Explore topic-wise MCQs in Graduate Aptitude Test (GATE).

Which of the following options is the closest in meaning to the word given below: 

Primeval

A number is as much greater than 75 as it is smaller than 117. The number is:

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?

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

 The number of non-isomorphic abelian groups of order 24 is ______

 Let G be a group of order 231. The number of elements of order 11 in G is ______

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)

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?

Suppose that R is a unique factorization domain and that a,b ∈R are distinct irreducible elements. Which of the following statements is TRUE?

The possible set of eigen values of a 4*4 skew-symmetric orthogonal real matrix is

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.

The number of 5-Sylow subgroup(s) in a group of order 45 is

 Let R = ℤ*ℤ*ℤ and I = ℤ*ℤ*{0}. Then which of the following statement is correct?

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

In Standard normal distribution, the value of median is

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’.

Find the percentage change power in the circuit if error in value of resistor is 1% and that of voltage source is .99%

Previous probabilities in Bayes Theorem that are changed with help of new available information are classified as

 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?

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?

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 fair coin is tossed thrice, what is the probability of getting all 3 same outcomes?

For two events A and B, if P (B) = 0.5 and P (A ∪ B) = 0.5, then
P (A|B) =

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 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 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

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

 If A and B are two events, then the probability of exactly one of them occurs is given by

Two unbiased coins are tossed. What is the probability of getting at most one head?

In a sample space S, if P(a) = 0, then A is independent of any other event

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

If A and B are two mutually exclusive events with P(a) > 0 and P(b) > 0 then it implies they are also independent

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 and B are two events such that P(A) = 0.4 and P(A ∩ B) = 0.2 Then P(A ∩ B) is equal to

 The necessary condition for the maclaurin expansion to be true for function f(x) is

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)

To find the value of sin(9) the Taylor Series expansion should be expanded with center as

 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 function f(x) with n roots should have n – 1 unique Lagrange points

f(x) = 3Sin(2x), is continuous over interval [0,π] and differentiable over interval (0,π) and c ∈(0,π)

 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)

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.

, then find the value of a, b and c.

If , then find the value of a and b.

Value of (dSin(x)Cos(x)) / dx is

The value of  , [x] denotes the greatest integer function

If E(x) = 2 and E(z) = 4, then E(z – x) =

If ‘X’ is a continuous random variable, then the expected value is given by

The expected value of a discrete random variable ‘x’ is given by

A table with all possible value of a random variable and its corresponding probabilities is called