MCQOPTIONS
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MCQOPTIONS
This section includes 67 Mcqs, each offering curated multiple-choice questions to sharpen your Graduate Aptitude Test (GATE) knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Which of the following options is the closest in meaning to the word given below: Primeval |
| A. | Modern |
| B. | Historic |
| C. | Primitive |
| D. | Antique |
| Answer» D. Antique | |
| 2. |
A number is as much greater than 75 as it is smaller than 117. The number is: |
| A. | 91 |
| B. | 93 |
| C. | 89 |
| D. | 96 |
| Answer» E. | |
| 3. |
Let X be a convex region in the plane bounded by straight lines. Let X have 7 vertices. Suppose f(x,y) = ax + by + c has maximum value M and minimum value N on X and N < M. Let S = {P ∶ P is a vertex of X and N < f(P) < M}. If S has n elements, then which of the following statements is TRUE? |
| A. | n cannot be 5 |
| B. | n can be 2 |
| C. | n cannot be 3 |
| D. | n can be 4 |
| Answer» E. | |
| 4. |
Let X be an arbitrary random variable that takes values in{0,1,…,10}. The minimum and maximum possible values of the variance of X are |
| A. | 0 and 30 |
| B. | 1 and 30 |
| C. | 0 and 25 |
| D. | 1 and 25 |
| Answer» D. 1 and 25 | |
| 5. |
The number of non-isomorphic abelian groups of order 24 is ______ |
| A. | 3 |
| B. | 6 |
| C. | 12 |
| D. | 24 |
| Answer» B. 6 | |
| 6. |
Let G be a group of order 231. The number of elements of order 11 in G is ______ |
| A. | 10 |
| B. | 15 |
| C. | 20 |
| D. | 25 |
| Answer» B. 15 | |
| 7. |
Let f be an entire function on ℂ such that |f(z)| ≤ 100 log|z| for each z with |z| ≥ 2. If F(i) = 2i then f(1) |
| A. | must be 2 |
| B. | must be 2i |
| C. | must be i |
| D. | cannot be determined from the given data |
| Answer» C. must be i | |
| 8. |
Let X be a compact Hausdorff topological space and let Y be a topological space. Let f: X --> Y be a bijective continuous mapping. Which of the following is TRUE? |
| A. | f is a closed mapbut not necessarily an open map |
| B. | f is an open map but not necessarily a closed map |
| C. | f is both an open map and a closed map |
| D. | f need not be an open map or a closed map |
| Answer» E. | |
| 9. |
Suppose that R is a unique factorization domain and that a,b ∈R are distinct irreducible elements. Which of the following statements is TRUE? |
| A. | The ideal 〈1+a〉 is a prime ideal |
| B. | The ideal 〈a+b〉 is a prime ideal |
| C. | The ideal 〈1+ab〉 is a prime ideal |
| D. | The ideal 〈a〉 is not necessarily a maximal ideal |
| Answer» E. | |
| 10. |
The possible set of eigen values of a 4*4 skew-symmetric orthogonal real matrix is |
| A. | {±i} |
| B. | {±i, ±1} |
| C. | {±1} |
| D. | {0 , ±i} |
| Answer» B. {±i, ±1} | |
| 11. |
Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ___ was impressive. |
| A. | beggary |
| B. | nomenclature |
| C. | jealousy |
| D. | nonchalance |
| Answer» E. | |
| 12. |
The number of 5-Sylow subgroup(s) in a group of order 45 is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 13. |
Let R = ℤ*ℤ*ℤ and I = ℤ*ℤ*{0}. Then which of the following statement is correct? |
| A. | I is a maximal ideal but not a prime ideal of R . |
| B. | I is a prime ideal but not a maximal ideal of R . |
| C. | I is both maximal ideal as well as a prime ideal of R . |
| D. | I is neither a maximal ideal nor a prime ideal of R . |
| Answer» C. I is both maximal ideal as well as a prime ideal of R . | |
| 14. |
Newton-Raphson method is used to find the root of the equation x2 - 2 = 0. If iterations are started from - 1, then iterations will be |
| A. | converge to -1 |
| B. | converge to √2 |
| C. | converge to -√2 |
| D. | no coverage |
| Answer» D. no coverage | |
| 15. |
In Standard normal distribution, the value of median is |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | Not fixed |
| Answer» C. 2 | |
| 16. |
Find the approximate value of log(11.01-log(10.1)), Given log(10) = 2.30 and and log(8.69) = 2.16, all the log are in base ‘e’. |
