# Deepa Maths Mastery > Best Online & Offline Mathematics Coaching for Classes 9 to 12 ## Posts - [CBSE Class 10 Maths Chapter 14 Probability Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-14-model-questions-part-4/): Q76. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is red? - [CBSE Class 10 Maths Chapter 14 Probability Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-14-model-questions-part-2/): Total outcomes = $2$ (Head, Tail). Favorable outcome for Head = $1$. - [CBSE Class 10 Maths Chapter 14 Probability Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-14-model-questions-part-1/): An impossible event cannot happen by definition, so its probability is $0$. - [CBSE Class 10 Maths Chapter 14 Probability Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-14-model-questions-part-3/): A standard deck of playing cards contains a total of $52$ cards. - [CBSE Class 10 Maths Chapter 13 Statistics Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-13-model-questions-part-3/): The standard formula for the mode of grouped data is $L + left(frac{f_1 - f_0}{2f_1 - f_0 - f_2}right) times h$. - [CBSE Class 10 Maths Chapter 13 Statistics Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-13-model-questions-part-2/): The standard formula for the median of a grouped frequency distribution is $L + left(frac{frac{n}{2} - cf}{f}right) times h$. - [CBSE Class 10 Maths Chapter 13 Statistics Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-13-model-questions-part-1/): Q1. Which of the following is a measure of central tendency? - [CBSE Class 10 Maths Chapter 13 Statistics Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-13-model-questions-part-4/): A cumulative frequency distribution curve is graphically represented as an ogive. - [CBSE Class 10 Maths Chapter 12 Surface Areas and Volumes Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-12-model-questions-part-4/): Q76. A solid toy is in the form of a hemisphere surmounted by a right circular cone. - [CBSE Class 10 Maths Chapter 12 Surface Areas and Volumes Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-12-model-questions-part-3/): The slant height ($l$) of a frustum of a cone is derived using the Pythagorean theorem on its vertical cross-section: $l = sqrt{h^2 + (r_1 - r_2)^2}$. - [CBSE Class 10 Maths Chapter 12 Surface Areas and Volumes Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-12-model-questions-part-2/): Q26. The height of a cone is $12text{ cm}$ and its base radius is $5text{ cm}$. - [CBSE Class 10 Maths Chapter 12 Surface Areas and Volumes Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-12-model-questions-part-1/): $text{Total Surface Area} = 6a^2 = 6 times (5)^2 = 6 times 25 = 150text{ cm}^2$. - [CBSE Class 10 Maths Chapter 11 Areas Related to Circles Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-11-model-questions-part-4/): Q76. The side of a square is 10 cm. - [CBSE Class 10 Maths Chapter 11 Areas Related to Circles Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-11-model-questions-part-3/): Right angle means $theta = 90^circ$. - [CBSE Class 10 Maths Chapter 11 Areas Related to Circles Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-11-model-questions-part-2/): Q26. The wheels of a car are of diameter 80 cm each. The speed of the car is 66 km/h. - [CBSE Class 10 Maths Chapter 11 Areas Related to Circles Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-11-model-questions-part-1/): The ratio of the circumference of a circle to its diameter is a constant known as $pi$ ($pi = frac{text{Circumference}}{text{Diameter}}$). - [CBSE Class 10 Maths Chapter 10 Circles Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-10-model-questions-part-4/): The angle between the tangents and the angle between the radii are supplementary: $180^circ - 100^circ = 80^circ$. - [CBSE Class 10 Maths Chapter 10 Circles Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-10-model-questions-part-3/): The angle between the tangents at the ends of a chord and the angle subtended by the chord at the centre are supplementary. - [CBSE Class 10 Maths Chapter 10 Circles Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-10-model-questions-part-2/): By theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact. - [CBSE Class 10 Maths Chapter 10 Circles Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-10-model-questions-part-1/): Q1. A tangent is drawn from a point at a distance of 17 cm from the centre of a circle of radius 8 cm. - [CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-9-model-questions-part-4/): $tantheta = frac{h}{d}$. If both $h$ and $d$ are doubled, $tantheta' = frac{2h}{2d} = frac{h}{d} = tantheta$. Thus, the angle remains unchanged. - [CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-9-model-questions-part-3/): $tantheta = frac{text{Height}}{text{Shadow}} = frac{30}{10sqrt{3}} = frac{3}{sqrt{3}} = sqrt{3} implies theta = 60^circ$. - [CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-9-model-questions-part-2/): Q26. A flagstaff stands on the top of a $5text{ m}$ high tower. - [CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-9-model-questions-part-1/): Q1. A ladder 15 m long just reaches the top of a vertical wall. - [CBSE Class 10 Maths Chapter 7 Coordinate Geometry Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-7-model-questions-part-4/): $text{Distance} = sqrt{(-6)^2 + 8^2} = sqrt{36 + 64} = sqrt{100} = 10$. - [CBSE Class 10 Maths Chapter 7 Coordinate Geometry Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-7-model-questions-part-3/): 1 Mark Q51. If the points $(0, 0)$, $(2, 0)$, and $(0, k)$ form a triangle of area $4text{ sq. - [CBSE Class 10 Maths Chapter 7 Coordinate Geometry Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-7-model-questions-part-2/): 1 Mark Q26. The area of the rhombus whose vertices, taken in order, are $(3, 0)$, $(4, 5)$, $(-1, 4)$, and $(-2, -1)$ is: (a) $24 text{ sq. - [CBSE Class 10 Maths Chapter 7 Coordinate Geometry Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-7-model-questions-part-1/): $= sqrt{a^2cos^2theta + b^2sin^2theta + a^2sin^2theta + b^2cos^2theta} = sqrt{a^2(cos^2theta+sin^2theta) + b^2(sin^2theta+cos^2theta)} = sqrt{a^2 + b^2}$. - [CBSE Class 10 Maths Chapter 6 Triangles Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-6-model-questions-part-4/): Taking square roots: $frac{3}{4} = frac{4.5}{QR} implies QR = frac{4.5 times 4}{3} = 6text{ cm}$. - [CBSE Class 10 Maths Chapter 6 Triangles Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-6-model-questions-part-3/): Q51. In $triangle ABC$, $D$ and $E$ are points on sides $AB$ and $AC$ respectively such that $DE parallel BC$. - [CBSE Class 10 Maths Chapter 6 Triangles Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-6-model-questions-part-2/): Q26. In trapezium $ABCD$ with $AB parallel DC$, diagonals $AC$ and $BD$ intersect at $O$. - [CBSE Class 10 Maths Chapter 6 Triangles Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-6-model-questions-part-1/): Q1. In $triangle ABC$, $DE parallel BC$ such that $AD = x$, $DB = x - 2$, $AE = x + 2$, and $EC = x - 1$. - [CBSE Class 10 Maths Chapter 5 Arithmetic Progressions Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-5-model-questions-part-1/): Let first term be $a$ and common difference be $d$. - [CBSE Class 10 Maths Chapter 5 Arithmetic Progressions Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-5-model-questions-part-4/): Rationalizing each term by multiplying numerator and denominator by the conjugate difference gives terms proportional to $sqrt{c}-sqrt{b}$, $sqrt{a}-sqrt{c}$, etc., which form an AP. - [CBSE Class 10 Maths Chapter 5 Arithmetic Progressions Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-5-model-questions-part-3/): AM between $a$ and $b$ is $frac{a+b}{2}$. - [CBSE Class 10 Maths Chapter 5 Arithmetic Progressions Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-5-model-questions-part-2/): In an AP, the sum of terms equidistant from the beginning and end is equal: $a_1 + a_{24} = a_5 + a_{20} = a_{10} + a_{15}$. - [CBSE Class 10 Maths Chapter 4 Quadratic Equations Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-4-model-questions-part-4/): Substitute $x = 1$ in $a(1)^2 + a(1) + 3 = 0 implies 2a + 3 = 0 implies a = -frac{3}{2}$. - [CBSE Class 10 Maths Chapter 4 Quadratic Equations Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-4-model-questions-part-3/): For $x^2 - x - 1 = 0$, sum $alpha + beta = 1$ and product $alphabeta = -1$. - [CBSE Class 10 Maths Chapter 4 Quadratic Equations Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-4-model-questions-part-2/): Sum of new roots = $frac{1}{alpha} + frac{1}{beta} = frac{alpha + beta}{alphabeta} = frac{-p}{q}$. - [CBSE Class 10 Maths Chapter 4 Quadratic Equations Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-4-model-questions-part-1/): Let the roots be $alpha$ and $6alpha$. - [CBSE Class 11 Maths Study Material: Question Bank & Formula Sheets](https://deepamaths.com/cbse-class-11-maths-study-material/): Comprehensive revision notes, theorem proofs, and concept explanations for all 14 chapters. - [CBSE Class 9 Maths Study Material: Question Bank & Formula Sheets](https://deepamaths.com/cbse-class-9-maths-study-material/): Comprehensive revision notes and concept explanations for all chapters. - [CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-3-model-questions-part-4/): Adding the two equations: $(3x + 2y) + (3x - 2y) = 13 + 5 implies 6x = 18 implies x = 