InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Let the sum of the first n terms of a non-constant A.P., `a_(1), a_(2), a_(3),... " be " 50n + (n (n -7))/(2)A`, where A is a constant. If d is the common difference of this A.P., then the ordered pair `(d, a_(50))` is equal toA. `(A, 50 + 46 A)`B. `(A,50 + 45A)`C. `(50, 50 + 46 A)`D. `(50 , 50 + 45 A)` |
| Answer» Correct Answer - A | |
| 2. |
For any three positive real numbers a, b and c, `9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c)` Then: (1) b, c and a are in G.P. (2) b, c and a are in A.P. (3) a, b and c are in A.P (4) a, b and c are in G.PA. a, b and c are in G.P.B. b,c and a are in G.PC. b, c and a are in A.PD. a, b and c are in A.P. |
| Answer» Correct Answer - C | |
| 3. |
Let a,b and c be in G.P. with common ratio r, where `a != 0 and 0 lt r le (1)/(2)`. If 3a, 7b and 15c are the first three terms of an A.P., then the `4^(th)` term of this A.P. isA. `(7)/(3)a`B. aC. `(2)/(3)a`D. `5a` |
| Answer» Correct Answer - B | |
| 4. |
Let `a_1,a_2,a_3,...`be in harmonic progression with `a_1=5a n da_(20)=25.`The least positive integer `n`for which `a_n |
| Answer» Correct Answer - D | |
| 5. |
`"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).`A. `(ab)/(c)`B. `(ac)/(b)`C. `(bc)/(a)`D. None of these |
| Answer» Correct Answer - A | |
| 6. |
The value of `1^(2) + 3^(2) + 5^(2) + ..... + 25^(2)` isA. 1728B. 1456C. 2925D. 1469 |
| Answer» Correct Answer - C | |
| 7. |
`2 + 4 + 7 + 11 + 16 +`.... to `n` term =A. `(1)/(6) (n^(2) + 3n + 8)`B. `(n)/(6) (n^(2) + 3n + 8)`C. `(1)/(6) (n^(2) - 3n + 8)`D. `(n)/(6) (n^(2) - 3n + 8)` |
| Answer» Correct Answer - B | |
| 8. |
In a GP, first term is 1. If `4T_(2) + 5T_(3)` is minimum, then its common ratio isA. `(2)/(5)`B. `-(2)/(5)`C. `(3)/(5)`D. `-(3)/(5)` |
| Answer» Correct Answer - B | |
| 9. |
If the 2nd , 5th and 9thterms of anon-constant A.P. are in G.P., then thecommon ratio of this G.P. is :(1) `8/5`(2)`4/3`(3)1 (4) `7/4`A. `(7)/(4)`B. `(8)/(5)`C. `(4)/(3)`D. 1 |
| Answer» Correct Answer - C | |
| 10. |
The sum of the series : `(2)^(2) + 2(4)^(2) + 3(6)^(2)+`.... Upon 10 terms isA. 11300B. 12100C. 12300D. 11200 |
| Answer» Correct Answer - B | |
| 11. |
In a set of four number, the first three are in GP & the last three are in A.P. with common difference 6. If the first number is the same as the fourth, find the four numbers.A. 8B. 16C. 2D. 4 |
| Answer» Correct Answer - A | |
| 12. |
If `(1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n terms") = (20)/(7 " log"_(10)x) and n = log_(10)x + log_(10) x^((1)/(2)) + log_(10) x^((1)/(4)) + log_(10) x^((1)/(8)) + ... + oo`, then x is equal toA. `10^(3)`B. `10^(5)`C. `10^(6)`D. `10^(7)` |
| Answer» Correct Answer - Bcrrct. ans. = B | |
| 13. |
An H.M. is inserted between the number 1/3 and an unknown number. If we diminish the reciprocal of the inserted number by 6, it is the G.M. of the reciprocal of 1/3 and that of the unknown number. If all the terms of the respective H.P. are distinct thenA. the unknown number is 27B. the unknown number is 1/27C. the H.M. is 15D. the G.M. is 21 |
| Answer» Correct Answer - B | |
| 14. |
Let `b_1 > 1` for `i=1,2,......,101.` Suppose `log_eb_1,log_eb_10` are in Arithmetic progression `(A.P.)` with the common difference `log_e2.` suppose `a_1,a_2..........a_101` are in A.P. such `a_1=b_1 and a_51=b_51.` If `t=b_1+b_2+......+b_51 and s=a_1+a_2+......+a_51` thenA. `s gt t and a_(101) gt b_(101)`B. `s gt t and a_(101) lt b_(101)`C. `s lt t and a_(101) gt b_(101)`D. `s lt t and a_(101) lt b_(101)` |
| Answer» Correct Answer - B | |
| 15. |
If G be the GM between x and y, then the value of `(1)/(G^(2) - x^(2)) + (1)/(G^(2) - y^(2))` is equal toA. `G^(2)`B. `(2)/(G^(2))`C. `(1)/(G^(2))`D. `3G^(2)` |
| Answer» Correct Answer - C | |
| 16. |
If a,b and c are positive real number then `(a)/(b) + (b)/(c) + (c)/(a)` is greater than or equal toA. 3B. 6C. 27D. 5 |
| Answer» Correct Answer - A | |
| 17. |
The arithmetic mean of the nine number in the given set {9,99,999, ...... 999999999} is a 9 digit number N, all whose digits are distinct. The number N does not contain the digit |
| Answer» Correct Answer - A | |
| 18. |
