35 Year JEE Previous Questions: Miscellaneous Sets, Relations, Statistics

Consider the following statements [2011]
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as

If the mean deviation about the median of the numbers a, 2a,.......,50a is 50, then | a | equals [2011]

The negation of the statement [2012] "If I become a teacher, then I will open a school", is :

Let x₁ , x₂,...., x_n be n observation s, an d let be their arithmetic mean and σ² be the variance. [2012]
Statement-1 : Variance of 2x₁, 2x₂, ..., 2x_n is 4σ².
Statement-2 : Arithmetic mean 2x₁, 2x₂, ..., 2x_n is 4 .

Let X ={1,2,3,4,5}. The number of different ordered pairs (Y,Z) that can formed such that Y ⊆ X , Z ⊆ X and Y ∩ Z is empty is : [2012]

Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is [JEE M 2013]

Consider
Statement-1 : (p ^ ~ q) ^ (~ p ^ q) is a fallacy.
Statement-2 : (p → q) ⇿ (~ q → ~ p) is a  tautology. [JEE M 2013]

All the studen ts of a class per for med poor ly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ? [JEE M 2013]

 If X = {4ⁿ - 3n -1: n∈N} and Y = {9 (n -1) : n∈N}, where N is the set of natural numbers, then X ∪ Y is equal to:         [JEE M 2014]

The variance of first 50 even natural numbers is [JEE M 2014]

The statement : ~ (p ⇿ ~ q) is :                 [JEE M 2014]

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is :           [JEE M 2015]

The negation of ~ s ν (~ r ∧ s) is equivalent to : [JEE M 2015]

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is:           [JEE M 2015]

If f(x) + and S = {x ∈ R : f(x) = f(–x)}; then S:                 [JEE M 2016]

The Boolean Expression (p ∧ ~ q ) ν q ν (~ p∧ q) is equivalent to:                 [JEE M 2016]

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?                [JEE M 2016]

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60°. Then the time taken (in minutes) by him, from B to reach the pillar, is:                [JEE M 2016]