MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 992 Mcqs, each offering curated multiple-choice questions to sharpen your General Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 501. |
The probability distribution having shape of bell and in which the values of mean lies in center of probability distribution is classified as |
| A. | continuous distribution |
| B. | normal distribution |
| C. | discrete distribution |
| D. | hyper geometric distribution |
| Answer» C. discrete distribution | |
| 502. |
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is: |
| A. | 1/13 |
| B. | 2/13 |
| C. | 1/26 |
| D. | 1/52 |
| Answer» D. 1/52 | |
| 503. |
The variance of random variable x of gamma distribution can be calculated as |
| A. | Var(x) = n + 2 ⁄ μ²; |
| B. | Var(x) = n ⁄ μ²; |
| C. | Var (x) = n * 2 ⁄ μ²; |
| D. | Var(x) = n - 2 ⁄ μ³; |
| Answer» C. Var (x) = n * 2 ⁄ μ²; | |
| 504. |
In binomial probability distribution, the dependents of standard deviations must includes |
| A. | probability of q |
| B. | probability of p |
| C. | trials |
| D. | all of above |
| Answer» E. | |
| 505. |
The formula to calculate standardized normal random variable is |
| A. | x - μ ⁄ σ |
| B. | x + μ ⁄ σ |
| C. | x - σ ⁄ μ |
| D. | x + σ ⁄ μ |
| Answer» B. x + μ ⁄ σ | |
| 506. |
In random experiment, the observations of random variable are classified as |
| A. | events |
| B. | composition |
| C. | trials |
| D. | functions |
| Answer» D. functions | |
| 507. |
In binomial distribution, the formula of calculating standard deviation is |
| A. | square root of p |
| B. | square root of pq |
| C. | square root of npq |
| D. | square root of np |
| Answer» D. square root of np | |
| 508. |
What is multiplication of the sequence 1, 2, 3, 4,… by the sequence 1, 3, 5, 7, 11,….? |
| A. | 1, 5, 14, 30,… |
| B. | 2, 8, 16, 35,… |
| C. | 1, 4, 7, 9, 13,… |
| D. | 4, 8, 9, 14, 28,… |
| Answer» B. 2, 8, 16, 35,… | |
| 509. |
What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…? |
| A. | aₙ = 3aₙ₋₁−2aₙ₊₂ |
| B. | aₙ = 3aₙ₋₁−2aₙ₋₂ |
| C. | aₙ = 3aₙ₋₁−2aₙ₋₁ |
| D. | aₙ = 3aₙ₋₁−2aₙ₋₃ |
| Answer» C. aₙ = 3aₙ₋₁−2aₙ₋₁ | |
| 510. |
What is the generating function for the sequence with closed formula aₙ=4(7ⁿ)+6(−2)ⁿ? |
| A. | (4/1−7x)+6! |
| B. | (3/1−8x) |
| C. | (4/1−7x)+(6/1+2x) |
| D. | (6/1-2x)+8 |
| Answer» D. (6/1-2x)+8 | |
| 511. |
Find the sequence generated by 1/1−x²−x⁴. (Assume that 1, 1, 2, 3, 5, 8,… has generating function 1/1−x−x².) |
| A. | 0, 0, 1, 1, 2, 3, 5, 8,… |
| B. | 0, 1, 2, 3, 5, 8,… |
| C. | 1, 1, 2, 2, 4, 6, 8,… |
| D. | 1, 4, 3, 5, 7,… |
| Answer» B. 0, 1, 2, 3, 5, 8,… | |
| 512. |
Computation of the discrete logarithm is the basis of the cryptographic system _______ |
| A. | Symmetric cryptography |
| B. | Asymmetric cryptography |
| C. | Diffie-Hellman key exchange |
| D. | Secret key cryptography |
| Answer» D. Secret key cryptography | |
| 513. |
The numbers between 1 and 520, including both, are divisible by 2 or 6 is _______ |
| A. | 349 |
| B. | 54 |
| C. | 213 |
| D. | 303 |
| Answer» E. | |
| 514. |
Find the value of x: 3 x² aˡᵒᵍᵃˣ = 348? |
| A. | 7.1 |
| B. | 4.5 |
| C. | 6.2 |
| D. | 4.8 |
| Answer» E. | |
| 515. |