If `sin(x-y),sinx,sin(x+y)` are in H.P., then find the value of `sinxsec(y/2)`A. 2B. `sqrt2`C. `-sqrt2`D. `-2` |
| Answer» Correct Answer - B::C | |
| 19. |
If `a, b, c` are in HP, then `(a - b)/( b- c)` is equal toA. `(a)/(b)`B. `(b)/(a)`C. `(a)/(c)`D. `(c)/(b)` |
| Answer» Correct Answer - C | |
| 20. |
a, b, c are distinct positive real in HP, then the value of the expression,`((b+a)/(b-a))+((b+c)/(b-c))`is equal toA. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 21. |
If a, b and c be three distinct real number in G.P. and `a + b + c = xb`, then x cannot beA. 4B. `-3`C. `-2`D. 2 |
| Answer» Correct Answer - D | |
| 22. |
Four numbers are in A.P. If their sum is 20 and the sum of their squares is 120, then the middle terms areA. 2, 4B. 4, 6C. 6, 8D. 8, 10 |
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Answer» Correct Answer - B Let the number are `a - 3d, a - d, a + d, a + 3d` given, `a - 3d + a - d + a + d + a + 3d = 20 " " rArr 4a = 20 rArr a = 5` and `(a - 3d)^(2) + (a - d)^(2) + (a + d)^(2) + (a + 3d)^(2) = 120 rArr 4a^(2) + 20d^(2) = 120` `rArr 4 xx 5^(2) + 20 d^(2) = 120 " " rArr d^(2) = 1 rArr d = -+ 1` Hence number 2,4,6,8 or 8,6,4,2 |
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| 23. |
if a,b, c, d and p are distinct real number such that `(a^(2) + b^(2) + c^(2))p^(2) - 2p (ab + bc + cd) + (b^(2) + c^(2) + d^(2)) lt 0` then a, b, c, d are inA. A.P.B. G.P.C. H.P.D. None of these |
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Answer» Correct Answer - B Here, the given condition `(a^(2) + b^(2) + c^(2)) p^(2) - 2p (ab + bc+ ca) + b^(2) + c^(2) + d^(2) lt 0` `hArr (p - b)^(2) + (bp - c)^(2) + (cp - d)^(2) lt 0` `:.` a square can not be negative `:. ap - b = 0, bc - c = 0, cp - d = 0 hArr p = (b)/(a) = (c)/(b) = (d)/(c) hArr a, b, c, d` are in G.P. |
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| 24. |
If `x = sum_(n=0)^(oo) a^(n), y=sum_(n=0)^(oo) b^(n), z = sum_(n=0)^(oo) C^(n)` where a,b,c are in A.P. and `|a| lt 1, |b| lt 1, |c| lt 1`, then x,y,z are inA. HPB. Arithmetic -Geometric ProgressionC. APD. GP |
| Answer» Correct Answer - A | |
| 25. |
If `x and y` are positive real numbers and `m, n` are any positive integers, then `(x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4`A. `(1)/(2)`B. `(1)/(4)`C. `(m + n)/(6mn)`D. `1` |
| Answer» Correct Answer - B | |
| 26. |
Let `s_(1), s_(2), s_(3).... and t_(1), t_(2), t_(3)`.... are two arithmetic sequences such that `s_(1) = t_(1) != 0, s_(2) = 2t_(2) and sum_(i=1)^(10) s_(i) = sum_(i=1)^(15) t_(i)`. Then the value of `(s_(2) -s_(1))/(t_(2) - t_(1))` isA. `8//3`B. `3//2`C. 19/8D. 2 |
| Answer» Correct Answer - C | |
| 27. |
Sum up to 16 terms of the series `(1^(3))/(1) + (1^(3) + 2^(3))/(1 + 3) + (1^(3) + 2^(3) + 3^(3))/(1 + 3 + 5) + ..` isA. 450B. 456C. 446D. None of these |
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Answer» Correct Answer - C `t_(n) = (1^(3) + 2^(3) + 3^(3) + .... + n^(3))/(1 +3 + 5 + ...(2n -1)) = ({(n(n + 1))/(2)}^(2))/((n)/(2) {2 + 2 (n -1)}) = ((n^(2) (n + 1)^(2))/(4))/(n^(2)) = ((n+1)^(2))/(4) ==(n^(2))/(4) + (n)/(2) + (1)/(4)` `:. S_(n) = Sigmat_(n) = (1)/(4) Sigman^(2) + (1)/(2) Sigman + (1)/(4) Sigma 1 = (1)/(4) .(n(n + 1)(2n + 1))/(6) + (1)/(2). (n(n + 1))/(2) + (1)/(4). n` `:. S_(16) = (16.17.33)/(24) + (16.17)/(4) + (16)/(4) = 446` |
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| 28. |
Given sum of the first `n` terms of an A.P is `2n + 3n^(2)`. Another A.P. is formed with the same first term and double of the common difference, the sum of `n` termsA. `n + 4n^(2)`B. `n^(2) + 4n`C. `3n + 2n^(2)`D. `6n^(2) - n` |
| Answer» Correct Answer - D | |
| 29. |
The first term of an infinite G.P. is 1 and every term is equals to the sum of the successive terms, then its fourth term will beA. `(1)/(2)`B. `(1)/(8)`C. `(1)/(4)`D. `(1)/(16)` |
| Answer» Correct Answer - B | |
| 30. |
If a, b, c are in AP, then `(a - c)^(2)` equalsA. `4(b^(2) - ac)`B. `4(b^(2) + ac)`C. `4b^(2) - ac`D. `b^(2) - 4ac` |
| Answer» Correct Answer - A | |
| 31. |
The rational number, which equals the number `2.bar 357` with recurring decimal is:A. `(2357)/(999)`B. `(2379)/(997)`C. `(785)/(333)`D. `(2355)/(1001)` |
| Answer» Correct Answer - C | |