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MCQOPTIONS
This section includes 136 Mcqs, each offering curated multiple-choice questions to sharpen your Maharashtra CET knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct? |
| A. | q2 = pr |
| B. | r2 = pq |
| C. | pqr = 1 |
| D. | 2q = p + r |
| Answer» B. r2 = pq | |
| 2. |
Let a1, a2….a30 be an A.P\(S = \mathop \sum \limits_{i = 1}^{30} {a_i}{\rm{\;and\;}}T = \mathop \sum \limits_{i = 1}^{15} {a_{\left( {2i - 1} \right)}}\)If a5 = 27 and S – 2T = 75. Then a10 is equal to: |
| A. | 52 |
| B. | 57 |
| C. | 47 |
| D. | 42 |
| Answer» B. 57 | |
| 3. |
If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is: |
| A. | 4 : 1 |
| B. | 1 : 3 |
| C. | 3 : 1 |
| D. | 2 : 1 |
| Answer» D. 2 : 1 | |
| 4. |
If \({S_n} = nP + \frac{{n\left( {n - 1} \right)Q}}{2}\), where Sn denotes the sum of the first n terms of an AP, then the common difference is |
| A. | P + Q |
| B. | 2P + 3Q |
| C. | 2Q |
| D. | Q |
| Answer» E. | |
| 5. |
If p, q, r, s are in G.P., then \(\frac{1}{{{p^2} + {q^2}}}\), \(\frac{1}{{{q^2} + {r^2}}}\), \(\frac{1}{{{r^2} + {s^2}}}\) are in |
| A. | A. P. |
| B. | G. P. |
| C. | H. P. |
| D. | None of these |
| Answer» C. H. P. | |
| 6. |
If a, b > 0, then the maximum value of \(\dfrac{a^3b}{(a + b)^4}\)is: |
| A. | \(\dfrac{27}{512}\) |
| B. | \(\dfrac{81}{256}\) |
| C. | \(\dfrac{81}{512}\) |
| D. | \(\dfrac{27}{256}\) |
| Answer» E. | |
| 7. |
If the nth term of an AP be (2n - 1), then the sum of its first n terms will be: |
| A. | n2 - 1 |
| B. | (2n - 1)2 |
| C. | n2 |
| D. | n2 + 1 |
| Answer» D. n2 + 1 | |
| 8. |
If the geometric mean of two numbers is 6.0 and the arithmetic mean is 6.5, then the difference of squares of these numbers is |
| A. | 65 |
| B. | 120 |
| C. | 130 |
| D. | 140 |
| Answer» B. 120 | |
| 9. |
Let Tr be the rth term of an AP for r = 1, 2, 3, …… If for some distinct positive integers m and n we have Tm = 1/n and Tn = 1/m, then what is Tmn equal to? |
| A. | (mn) - 1 |
| B. | m - 1 + n - 1 |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 10. |
Let a1, a2, a3,…. , a10 be in G.P. with ai > 0 for I = 1, 2, …, 10 and S be the set of pairs (r, k), r, k ∈ N (the set of natural numbers) for which\(\left| {\begin{array}{*{20}{c}}{{\rm{lo}}{{\rm{g}}_e}a_1^ra_2^k}&{{\rm{lo}}{{\rm{g}}_e}a_2^ra_3^k}&{{\rm{lo}}{{\rm{g}}_e}a_3^ra_4^k}\\{{\rm{lo}}{{\rm{g}}_e}a_4^ra_5^k}&{{\rm{lo}}{{\rm{g}}_e}a_5^\pi a_6^k}&{{\rm{lo}}{{\rm{g}}_e}a_6^ra_7^k}\\{{\rm{lo}}{{\rm{g}}_e}a_7^ra_8^k}&{{\rm{lo}}{{\rm{g}}_e}a_8^\pi a_9^k}&{{\rm{lo}}{{\rm{g}}_e}a_9^ra_{10}^k}\end{array}} \right| = 0\)Then the number of elements in S, is: |
| A. | 4 |
| B. | Infinitely many |
| C. | 2 |
| D. | 10 |
| Answer» C. 2 | |
| 11. |
If \(\rm \frac {a^{n + 1} + b^{n + 1}}{a^n + b^n}\) be the harmonic mean of a and b then value of n is: |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | 2 |
| Answer» C. 0 | |
| 12. |
Consider the following statements:1. cos θ + sec θ can never be equal to 1.5.2. tan θ + cot θ can never be less than 2.Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 13. |