An integer from 300 through 780, inclusive is to be chosen at random. Find the probability that the number is chosen will have 1 as at least one digit. |
| A. | \(\frac{171}{900}\) |
| B. | \(\frac{43}{860}\) |
| C. | \(\frac{231}{546}\) |
| D. | \(\frac{31}{701}\) |
| Answer» B. \(\frac{43}{860}\) | |
| 516. |
A family has two children. Given that one of the children is a girl and that she was born on a Monday, what is the probability that both children are girls? |
| A. | \(\frac{13}{27}\) |
| B. | \(\frac{23}{54}\) |
| C. | \(\frac{12}{19}\) |
| D. | \(\frac{43}{58}\) |
| Answer» B. \(\frac{23}{54}\) | |
| 517. |
In a renowned software development company of 240 computer programmers 102 employees are proficient in Java, 86 in C#, 126 in Python, 41 in C# and Java, 37 in Java and Python, 23 in C# and Python, and just 10 programmers are proficient in all three languages. How many computer programmers are there those are not proficient in any of these three languages? |
| A. | 138 |
| B. | 17 |
| C. | 65 |
| D. | 49 |
| Answer» C. 65 | |
| 518. |
At a software company, skilled workers have been hired for a project. Out of 75 candidates, 48 of them were software engineer; 35 of them were hardware engineer; 42 of them were network engineer; 18 of them had skills in all three jobs and all of them had skills in at least one of these jobs. How many candidates were hired who were skilled in exactly 2 jobs? |
| A. | 69 |
| B. | 14 |
| C. | 32 |
| D. | 8 |
| Answer» C. 32 | |
| 519. |
What is the sequence depicted by the generating series 4 + 15x² + 10x³ + 25x⁵ + 16x⁶+⋯? |
| A. | 10, 4, 0, 16, 25, … |
| B. | 0, 4, 15, 10, 16, 25,… |
| C. | 4, 0, 15, 10, 25, 16,… |
| D. | 4, 10, 15, 25,… |
| Answer» D. 4, 10, 15, 25,… | |
| 520. |
A single card is drawn from a standard deck of playing cards. What is the probability that the card is a face card provided that a queen is drawn from the deck of cards? |
| A. | \(\frac{3}{13}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{4}{13}\) |
| D. | \(\frac{1}{52}\) |
| Answer» C. \(\frac{4}{13}\) | |
| 521. |
A bucket contains 6 blue, 8 red and 9 black pens. If six pens are drawn one by one without replacement, find the probability of getting all black pens? |
| A. | \(\frac{8}{213}\) |
| B. | \(\frac{8}{4807}\) |
| C. | \(\frac{5}{1204}\) |
| D. | \(\frac{7}{4328}\) |
| Answer» C. \(\frac{5}{1204}\) | |
| 522. |
A random variable X can take only two values, 2 and 4 i.e., P(2) = 0.45 and P(4) = 0.97. What is the Expected value of X? |
| A. | 3.8 |
| B. | 2.9 |
| C. | 4.78 |
| D. | 5.32 |
| Answer» D. 5.32 | |
| 523. |
A Random Variable X can take only two values, 4 and 5 such that P(4) = 0.32 and P(5) = 0.47. Determine the Variance of X. |
| A. | 8.21 |
| B. | 12 |
| C. | 3.7 |
| D. | 4.8 |
| Answer» D. 4.8 | |
| 524. |
Mangoes numbered 1 through 18 are placed in a bag for delivery. Two mangoes are drawn out of the bag without replacement. Find the probability such that all the mangoes have even numbers on them? |
| A. | 43.7% |
| B. | 34% |
| C. | 6.8% |
| D. | 9.3% |
| Answer» D. 9.3% | |
| 525. |
Transform 54ʸ = n+1 into equivalent a logarithmic expression. |
| A. | log₁₂ (n+1) |
| B. | log₄₁ (n²) |
| C. | log₆₃ (n) |
| D. | log₅₄ (n+1) |
| Answer» E. | |
| 526. |
What is the generating function for generating series 1, 2, 3, 4, 5,… ? |
