382. ABC is right-angled triangle in which and If n points on AB are such that AB is divided in equal parts and are line segments parallel to BC and are on AC then the sum of the lengths of is (a) (b) (c) (d) Impossible to find from the given data