If y = x + x2 + x3 + … up to infinite terms where x < 1, then which one of the following is correct? |
| A. | \(x = \frac{y}{{1 + y}}\) |
| B. | \(x = \frac{y}{{1 - y}}\) |
| C. | \(x = \frac{{1 + y}}{y}\) |
| D. | \(x = \frac{{1 - y}}{y}\) |
| Answer» B. \(x = \frac{y}{{1 - y}}\) | |
| 14. |
If the sum of first n terms of a series is (n + 12) , then what is its third term? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 15. |
In an acute angled ΔABC, the least value of sec A + sec B + sec C is: |
| A. | 6 |
| B. | 8 |
| C. | 3 |
| D. | 2 |
| Answer» B. 8 | |
| 16. |
Let Sn = 1 + q + q2 +…+ qn and \({{\rm{T}}_{\rm{n}}} = 1 + \left( {\frac{{{\rm{q}} + 1}}{2}} \right) + {\left( {\frac{{{\rm{q}} + 1}}{2}} \right)^2} + \ldots + {\left( {\frac{{{\rm{q}} + 1}}{2}} \right)^{\rm{n}}}\) where q is a real number and q ≠ 1. If 101C1 + 101C2S2 +…+ 101C101S100 = αT100, then α is equal to: |
| A. | 299 |
| B. | 202 |
| C. | 200 |
| D. | 2100 |
| Answer» E. | |
| 17. |
If log10 2, log10(2x-1) and log10(2x+ 3) are three consecutive terms of an AP, then the value of x is |
| A. | 1 |
| B. | log5 2 |
| C. | log2 5 |
| D. | log10 5 |
| Answer» D. log10 5 | |
| 18. |
Consider the following statements:1. The sum of cubes of first 20 natural numbers is 444000.2. The sum of squares of first 20 natural numbers is 2870.Which of the above statements is / are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 19. |
If \(a_1, a_2, a_3,...,a_n\) are positive real numbers whose product is a fixed number C, then the minimum value of \(a_1+a_2+...+a_n\) is |
| A. | \(\dfrac{n(2c)^1}{n}\) |
| B. | \(\dfrac{(n+1)C^1}{n}\) |
| C. | \(n{(C)}^{1/n}\) |
| D. | \(((n+1)(2c)^1/n\) |
| Answer» D. \(((n+1)(2c)^1/n\) | |
| 20. |
Let a1, a2, …, a10 be a GP. If \(\frac{{{a_3}}}{{{a_1}}} = 25\), then a9/a5 equals: |
| A. | 54 |
| B. | 4(52) |
| C. | 53 |
| D. | 2(52) |
| Answer» B. 4(52) | |
| 21. |
If \(\rm x^a=y^b=z^c\) and x, y and z are in GP, then a, b and c are in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | NOne of these |
| Answer» D. NOne of these | |
| 22. |
If p2, q2 and r2 (where p, q, r > 0) are in GP, then which of the following is / are correct?1. p. q and r are in GP.2. p, q and r are in AP.Select the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 23. |
In a geometric progression, first term is 7, the last term is 448 and the sum is 889. The common ratio of the geometric progression is |
| A. | 3/2 |
| B. | 2 |
| C. | 3 |
| D. | 3.5 |
| Answer» C. 3 | |
| 24. |
If a, b and c be three distinct real numbers in G.P. and a + b + c = xb, then x cannot be: |
| A. | -2 |
| B. | -3 |
| C. | 4 |
| D. | 2 |
| Answer» E. | |
| 25. |
Let Sn be the sum of the first n terms of an AP. If S2n = 3n + 14n2, then what is the common difference? |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | 9 |
| Answer» D. 9 | |
| 26. |
How many possible values can n have? |
| A. | One |
| B. | Two |
| C. | Three |
| D. | Infinitely many |
| Answer» B. Two | |
| 27. |