| A. | \(\frac{2}{(1-3x)}\) |
| B. | \(\frac{1}{(1+x)}\) |
| C. | \(\frac{1}{(1−x)^2}\) |
| D. | \(\frac{1}{(1-x2)}\) |
| Answer» D. \(\frac{1}{(1-x2)}\) | |
| 527. |
Suppose a fair eight-sided die is rolled once. If the value on the die is 1, 3, 5 or 7 the die is rolled a second time. Determine the probability that the sum of values that turn up is at least 8? |
| A. | \(\frac{32}{87}\) |
| B. | \(\frac{12}{43}\) |
| C. | \(\frac{6}{13}\) |
| D. | \(\frac{23}{64}\) |
| Answer» E. | |
| 528. |
A bin contains 4 red and 6 blue balls and three balls are drawn at random. Find the probability such that both are of the same color. |
| A. | \(\frac{10}{28}\) |
| B. | \(\frac{1}{5}\) |
| C. | \(\frac{1}{10}\) |
| D. | \(\frac{4}{7}\) |
| Answer» C. \(\frac{1}{10}\) | |
| 529. |
Evaluate: 16ˣ – 4ˣ – 9 = 0. |
| A. | ln [( 5 + \(\sqrt{21}\)) / 2] / ln 8 |
| B. | ln [( 2 + \(\sqrt{33}\)) / 2] / ln 5 |
| C. | ln [( 1 + \(\sqrt{37}\)) / 2] / ln 4 |
| D. | ln [( 1 – \(\sqrt{37}\)) / 2] / ln 3 |
| Answer» D. ln [( 1 – \(\sqrt{37}\)) / 2] / ln 3 | |
| 530. |
If logₐ\((\frac{1}{8}) = -\frac{3}{4}\), than what is x? |
| A. | 287 |
| B. | 469 |
| C. | 512 |
| D. | 623 |
| Answer» D. 623 | |
| 531. |
Determine the radius of convergence and interval of convergence for the power series: ∞∑ₙ₌₀ (x−7)ⁿ⁺¹/nⁿ. |
| A. | 0, −1<x<1 |
| B. | ∞, −∞<x<∞ |
| C. | 1, −2<x<2 |
| D. | 2, −1<x<1 |
| Answer» C. 1, −2<x<2 | |
| 532. |
What is the radius of convergence and interval of convergence for the power series ∞∑ₙ₌₀m!(2x-1)ᵐ? |
| A. | 3, 12 |
| B. | 1, 0.87 |
| C. | 2, 5.4 |
| D. | 0, 1/2 |
| Answer» E. | |
| 533. |
The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term. |
| A. | 3¹² |
| B. | 4¹⁵ |
| C. | 6⁸ |
| D. | 5⁹ |
| Answer» B. 4¹⁵ | |
| 534. |
Which of the following series is called the “formal power series”? |
| A. | b₀+b₁x+b₂x²+…+bₙxⁿ |
| B. | b₁x+b₂x²+…+bₙxⁿ |
| C. | 1/2b₀+1/3b₁x+1/4b₂x²+…+1/nbₙxⁿ |
| D. | n²(b₀+b₁x+b₂x²+…+bₙxⁿ) |
| Answer» B. b₁x+b₂x²+…+bₙxⁿ | |
| 535. |
A card is drawn randomly from a standard deck of cards. Determine the probability that the card drawn is a queen or a heart. |
| A. | \(\frac{1}{4}\) |
| B. | \(\frac{13}{56}\) |
| C. | \(\frac{4}{13}\) |
| D. | \(\frac{5}{52}\) |
| Answer» D. \(\frac{5}{52}\) | |
| 536. |
There are 9 letters having different colors (red, orange, yellow, green, blue, indigo, violet) and 4 boxes each of different shapes (tetrahedron, cube, polyhedron, dodecahedron). How many ways are there to place these 9 letters into the 4 boxes such that each box contains at least 1 letter? |
| A. | 260100 |
| B. | 878760 |
| C. | 437102 |
| D. | 256850 |
| Answer» B. 878760 | |
| 537. |
From 1, 2, 3, …, 320 one number is selected at random. Find the probability that it is either a multiple of 7 or a multiple of 3. |
| A. | 72% |
| B. | 42.5% |
| C. | 12.8% |
| D. | 63.8% |
| Answer» C. 12.8% | |
| 538. |
Solve for x: log₂(x²-3x)=log₂(5x-15). |
| A. | 2, 5 |
| B. | 7 |
| C. | 23 |
| D. | 3, 5 |
| Answer» E. | |
| 539. |
The sum of all integers from 1 to 520 that are multiples of 4 or 5? |
| A. | 187 |
| B. | 208 |
| C. | 421 |
| D. | 52 |
| Answer» C. 421 | |
| 540. |
Solve for x the equation 2ˣ⁺³ = 5ˣ⁺². |
| A. | ln (24/8) |
