Practice

Comprehensive Question Bank & Study Notes

Multiple Choice Questions

1 Competency APPLY MCQ_SINGLE 0 Mark(s) 2025 JEE Main 2025
#960
Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x,y} ∈ {3, 4}. Then among the statements
(S₁): The number of elements in R is 18, and
(S2): The relation R is symmetric but neither reflexive nor transitive
(A) both are false
(B) only (S₁) is true
(C) only (S2) is true
(D) both are true
HARD
2 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2023
#716
The number of real solutions of the equation x^2 + 5|x| + 6 = 0 is:
MEDIUM
3 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2023
#712
If the complex number z satisfies |z| = 1 and z ≠ -1, then z/(1+z^2) is purely:
MEDIUM
4 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2023
#707
A particle moves along a straight line such that its displacement x changes with time t as x = t^3 - 6t^2 + 3t + 4. What is the velocity when acceleration is zero?
MEDIUM
5 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2021
#714
A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip. The acceleration is:
MEDIUM
6 Competency APPLY MCQ_SINGLE 1 Mark(s) AI Import
#964
Let A be the set of all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ and R be a relation on A such that $R = \{(f, g): f(0) = g(1)$ and $f(1) = g(0)\}$. Then R is :
(A) Symmetric and transitive but not reflective
(B) Symmetric but neither reflective nor transitive
(C) Transitive but neither reflexive nor symmetric
(D) Reflexive but neither symmetric nor transitive
HARD
7 Competency APPLY MCQ_SINGLE 1 Mark(s) AI Import
#963
Let A = {1, 2, 3, ...., 100} and R be a relation on A such that R = {(a, b): a = 2b+1}. Let (a1, аг), (аг, аз), (аз, а4),...., (ak, ak+1) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is
equal to :
(A) 6
(B) 8
(C) 7
(D) 5
HARD
8 Competency APPLY MCQ_SINGLE 1 Mark(s) Smart Import
#962
Let A = {-3, -2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by xRy if and only if 0 < x² + 2y < 4. Let l be
the number of elements in R and m be the minimum number of elements required to be added in R to make it a
reflexive relation. Then l + m is equal to
(A) 18
(B) 20
(C) 17
(D) 19
HARD
9 Competency APPLY MCQ_SINGLE Mark(s)
#961
Let A = {-2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by Ry if and only if y = max{x, 1}. Let I be the
number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it
reflexive and symmetric relations, respectively. Then l + m + n is equal to
(A) 11
(B) 12
(C) 14
(D) 13
MEDIUM

Multiple Selection Questions

1 Knowledge REMEMBER MCQ_MULTI 4 Mark(s) 2022
#713
Which of the following ores contain Iron?
EASY
2 Knowledge REMEMBER MCQ_MULTI 4 Mark(s) 2022
#708
Which of the following compounds show Hydrogen bonding?
EASY

Assertion & Reason

1 Competency APPLY ASSERTION_REASON 4 Mark(s) 2020
#715
Assertion: Assertion: The boiling point of water is higher at lower elevations. Reason: Atmospheric pressure increases as elevation decreases.
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is NOT the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.
MEDIUM