If nC4, nC5 and nC6 are in AP, then n can be |
| A. | 9 |
| B. | 11 |
| C. | 14 |
| D. | 12 |
| Answer» D. 12 | |
| 28. |
If the arithmetic mean of a, b, c is \(\rm \frac M 3\) and \(\rm \frac{1}{a} + \frac{1}{b} = -\frac{1}{c} \), then the arithmetic mean of a2, b2, c2 is |
| A. | M2/3 |
| B. | 3M2 |
| C. | 6M2 |
| D. | 9M2 |
| Answer» B. 3M2 | |
| 29. |
\(\mathop {\lim }\limits_{n \to \infty } {\left( {1 - \frac{1}{{2n}}} \right)^{n + 1}}\) is equal to |
| A. | \(\sqrt{e}\) |
| B. | \(\frac{1}{{\sqrt e }}\) |
| C. | e |
| D. | \(\frac{1}{{e }}\) |
| Answer» C. e | |
| 30. |
If roots of equation (a - b) x2 + (c - a) x + (b - c) = 0 are equal, then a, b, c are in: |
| A. | AP |
| B. | HP |
| C. | GP |
| D. | None of these |
| Answer» B. HP | |
| 31. |
If an infinite GP has the first term x and the sum 5, then which one of the following is correct? |
| A. | x <- 10 |
| B. | -10 < x < 0 |
| C. | 0 < x < 10 |
| D. | x > 10 |
| Answer» D. x > 10 | |
| 32. |
If in an A.P. Sn = p.n2 and Sm = p.m2, where Sr denotes the sum of r terms of the A.P. then Sp is equal to: |
| A. | p3 |
| B. | (m + n)p2 |
| C. | mnp |
| D. | \(\dfrac{p^3}{2}\) |
| Answer» B. (m + n)p2 | |
| 33. |
If a, b, c, d are in HP, then |
| A. | a + b > c + d |
| B. | a + c > b + d |
| C. | a + d > b + c |
| D. | None of these |
| Answer» D. None of these | |
| 34. |
If the side of a right angle triangle are a, ar, ar2 (r < 1), then r2 is equal to |
| A. | \(\frac{{\sqrt 5 - 1}}{2}\) |
| B. | \(\frac{{\sqrt 5 + 1}}{2}\) |
| C. | \(\sqrt 5 - 1\) |
| D. | \(\sqrt 5 + 1\) |
| Answer» B. \(\frac{{\sqrt 5 + 1}}{2}\) | |
| 35. |
If x2, x, -8 are in AP, then which one of the following is correct? |
| A. | x ∈ {-2} |
| B. | x ∈ {4} |
| C. | x ∈ {-2, 4} |
| D. | x ∈ {-4, 2} |
| Answer» D. x ∈ {-4, 2} | |
| 36. |
If x = 1 – y + y2 – y3 + … up to infinite terms, where |y| < 1, then which one of the following is correct? |
| A. | \(x = \frac{1}{{1 + y}}\) |
| B. | \(x = \frac{1}{{1 - y}}\) |
| C. | \(x = \frac{y}{{1 + y}}\) |
| D. | \(x = \frac{y}{{1 - y}}\) |
| Answer» B. \(x = \frac{1}{{1 - y}}\) | |
| 37. |
If x1 = 1, x2 = 1 + 1/2, x3 = 1 + 1/2 + 1/22, ........, xn = 1 + 1/2 + 1/22 + ..... + 1/2n-1 , then which of the following statements is true? |
| A. | 2 < xn < 3, for n ≥ 10 |
| B. | xn ≤ 1.8 for every n |
| C. | xn = 2 for some n |
| D. | xn < 2 for every n |
| Answer» D. xn < 2 for every n | |
| 38. |
If Sr, denotes the sum of the first r terms of an AP then, \(\dfrac{S_{3r} - S_{r - 1}}{S_{2r} - S_{2r-1} }\)is |
| A. | 2r + 1 |
| B. | 2r + 3 |
| C. | 2r - 1 |
| D. | 4r + 1 |
| Answer» B. 2r + 3 | |
| 39. |
Let p be the mean of m observations and q be the mean of n observations, where p ≤ q. If the combined mean of (m + n) observations is c, then which one of the following is correct? |
| A. | c ≤ p |
| B. | c ≥ q |
| C. | p ≤ c ≤ q |
| D. | q ≤ c ≤ p |
| Answer» D. q ≤ c ≤ p | |
| 40. |
If p, q, r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in |
| A. | Arithmetic progression |
| B. | Geometric progression |
| C. | Harmonic progression |
