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Class XI Maths Sets, Relations and Functions 6

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Question 1

Let P be the relation defined on the set of all real numbers such that
P={(a,b):sec²a - tan²b=1}. Then P is :

Question 2

Let R be the set of real numbers.
Statement-1: A = {(x, y) ∈ R × R : y - x is an integer} is an equivalence relation on R.
Statement-2: B = {(x, y) ∈ R × R : x = αy for some rational number α} is an equivalence relation on R.

Question 3

It is given that the events A and B are such that P(A)= 1/4, P(A|B)= 1/2 and P(B|A)= 2/3. Then P(B) is

Question 4

In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements:
(a) 5% families own both a car and a phone.
(b) 35% families own either a car or a phone.
(c) 40,000 families live in the town.
Then,

Question 5

Directions: Assertion– Reason type questions. Each of these questions contains two statements;

Statement – 1 (Assertion) and

Statement – 2 (Reason)

Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Let A be a 2 × 2 matrix
Statement 1 : adj (adj A) = A
Statement 2 : |adj A| = |A|

Question 6

f(x) = x+cos x is

Question 7

f(x)=log(x+√(1+x²)) is

Question 8

f(x)=2 tan x;(,3)R is

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Jul 13JEE & BITSAT