| A. | 2.1654 |
| B. | 2.1632 |
| C. | 2.1645 |
| D. | 2.1623 |
| Answer» E. | |
| 17. |
Find the percentage change power in the circuit if error in value of resistor is 1% and that of voltage source is .99% |
| A. | z should be homogeneous and of order n |
| B. | z should not be homogeneous but of order n |
| C. | z should be implicit |
| D. | z should be the function of x and y only |
| Answer» B. z should not be homogeneous but of order n | |
| 18. |
Previous probabilities in Bayes Theorem that are changed with help of new available information are classified as |
| A. | independent probabilities |
| B. | posterior probabilities |
| C. | interior probabilities |
| D. | dependent probabilities |
| Answer» C. interior probabilities | |
| 19. |
At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The total student population is divided in the ratio 3:2 in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman? |
| A. | 2⁄5 |
| B. | 3⁄5 |
| C. | 3⁄11 |
| D. | 1⁄100 |
| Answer» D. 1⁄100 | |
| 20. |
Suppose box A contains 4 red and 5 blue coins and box B contains 6 red and 3 blue coins. A coin is chosen at random from the box A and placed in box B. Finally, a coin is chosen at random from among those now in box B. What is the probability a blue coin was transferred from box A to box B given that the coin chosen from box B is red? |
| A. | 15⁄29 |
| B. | 14⁄29 |
| C. | 1⁄2 |
| D. | 7⁄10 |
| Answer» B. 14⁄29 | |
| 21. |
Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past experience shows that 5%, 4% and 2% of the notebooks produced by these companies are defective. If a notebook was found to be defective, what is the probability that the notebook was supplied by A? |
| A. | 44⁄69 |
| B. | 25⁄69 |
| C. | 13⁄24 |
| D. | 11⁄24 |
| Answer» C. 13⁄24 | |
| 22. |
A fair coin is tossed thrice, what is the probability of getting all 3 same outcomes? |
| A. | 3⁄4 |
| B. | 1⁄4 |
| C. | 1⁄2 |
| D. | 1⁄6 |
| Answer» C. 1⁄2 | |
| 23. |
For two events A and B, if P (B) = 0.5 and P (A ∪ B) = 0.5, then P (A|B) = |
| A. | 0.5 |
| B. | 0 |
| C. | 0.25 |
| D. | 1 |
| Answer» E. | |
| 24. |
Husband and wife apply for two vacant spots in a company. If the probability of wife getting selected and husband getting selected are 3/7 and 2/3 respectively, what is the probability that neither of them will be selected? |
| A. | 2⁄7 |
| B. | 5⁄7 |
| C. | 4⁄21 |
| D. | 17⁄21 |
| Answer» D. 17⁄21 | |
| 25. |
A coin is biased so that its chances of landing Head is 2⁄3 . If the coin is flipped 3 times, the probability that the first 2 flips are heads and the 3rd flip is a tail is |
| A. | 4⁄27 |
| B. | 8⁄27 |
| C. | 4⁄9 |
| D. | 2⁄9 |
| Answer» B. 8⁄27 | |
| 26. |
A survey determines that in a locality, 33% go to work by Bike, 42% go by Car, and 12% use both. The probability that a random person selected uses neither of them is |
| A. | 0.29 |
| B. | 0.37 |
| C. | 0.61 |
| D. | 0.75 |
| Answer» C. 0.61 | |
| 27. |
The probability that at least one of the events M and N occur is 0.6. If M and N have probability of occurring together as 0.2, then P(~M) + P(~N) is |
| A. | 0.4 |
| B. | 1.2 |
| C. | 0.8 |
| D. | Indeterminate |
| Answer» C. 0.8 | |
| 28. |
If A and B are two events, then the probability of exactly one of them occurs is given by |
| A. | P(A ∩ B) + P( A ∩ B) |
| B. | P(A) + P(B) – 2P(A) P(B) |
| C. | P(A) + P(B) – 2P(A) P(B) |
| D. | P(A) + P(B) – P(A ∩ B) |
| Answer» B. P(A) + P(B) – 2P(A) P(B) | |
| 29. |
Two unbiased coins are tossed. What is the probability of getting at most one head? |
| A. | 1⁄2 |
| B. | 1⁄3 |
| C. | 1⁄6 |
| D. | 3⁄4 |
| Answer» E. | |
| 30. |
In a sample space S, if P(a) = 0, then A is independent of any other event |
| A. | True |
| B. | False |
| Answer» B. False | |
| 31. |
Let A and B be two events such that the occurrence of A implies occurrence of B, But not vice-versa, then the correct relation between P(a) and P(b) is |