| D. | None of the above |
| Answer» C. Harmonic progression | |
| 41. |
If a, b, c are in geometric progression, then logax x, logbx x and logcx x are in |
| A. | Arithmetic progression |
| B. | Geometric progression |
| C. | Harmonic progression |
| D. | Arithmetico-geometric progression |
| Answer» D. Arithmetico-geometric progression | |
| 42. |
If the sum of 16 terms of an A.P. is 1624 and the first term is 500 times the common difference, then find the common difference: |
| A. | 2 |
| B. | 1/5 |
| C. | 1/2 |
| D. | 5 |
| Answer» C. 1/2 | |
| 43. |
If a1, a2, ..., an are in A.P. and a1 = 0, then the value of \(\rm \left(\frac {a_3}{a_2} + \frac {a_4}{a_3} + ...+\frac {a_n}{a_{n-1}}\right)-a_2\left(\frac 1 {a_2} + \frac 1 {a_3} + ...+\frac 1 {a_{n-2}}\right)\) is equal to |
| A. | \(\rm (n - 2) + \frac 1 {n-2}\) |
| B. | \(\rm \frac 1 {n - 2}\) |
| C. | n - 2 |
| D. | \(\rm n - \frac 1 {n - 2}\) |
| Answer» B. \(\rm \frac 1 {n - 2}\) | |
| 44. |
If m is the geometric mean of \({\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)^{\log \left( {{\rm{yz}}} \right)}},{\rm{\;}}{\left( {\frac{{\rm{z}}}{{\rm{x}}}} \right)^{\log \left( {{\rm{zx}}} \right)}}{\rm{\;and\;}}{\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)^{\log \left( {{\rm{xy}}} \right)}}\) then what is the value of m? |
| A. | 1 |
| B. | 3 |
| C. | 6 |
| D. | 9 |
| Answer» B. 3 | |
| 45. |
Let \({\rm{f}}\left( {\rm{n}} \right) = \left[ {\frac{1}{4} + \frac{{\rm{n}}}{{1000}}} \right]\), where [x] denote the integral part of x. Then the value of \(\mathop \sum \limits_{{\rm{n}} = 1}^{1000} {\rm{f}}\left( {\rm{n}} \right)\) is |
| A. | 251 |
| B. | 250 |
| C. | 1 |
| D. | 0 |
| Answer» B. 250 | |
| 46. |
102 + 112 + 122 + .... + 192 is equal to |
| A. | 1580 |
| B. | 2010 |
| C. | 2121 |
| D. | 2185 |
| Answer» E. | |
| 47. |
If three distinct numbers a, b, c are in G.P. and the equations ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have a common root, then which one of the following statements is correct? |
| A. | \(\frac{{\rm{d}}}{{\rm{a}}},\frac{{\rm{e}}}{{\rm{b}}},\frac{{\rm{f}}}{{\rm{c}}}{\rm{\;are\;in\;A}}{\rm{.P}}{\rm{.}}\) |
| B. | \({\rm{d}},{\rm{e}},{\rm{f\;are\;in\;A}}.{\rm{P}}.\) |
| C. | \({\rm{d}},{\rm{e}},{\rm{f\;are\;in\;G}}{\rm{.P}}{\rm{.}}\) |
| D. | \(\frac{{\rm{d}}}{{\rm{a}}},\frac{{\rm{e}}}{{\rm{b}}},\frac{{\rm{f}}}{{\rm{c}}}{\rm{\;are\;in\;G}}{\rm{.P}}{\rm{.}}\) |
| Answer» B. \({\rm{d}},{\rm{e}},{\rm{f\;are\;in\;A}}.{\rm{P}}.\) | |
| 48. |
If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in ? |
| A. | HP |
| B. | Arithmetico-Geometric progression |
| C. | AP |
| D. | GP |
| Answer» B. Arithmetico-Geometric progression | |
| 49. |
An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. What is the common difference? |
| A. | \(\dfrac34\) |
| B. | \(\dfrac12\) |
| C. | \(\dfrac14\) |
| D. | \(\dfrac43\) |
| Answer» B. \(\dfrac12\) | |
| 50. |
Let Sn, denote the sum of the first n terms of an AP. If S2n = 3Sn, then S3n : Sn is equal to: |
| A. | 6 |
| B. | 8 |
| C. | 4 |
| D. | 10 |
| Answer» B. 8 | |