JEE Advanced Mathematics — practice by topic

Browse 1,761 questions across 59 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Vector Algebra and 3D Geometry (126)Statistics and Probability (125)Continuity, Differentiability & Derivatives (112)Integrals and Applications (90)Matrices and Determinants (89)Relations, Functions & Inverse Trigonometry (84)Straight Lines and Conic Sections (79)Determinants (73)Differential Equations (70)Matrices (47)Quadratic Equations (43)Unit 6A: Indefinite Integrals & Fundamental Theorem (43)Unit 9A: Parametric Equations and Plane Curves (43)Linear Programming (42)Unit 6B: Definite Integration & Riemann Sums (42)Mensuration: Surface Areas & Volumes (41)Complex Numbers and Quadratic Equations (40)Unit 4-5: Applications of Derivatives & Curve Sketching (39)Unit 7: Differential Equations and Modeling (38)Sequences and Series (37)Unit 8A: Areas Between Curves (37)Sets and Relations (36)Probability (33)Arithmetic Progression (27)Binomial Theorem (26)JEE Main 2023 Mixed (25)Limits and Derivatives (25)Unit 1B1: Limit Concepts and Graphical Limits (25)Integrals (18)Continuity and Differentiability (16)Inverse Trigonometric Functions (16)Unit 1A1: Relations, Functions and Graphs (16)Number Systems (15)Application of Integrals (14)Relations and Functions (13)Algebra: Expansions, Factorisation & Indices (12)Unit 3A: Chain Rule and Composite Functions (12)Algebra: Simultaneous Linear Equations & Quadratics (10)Probability & Statistics (10)Unit 2: Differentiation and Fundamental Derivative Rules (10)Unit 3B: Implicit Differentiation and Inverse Functions (9)Mathematics (8)Trigonometric Functions (8)Coordinate Geometry (6)Real Numbers and Polynomials (5)Introduction to Trigonometry (4)Permutations and Combinations (4)Vector Algebra (4)Definite Integration (3)Complex Numbers (2)Definite Integrals (2)Even/Odd Functions (2)Geometry: Circles (2)Integral Calculus (2)Limits and Continuity (2)Sets, Relations and Functions (2)Logarithms (1)Number Theory (1)Sequences and Series Gp (1)

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From a standard deck of 52 playing cards, what is the probability of drawing a heart?Read the answer and worked solution →Which property of conditional probability is correct?Read the answer and worked solution →Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.Read the answer and worked solution →The derivative of $a^x$ for $a>0$ and $a\neq 1$ isRead the answer and worked solution →

Worked practice questions

From a standard deck of 52 playing cards, what is the probability of drawing a heart?

$\dfrac{1}{2}$
$\dfrac{1}{4}$
$\dfrac{13}{52}$
Both B and C are correct

Show answer and solution

Correct answer: D. Both B and C are correct

A standard deck has 13 hearts out of 52 cards. So the probability is $\dfrac{13}{52}=\dfrac14$. **Hence both options B and C represent the same correct value, so D is the intended correct choice.**

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Which property of conditional probability is correct?

$P(A'/B)=P(A/B)$
$P(A'/B)=1-P(A/B)$
$P(A'/B)=1-P(B/A)$
$P(A'/B)=P(A\cap B)$

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Correct answer: B. $P(A'/B)=1-P(A/B)$

Within the reduced sample space where $B$ has occurred, the events $A$ and $A'$ are complementary. **Therefore their conditional probabilities add to 1, so $P(A'/B)=1-P(A/B)$.**

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Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.

$0$
$1$
$\ln a$
$a$

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Correct answer: C. $\ln a$

A fundamental limit is $\lim_{x\to 0}\dfrac{a^x-1}{x}=\ln a$. It is closely related to the derivative of $a^x$ at $x=0$.

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