| A. | P(A) < P(B) |
| B. | P(B) ≥ P(A) |
| C. | P(A) = P(B) |
| D. | P(A) ≥ P(B) |
| Answer» C. P(A) = P(B) | |
| 32. |
If A and B are two mutually exclusive events with P(a) > 0 and P(b) > 0 then it implies they are also independent |
| A. | True |
| B. | False |
| Answer» C. | |
| 33. |
If A and B are two events such that P(a) = 0.2, P(b) = 0.6 and P(A /B) = 0.2 then the value of P(A /~B) is |
| A. | 0.2 |
| B. | 0.5 |
| C. | 0.8 |
| D. | 1⁄3 |
| Answer» B. 0.5 | |
| 34. |
A and B are two events such that P(A) = 0.4 and P(A ∩ B) = 0.2 Then P(A ∩ B) is equal to |
| A. | 0.4 |
| B. | 0.2 |
| C. | 0.6 |
| D. | 0.8 |
| Answer» B. 0.2 | |
| 35. |
The necessary condition for the maclaurin expansion to be true for function f(x) is |
| A. | f(x) should be continuous |
| B. | f(x) should be differentiable |
| C. | f(x) should exists at every point |
| D. | f(x) should be continuous and differentiable |
| Answer» E. | |
| 36. |
The Taylor polynomial of degree 6 is approximated for cos(x). Then the interval in which the function can be accurately calculated using Taylor series (center = 80π) |
| A. | [ -3π, 3π]. |
| B. | [ 77.5π, 83.5π]. |
| C. | [ -2.5π, 2.5π]. |
| D. | [ 77π, 83π]. |
| Answer» C. [ -2.5π, 2.5π]. | |
| 37. |
To find the value of sin(9) the Taylor Series expansion should be expanded with center as |
| A. | 9 |
| B. | 8 |
| C. | 7 |
| D. | None of these. |
| Answer» E. | |
| 38. |
Find the equation of curve whose roots gives the point which lies in the curve f(x) = xSin(x) in the interval [0, π⁄2] where slope of a tangent to a curve is equals to the slope of a line joining (0, π⁄2) |
| A. | c = -Sec(c) – Tan(c) |
| B. | c = -Sec(c) – Tan(c) |
| C. | c = Sec(c) +Tan(c) |
| D. | c = Sec(c) – Tan(c) |
| Answer» E. | |
| 39. |
A function f(x) with n roots should have n – 1 unique Lagrange points |
| A. | True |
| B. | False |
| Answer» C. | |
| 40. |
f(x) = 3Sin(2x), is continuous over interval [0,π] and differentiable over interval (0,π) and c ∈(0,π) |
| A. | π |
| B. | π⁄2 |
| C. | π⁄4 |
| D. | π⁄8 |
| Answer» C. π⁄4 | |
| 41. |
Find the value of c(a point where slope of a atangent to curve is zero) if f(x) = Sin(x) is continuous over interval [0,π] and differentiable over interval (0, π) and c ∈(0,π) |
| A. | π |
| B. | π⁄2 |
| C. | π⁄6 |
| D. | π⁄4 |
| Answer» C. π⁄6 | |
| 42. |
If F(x) = f(x)g(x)h(x) and F’(x) = 10F(x) and f’(x) = 10f(x) , g’(x) = 10g(x) and h’(x) = 10kh(x), then find value of k. |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» D. 2 | |
| 43. |
, then find the value of a, b and c. |
| A. | 1.37, -4.13, 4.13 |
| B. | 1.37, 4.13, -4.13 |
| C. | -1.37, 4.13, 4.13 |
| D. | 1.37, 4.13, 4.13 |
| Answer» C. -1.37, 4.13, 4.13 | |
| 44. |
If , then find the value of a and b. |
| A. | 2.5, -1.5 |
| B. | -2.5, -1.5 |
| C. | -2.5, 1.5 |
| D. | 2.5, 1.5 |
| Answer» C. -2.5, 1.5 | |
| 45. |
Value of (dSin(x)Cos(x)) / dx is |
| A. | Cos(2x) |
| B. | Sin(2x) |
| C. | Cos(x) |
| D. | Sin(x) |
| Answer» B. Sin(2x) | |
| 46. |
The value of , [x] denotes the greatest integer function |
| A. | 0 |
| B. | 1 |
| C. | ∞ |
| D. | – ∞ |
| Answer» B. 1 | |
| 47. |
If E(x) = 2 and E(z) = 4, then E(z – x) = |
| A. | 2 |
| B. | 6 |
| C. | 0 |
| D. | Insufficient data |
| Answer» B. 6 | |
| 48. |
If ‘X’ is a continuous random variable, then the expected value is given by |
| A. | P(X) |
| B. | ∑ x P(x) |
| C. | ∫ X P(X) |
| D. | No value such as expected value |
| Answer» D. No value such as expected value | |
| 49. |
The expected value of a discrete random variable ‘x’ is given by |
| A. | P(x) |
| B. | ∑ P(x) |
| C. | ∑ x P(x) |
| D. | 1 |
| Answer» D. 1 | |
| 50. |
A table with all possible value of a random variable and its corresponding probabilities is called |
| A. | Probability Mass Function |
| B. | Probability Density Function |
| C. | Cumulative distribution function |
| D. | Probability Distribution |
| Answer» E. | |