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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.
| 51. |
A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m, and the sum of even terms of the GP is n, then what is its common ratio? |
| A. | m/n |
| B. | n/m |
| C. | m + (n/m) |
| D. | n + (m/n) |
| Answer» C. m + (n/m) | |
| 52. |
If the mth term of HP be n and nth term be m then the rth term will be: |
| A. | \(\dfrac{mn}{r}\) |
| B. | \(\dfrac{r}{mn}\) |
| C. | \(\dfrac{mn}{r+1}\) |
| D. | \(\dfrac{mn}{r-1}\) |
| Answer» B. \(\dfrac{r}{mn}\) | |
| 53. |
Let N be the set of natural numbers and two functions f and g be defined as f, g : N → N such that,\(f\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{{\rm{n}} + 1}}{2}}&{{\rm{\;if\;n\;is\;odd\;}}}\\{\frac{{\rm{n}}}{2}}&{{\rm{\;if\;n\;is\;even\;}}}\end{array}} \right.\)And g(n) = n - (-1)n. Then fog is: |
| A. | Onto but not one-one. |
| B. | One-one but not onto. |
| C. | Both one-one and onto. |
| D. | Neither one-one nor onto. |
| Answer» B. One-one but not onto. | |
| 54. |
If the sum of the first 15 terms of the series \({\left( {\frac{3}{4}} \right)^3} + {\left( {1\frac{1}{2}} \right)^3} + {\left( {2\frac{1}{4}} \right)^3} + {3^3} + {\left( {3\frac{3}{4}} \right)^3} + \ldots {\rm{\;}}\) is equal to 225k, then k is equal to |
| A. | 108 |
| B. | 27 |
| C. | 54 |
| D. | 9 |
| Answer» C. 54 | |
| 55. |
Let Sn denote the sum of the first n terms of an A.P. If S4 = 16 and S6 = -48, then S10 is equal to: |
| A. | - 260 |
| B. | - 410 |
| C. | - 320 |
| D. | - 380 |
| Answer» D. - 380 | |
| 56. |
A person is to count 4500 notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = a3 = … = a10 = 150, and a10, a11, a12, … are in AP with the common difference -2, then the time taken by him to count all the notes is |
| A. | 24 minutes |
| B. | 34 minutes |
| C. | 125 minutes |
| D. | 135 minutes |
| Answer» C. 125 minutes | |
| 57. |
Consider the following measures of central tendency for a set of N numbers:1. Arithmetic mean.2. Geometric mean.Which of the above uses/use all the data? |
| A. | 1 only. |
| B. | 2 only. |
| C. | Both 1 and 2. |
| D. | Neither 1 nor 2. |
| Answer» D. Neither 1 nor 2. | |
| 58. |
Let f(x) be a polynomial function of second degree and f(1) = f(-1). If a, b, c are in AP, then f'(a), f'(b), f'(c) are in: |
| A. | GP |
| B. | HP |
| C. | AGP |
| D. | AP |
| Answer» E. | |
| 59. |
If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is |
| A. | mn |
| B. | m + n |
| C. | 2(m + n) |
| D. | –(m + n) |
| Answer» E. | |
| 60. |
How many geometric progression is/are possible containing 27, 8 and 12 as three of its/their terms? |
| A. | One |
| B. | Two |
| C. | Four |
| D. | Infinitely many |
| Answer» E. | |
| 61. |
If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms? |
| A. | -500 |
| B. | -250 |
| C. | 500 |
| D. | 250 |
| Answer» C. 500 | |
| 62. |
If sin β is the harmonic mean of sin α and cos α and sin θ is the arithmetic mean of sin α and cos α then which of the following is/are correct?1) \(\sqrt 2 \sin \left( {\alpha + \frac{\pi }{4}} \right)\sin \beta = \sin 2a\)2) \(\sqrt 2 \sin \theta = \cos \left( {\alpha - \frac{\pi }{4}} \right)\)Select the correct answer using the code give below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 63. |
