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Maharashtra SSC (Class 10) Mathematics — practice by topic

Browse 694 questions across 20 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Real Numbers and Polynomials (89)Statistics and Probability (73)Arithmetic Progression (68)Quadratic Equations (63)Introduction to Trigonometry (50)Mensuration: Surface Areas & Volumes (50)Algebra: Simultaneous Linear Equations & Quadratics (45)Algebra: Equations, Inequations & Matrices (40)Triangles, Circles and Geometry (37)Coordinate Geometry (34)Linear Equations in One Variable (33)Algebra: Expansions, Factorisation & Indices (24)Number Systems (24)Arithmetic & Geometric Progressions (20)Triangles and Circles (19)Linear Equations in Two Variables (9)Statistics (5)Geometry: Circles (4)Geometry: Triangles, Pythagoras & Rectilinear Figures (4)Trigonometry (3)

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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?

  1. $\dfrac{1}{2}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{13}{52}$
  4. 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?

  1. $P(A'/B)=P(A/B)$
  2. $P(A'/B)=1-P(A/B)$
  3. $P(A'/B)=1-P(B/A)$
  4. $P(A'/B)=P(A\cap B)$
Show answer and solution

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 $a>0$.

  1. $0$
  2. $1$
  3. $\ln a$
  4. $a$
Show answer and solution

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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