Mathematics GATE previous year questions with answer

Ques 14 GATE 2021 SET-2

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The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21. The total number of students in all the three classes in the beginning was:

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Ques 15 GATE 2021 SET-2

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The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ₹1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year. The ratio of the selling price in Year 2 to the selling price in Year 3 is

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Ques 16 GATE 2021 SET-2

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Consider the following sets, where n ≥ 2:
S₁: Set of all n x n matrices with entries from the set {a,b,c}
S₂: Set of all functions from the set {0,1,2,...,n²-1} to the set {0,1,2}
Which of the following choice(s) is/are correct?

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Ques 17 GATE 2021 SET-2

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For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is _______.

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Ques 18 GATE 2021 SET-2

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Suppose that P is a 4 x 5 matrix such that every solution of the equation Px = 0 is a scalar multiple of [2 5 4 3 1]^T. The rank of P is _______.

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Ques 19 GATE 2021 SET-2

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Suppose that f: R → R is a continuous function on the interval [-3,3] and a differentiable function in the interval (-3,3) such that for every x in the interval, f'(x) ≤ 2. If f(-3) = 7 then f(3) is at most _______.

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Ques 20 GATE 2021 SET-2

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In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.
If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question. If both the questions are answered correctly, the student gets the sum of the marks of the two questions. The following table shows the probability of correctly answering a question and the marks of the question respectively.

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

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Ques 21 GATE 2021 SET-2

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Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B are subsets of S, and A ⊆ B is _______.

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Ques 22 GATE 2021 SET-1

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There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is __________ .

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Ques 23 Gate 2020

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Let A and B be two n×n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.

I. rank(AB) = rank(A)*rank (B)
II. det(AB) = det(A)*det(B)
III. rank(A+B) ≤ rank(A) + rank(B)
IV. det(A+B) ≤ det(A) + det(B)

Which of the above statements are TRUE ?

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