Let tr denotes the rth term of an arithmetic progression. If \(t_m = \dfrac{1}{n}\) and \(t_n = \dfrac{1}{m}\)then tmn equals: |
| A. | \(\dfrac{1}{mn}\) |
| B. | 4 |
| C. | \(\dfrac{1}{m} + \dfrac{1}{n}\) |
| D. | 1 |
| Answer» E. | |
| 64. |
In a GP consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of the GP is: |
| A. | \(\dfrac{1-\sqrt{5}}{2}\) |
| B. | \(\dfrac{\sqrt{5}}{2}\) |
| C. | \(\sqrt{5}\) |
| D. | \(\dfrac{\sqrt{5}-1}{2}\) |
| Answer» E. | |
| 65. |
If x, 2x + 2, 3x + 3 are the first three terms of a geometric progression, then 4th term in the geometric progression is |
| A. | -13.5 |
| B. | 13.5 |
| C. | -27 |
| D. | 27 |
| Answer» B. 13.5 | |
| 66. |
If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is |
| A. | \(8,{\rm{\;}}2,\frac{1}{2},\frac{1}{8},{\rm{\;}} \ldots \ldots ..\) |
| B. | \(10,{\rm{\;}}2,\frac{2}{5},\frac{2}{{{2^5}}},{\rm{\;}} \ldots \ldots .\) |
| C. | \(4,2,1,\frac{1}{2},\frac{1}{{{2^2}}}, \ldots \ldots .\) |
| D. | \(6,3,\frac{3}{2},\frac{3}{4}, \ldots ..\) |
| Answer» D. \(6,3,\frac{3}{2},\frac{3}{4}, \ldots ..\) | |
| 67. |
If \(\left| x \right| < 1\), then \(\frac{{{x^2}}}{2} + \frac{{2{x^3}}}{3} + \frac{{3{x^4}}}{4} + \ldots \) is equal to |
| A. | \(\frac{x}{{1 - x}} + {\log _{\rm{e}}}\left( {1 - x} \right)\) |
| B. | \(\frac{x}{{1 +x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\) |
| C. | \(\frac{x}{{1 - x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\) |
| D. | \(\frac{x}{{1 + x}} + {\log _{\rm{e}}}\left( {1 - x} \right)\) |
| Answer» B. \(\frac{x}{{1 +x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\) | |
| 68. |
Number of real solution of the equation sin (ex) = 5x + 5-x is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | Infinitely many |
| Answer» B. 1 | |
| 69. |
If the ratio of AM to GM of two positive numbers a and b is 5 : 3 then a : b is equal to |
| A. | 3 : 5 |
| B. | 2 : 9 |
| C. | 9 : 1 |
| D. | 5 : 3 |
| Answer» D. 5 : 3 | |
| 70. |
If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then value of its 11th term is? |
| A. | -35 |
| B. | 25 |
| C. | -36 |
| D. | -25 |
| Answer» E. | |
| 71. |
Let a1, a2, a3, …. be an A.P. with a6 = 2. Then the common difference of this A.P., which maximizes the product a1, a4, a5, is: |
| A. | \(\frac{3}{2}\) |
| B. | \(\frac{8}{5}\) |
| C. | \(\frac{6}{5}\) |
| D. | \(\frac{2}{3}\) |
| Answer» C. \(\frac{6}{5}\) | |
| 72. |
If \({{\rm{x}}^{{\rm{In}}\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)}} \cdot {{\rm{y}}^{{\rm{In}}{{\left( {{\rm{xz}}} \right)}^2}}} \cdot {{\rm{z}}^{{\rm{In}}\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)}} = {{\rm{y}}^{4{\rm{\;In\;y}}}}\) for any x > 1, y > 1 and z > 1, then which one of the following is correct? |
| A. | In y is the GM of In x, In x, In x and In z |
| B. | In y is the AM of In x, In x, In x, In z |
| C. | In y is the HM of In x, In x, In x and In z |
| D. | In y is the AM of In x, In x, In z and In z |
| Answer» C. In y is the HM of In x, In x, In x and In z | |
| 73. |
If log2x + log2y ≥ 6 then the least value of (x + y) is: |
| A. | 4 |
| B. | 9 |
| C. | 32 |
| D. | 16 |
| Answer» E. | |
| 74. |
If x1 and x2 are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is |
| A. | \({{\rm{x}}_1} + {{\rm{x}}_2} > 2\sqrt {{{\rm{x}}_1}{{\rm{x}}_2}} \) |
| B. | \(\sqrt {{{\rm{x}}_1}} + \sqrt {{{\rm{x}}_2}} > \sqrt 2 \) |
| C. | \(\left| {\sqrt {{{\rm{x}}_1}} - \sqrt {{{\rm{x}}_2}} } \right| > \sqrt 2 \) |