| B. | ln (25/8) / ln (2/5) |
| C. | ln (32/5) / ln (2/3) |
| D. | ln (3/25) |
| Answer» C. ln (32/5) / ln (2/3) | |
| 541. |
A cupboard A has 4 red carpets and 4 blue carpets and a cupboard B has 3 red carpets and 5 blue carpets. A carpet is selected from a cupboard and the carpet is chosen from the selected cupboard such that each carpet in the cupboard is equally likely to be chosen. Cupboards A and B can be selected in \(\frac{1}{5}\) and \(\frac{3}{5}\) ways respectively. Given that a carpet selected in the above process is a blue carpet, find the probability that it came from the cupboard B. |
| A. | \(\frac{2}{5}\) |
| B. | \(\frac{15}{19}\) |
| C. | \(\frac{31}{73}\) |
| D. | \(\frac{4}{9}\) |
| Answer» C. \(\frac{31}{73}\) | |
| 542. |
Solve the logarithmic function of ln(\(\frac{1+5x}{1+3x}\)). |
| A. | 2x – 8x² + \(\frac{152x^3}{3}\) – … |
| B. | x² + \(\frac{7x^2}{2} – \frac{12x^3}{5}\) + … |
| C. | x – \(\frac{15x^2}{2} + \frac{163x^3}{4}\) – … |
| D. | 1 – \(\frac{x^2}{2} + \frac{x^4}{4}\) – … |
| Answer» B. x² + \(\frac{7x^2}{2} – \frac{12x^3}{5}\) + … | |
| 543. |
Determine the logarithmic function of ln(1+5x)⁻⁵. |
| A. | 5x + \(\frac{25x^2}{2} + \frac{125x^3}{3} + \frac{625x^4}{4}\) … |
| B. | x – \(\frac{25x^2}{2} + \frac{625x^3}{3} – \frac{3125x^4}{4}\) … |
| C. | \(\frac{125x^2}{3} – 625x^3 + \frac{3125x^4}{5}\) … |
| D. | -25x + \(\frac{125x^2}{2} – \frac{625x^3}{3} + \frac{3125x^4}{4}\) … |
| Answer» E. | |
| 544. |
What is the generating function for the generating sequence A = 1, 9, 25, 49,…? |
| A. | 1+(A-x²) |
| B. | (1-A)-1/x |
| C. | (1-A)+1/x² |
| D. | (A-x)/x³ |
| Answer» C. (1-A)+1/x² | |
| 545. |
If a 12-sided fair die is rolled twice, find the probability that both rolls have a result of 8. |
| A. | \(\frac{2}{19}\) |
| B. | \(\frac{3}{47}\) |
| C. | \(\frac{1}{64}\) |
| D. | \(\frac{2}{9}\) |
| Answer» D. \(\frac{2}{9}\) | |
| 546. |
A fair cubical die is thrown twice and their scores summed up. If the sum of the scores of upper side faces by throwing two times a die is an event. Find the Expected Value of that event. |
| A. | 48 |
| B. | 76 |
| C. | 7 |
| D. | 132 |
| Answer» D. 132 | |
| 547. |
How many ways are there to select exactly four clocks from a store with 10 wall-clocks and 16 stand-clocks? |
| A. | 325 |
| B. | 468 |
| C. | 398 |
| D. | 762 |
| Answer» B. 468 | |
| 548. |
Mina has 6 different skirts, 3 different scarfs and 7 different tops to wear. She has exactly one orange scarf, exactly one blue skirt, and exactly one black top. If Mina randomly selects each item of clothing, find the probability that she will wear those clothings for the outfit. |
| A. | \(\frac{1}{321}\) |
| B. | \(\frac{1}{126}\) |
| C. | \(\frac{4}{411}\) |
| D. | \(\frac{2}{73}\) |
| Answer» C. \(\frac{4}{411}\) | |
| 549. |
How many positive divisors does 4000 = 2⁵ 5³ have? |
| A. | 49 |
| B. | 73 |
| C. | 65 |
| D. | 15 |
| Answer» E. | |
| 550. |
In a Press Conference, there are 450 foreign journalists. 275 people can speak German, 250 people can speak English, 200 people can speak Chinese and 260 people can speak Japanese. Find the maximum number of foreigners who cannot speak at least one language. |
| A. | 401 |
| B. | 129 |
| C. | 324 |
| D. | 415 |
| Answer» E. | |