Relations and Functions (Class 12)

JEE Main 2025 (Online) 23rd January Evening ShiftMCQEasy📈 Topic in 47% papers+4−1

Ques. 1JEE Main 2025, 23 January (Evening Shift)

Let X=R . Define a relation R on X as : (a1,b1)R(a2,b2) b1=b2 In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are true
Statement I is true but Statement II is false
Both Statement I and Statement II are false
Statement I is false but Statement II is true

Answer

(2) Statement I is true but Statement II is false

Solution

R, "same second coordinate", is reflexive (b1=b1), symmetric and transitive (equality of b) equivalence relation: Statement I true.

[figure]

Related points of (a,b) are all (x,y) with y=b: the horizontal line y=b (slope 0), never parallel to y=x (slope 1).

Statement II false.

Answer: (2)

Keep practising — Relations and Functions (Class 12)

Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x)f'(y)+f'(x)f(y) for all x,y . Then n=1100 ef(n) is equal to :

2406
5220
2525
2384

Ques. 3JEE Main 2025, 22 January (Morning Shift)

The number of non-empty equivalence relations on the set \1,2,3\ is :

Ques. 4JEE Main 2025, 22 January (Evening Shift)

Let A=\1,2,3,4\ and B=\1,4,9,16\. Then the number of many-one functions f:A B such that 1 f(A) is equal to :

Ques. 5JEE Main 2025, 22 January (Evening Shift)

Let A=\1,2,3\. The number of relations on A, containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is .

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All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)