| D. | \({{\rm{x}}_1} + {{\rm{x}}_2} < 2{\rm{\;}}\left( {\sqrt {{{\rm{x}}_1}{{\rm{x}}_2}} + 1} \right)\) |
| Answer» D. \({{\rm{x}}_1} + {{\rm{x}}_2} < 2{\rm{\;}}\left( {\sqrt {{{\rm{x}}_1}{{\rm{x}}_2}} + 1} \right)\) | |
| 75. |
How many two-digit numbers are divisible by 4? |
| A. | 21 |
| B. | 22 |
| C. | 24 |
| D. | 25 |
| Answer» C. 24 | |
| 76. |
If a, b, c are in A. P. and x, y, z are in G. P., then the value ofxb - c yc - a za - b is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | -1 |
| Answer» C. 2 | |
| 77. |
Let a, b and c be in G.P. with common ratio r, where a ≠ 0\(\;{\rm{and\;}}0 < r \le \frac{1}{2}\) . If 3a, 7b and 15c are the first three terms of an A.P., then the 4th term of this A.P. is: |
| A. | \(\frac{2}{3}{\rm{a}}\) |
| B. | 5 a |
| C. | \(\frac{7}{3}{\rm{a}}\) |
| D. | a |
| Answer» E. | |
| 78. |
If 1.3 + 2.32 + … + n.3n \(= \frac{{\left( {2n - 1} \right){3^a} + b}}{4}\) then a and b are respectively |
| A. | n, 2 |
| B. | n, 3 |
| C. | n + 1, 2 |
| D. | n + 1, 3 |
| Answer» E. | |
| 79. |
Let m and n (m < n) be the roots of the equation x2 - 16x + 39 = 0. If four terms p, q, r and s are inserted between m and n to form an AP, then what is the value of p + q + r + s? |
| A. | 29 |
| B. | 30 |
| C. | 32 |
| D. | 35 |
| Answer» D. 35 | |
| 80. |
If a, b, c are in AP or GP or HP, then \(\frac{{a - b}}{{b - c}}\) is equal to |
| A. | \(\frac{b}{a}or{\rm{\;}}1{\rm{\;}}or\frac{b}{c}\) |
| B. | \(\frac{c}{a}or\frac{c}{b}or{\rm{\;}}1\) |
| C. | \(1or\frac{a}{b}or\frac{a}{c}\) |
| D. | \(1or\frac{a}{b}or\frac{c}{a}\) |
| Answer» D. \(1or\frac{a}{b}or\frac{c}{a}\) | |
| 81. |
If α, β, and γ are three consecutive terms of a non-constant G.P such that the equations αx2 + 2βx + γ = 0 and x2 + x – 1 = 0 have a common root, then α(β + γ) is equal to: |
| A. | 0 |
| B. | αβ |
| C. | αγ |
| D. | βγ |
| Answer» E. | |
| 82. |
If β, 2, 2m are in GP, then what is the value of \({\rm{\beta }}\sqrt {\rm{m}} \)? |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» B. 2 | |
| 83. |
Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct? |
| A. | 5m = 4n |
| B. | 2m = n |
| C. | 4m = 5n |
| D. | m = 4n |
| Answer» E. | |
| 84. |
Let a, b and c be the7th, 11th and 13th terms respectively of a non-constant A. P. If these are also the three consecutive terms of a G.P., then a/c is equal to: |
| A. | 2 |
| B. | 1/2 |
| C. | 7/13 |
| D. | 4 |
| Answer» E. | |
| 85. |
\((a + b + c) \left ( \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} \right)\) is: |
| A. | Less than or equal to 9 |
| B. | Less than or equal to 3 |
| C. | Greater than or equal to 9 |
| D. | Greater than or equal to 3 |
| Answer» D. Greater than or equal to 3 | |
| 86. |
If a variable takes values 0, 1, 2, 3, …, n with frequencies 1, C(n, 1), C(n, 2), C(n, 3),…, C(n, n) respectively, then the arithmetic mean is |
| A. | 2n |
| B. | n + 1 |
| C. | n |
| D. | \(\frac{{\rm{n}}}{2}\) |
| Answer» E. | |
| 87. |
If x, 3/2, z are in AP; x, 3, z are in GP; then which one of the following will be in HP? |
| A. | x, 6, z |
| B. | x, 4, z |
| C. | x, 2, z |
| D. | x, 1, z |
| Answer» B. x, 4, z | |
| 88. |
For x ∈ R, let [x] denote the greatest integer ≤ x, then the sum of the series\(\left[ -\frac{1}{3} \right]+\left[ -\frac{1}{3}-\frac{1}{100} \right]+\left[ -\frac{1}{3}-\frac{2}{100} \right]+\cdots +\left[ -\frac{1}{3}-\frac{99}{100} \right]\) is: |
| A. | -153 |
| B. | -133 |
| C. | -131 |
| D. | -135 |
| Answer» C. -131 | |
| 89. |
Consider the following statements:1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.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 | |
| 90. |
If a, a1, a2, a3, ..., a2n - 1, b are in AP, a, b1, b2, ... b2n - 1, b are in GP and a, c1, c2, c3, ..., c2n - 1, b re in HP, where a, b are positive, then the equation anx2 - bnx + cn = 0 has its roots |
| A. | Real and equal |
| B. | Real and unequal |
| C. | Imaginary |
| D. | One real and one imaginary |
| Answer» D. One real and one imaginary | |
| 91. |
A scientist collected 11 observations in connection with a particular experiment and calculated the summary measures such as mean, median, variance, maximum and minimum. Later, the scientist found that two observations 54 and 43 were wrongly recorded as 45 and 34. Which of the following statements are true in this context ?(i) Corrected mean will be larger than the initial mean.(ii) If the initial median was 36, then the corrected median would be less than 36.(iii) The initial variance and the corrected variance are same. |
| A. | (i) and (iii) |
| B. | (ii) and (iii) |
| C. | (iii) only |
| D. | (i) only |
| Answer» E. | |
| 92. |
If sum of n terms of an arithmetical progression is 5n2 - 3n, then its pth term is. |
| A. | 10p + 8 |
| B. | 10p - 8 |
| C. | 10p + 3 |
| D. | 10p - 3 |
| Answer» C. 10p + 3 | |
| 93. |
If b2, a2, c2 are in AP then a + b, b + c, c + a will be in: |
| A. | AP |
| B. | GP |
| C. | HP |
| D. | None of these |
| Answer» D. None of these | |
| 94. |
If the product of n positive numbers is unity, then their sum is? |
| A. | a positive integer |
| B. | divisible by n |
| C. | equal to \(\rm n + \frac{1}{n}\) |
| D. | never less than n |
| Answer» E. | |
| 95. |
For the sequence, 1/2, 2/3, 3/4, ____ n/n + 1, ____ which of the following is not true ? |
| A. | The sequence is strictly increasing |
| B. | The sequence is bounded above by 0.9 |
| C. | The sequence is bounded below and bounded above |
| D. | The sequence contains no number between 3/4 and 4/5 |
| Answer» C. The sequence is bounded below and bounded above | |
| 96. |
If non zero number a, b, c are in H.P, then the straight line \(\rm \frac x a + \frac y b + \frac 1 c = 0\) always passes through a fixed point, then the point is |
| A. | (1, -2) |
| B. | \(\left(1,\frac 1 2\right)\) |
| C. | (-1, 2) |
| D. | None |
| Answer» B. \(\left(1,\frac 1 2\right)\) | |
| 97. |
Let x, y, z be positive real numbers such that x, y, z are in GP and tan-1 x, tan-1 y and tan-1 z are in AP. Then which one of the following is correct? |
| A. | x = y = z |
| B. | xz = 1 |
| C. | x ≠ y and y = z |
| D. | x = y and y ≠ z |
| Answer» B. xz = 1 | |
| 98. |
If a1, a2, a3, …..., an are in A. P. and a1 + a4 + a7 + ...... + a16 = 114, then a1 + a6 + a11 + a16 is equal to: |
| A. | 98 |
| B. | 76 |
| C. | 38 |
| D. | 64 |
| Answer» C. 38 | |
| 99. |
If a1, a2, a3, … are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P. is: |
| A. | 200 |
| B. | 280 |
| C. | 120 |
| D. | 150 |
| Answer» B. 280 | |
| 100. |
Let \({S_k} = \frac{{1 + 2 + 3 + \ldots + k}}{k}.{\rm{\;If\;}}S_1^2 + S_2^2 + \ldots + S_{10}^2 = \frac{5}{{12}}A\), then A is equal to |
| A. | 156 |
| B. | 301 |
| C. | 283 |
| D. | 303 |
| Answer» E. | |