3$. - [CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-3-model-questions-part-3/): Let $u = frac{1}{x+y}$ and $v = frac{1}{x-y}$. - [CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-3-model-questions-part-2/): Q26. A fraction becomes $frac{4}{5}$ if $1$ is added to both numerator and denominator. If $5$ is subtracted from both, it becomes $frac{1}{2}$. - [CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-3-model-questions-part-1/): Q1. For what values of $a$ and $b$ does the pair of linear equations have infinitely many solutions? - [CBSE Class 10 Maths Chapter 1 Real Numbers Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-1-model-questions-part-2/): $frac{33}{2^2 times 5} = frac{33}{20} = frac{33 times 5}{20 times 5} = frac{165}{100} = 1.65$. - [CBSE Class 10 Maths Chapter 1 Real Numbers Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-1-model-questions-part-4/): Q76. The LCM of two numbers is $1400$. Which of the following cannot be their HCF? - [CBSE Class 10 Maths Chapter 1 Real Numbers Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-1-model-questions-part-3/): $40 = 2^3 times 5^1$. - [CBSE Class 10 Maths Chapter 8 Introduction to Trigonometry Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-8-model-questions-part-4/): $sin theta = 1 - sin^2 theta = cos^2 theta$. - [CBSE Class 10 Maths Chapter 8 Introduction to Trigonometry Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-8-model-questions-part-3/): Given $sin theta + cos theta = sqrt{2} cos theta implies sin theta = (sqrt{2} - 1)cos theta$. - [CBSE Class 10 Maths Chapter 8 Introduction to Trigonometry Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-8-model-questions-part-2/): Given $m = sin theta + cos theta implies m^2 = (sin theta + cos theta)^2 = 1 + 2sin theta cos theta implies m^2 - 1 = 2sin theta cos theta$. - [CBSE Class 10 Maths Chapter 2 Polynomials Model Questions with Answers - Part 4 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-2-model-questions-part-4/): $alpha + beta = 2$, $alphabeta = 3$. - [CBSE Class 10 Maths Chapter 2 Polynomials Model Questions with Answers - Part 3 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-2-model-questions-part-3/): $alpha + beta = -frac{b}{a}$, $alphabeta = frac{c}{a}$. - [CBSE Class 10 Maths Chapter 2 Polynomials Model Questions with Answers - Part 2 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-2-model-questions-part-2/): $alpha + beta = 5$ and $alphabeta = k$. We know that $(alpha - beta)^2 = (alpha + beta)^2 - 4alphabeta$. - [CBSE Class 10 Maths Chapter 4 | Model Questions | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-model-questions-chapter-4/): நமது அகாடமியின் மூலம் பதிவிறக்கம் செய்யப்படும் / விலைக்குப் பெறப்படும் ஒவ்வொரு PDF கேள்வி வங்கியிலும், வாங்கும் மாணவரின் பெயர், தொலைபேசி எண் மற்றும் வாங்கிய கல்வி ஆண்டு (உதாரணமாக: Purchased by [Student Name] - 2026-2027 Academic Year Only) ஆகியவை வாட்டர்மார்க் (Watermark) முத்திரையாகப் பதிவு செய்யப்படும். - [CBSE Class 10 Maths Chapter 8 Introduction to Trigonometry Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-model-questions-chapter-8/): $= (2tantheta)(2sintheta) = 4tanthetasintheta$. - [CBSE Class 10 Maths Chapter 1 Real Numbers Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-1-model-questions-part-1/): $text{HCF}$ is the product of the smallest power of each common prime factor involved in the numbers. - [CBSE Class 10 Maths Chapter 2 Polynomials Model Questions with Answers - Part 1 | Deepa Maths](https://deepamaths.com/dmm-courses-cbse-class-10-maths-chapter-2-model-questions-part-1/): The total number of zeroes of a polynomial is equal to the total number of points where its graph intersects or touches the x-axis. ## Pages - [Success Stories & Testimonials](https://deepamaths.com/news-opinion-2/success-stories-testimonials/): Read what our students and parents have to say about their journey with Deepa Maths! - [Expert Math Articles](https://deepamaths.com/news-opinion-2/expert-math-articles/): Deep dives into advanced mathematical concepts, theories, and analytical explorations. - [Study Tips & Strategies](https://deepamaths.com/news-opinion-2/study-tips-strategies/): Smart techniques and proven strategies to conquer mathematics and boost your exam scores! - [Exam News & Notifications](https://deepamaths.com/news-opinion-2/exam-news-notifications/): Stay updated with the latest updates on board exams, entrance tests, and important academic schedules! - [Student Research Corner](https://deepamaths.com/research/student-research-corner/): The Student Research Corner is a dedicated platform designed to encourage students to dive deeper into mathematical thinking, investigative projects, and analytical problem-solving beyond standard classroom textbooks. - [Applied Mathematics & Graph Theory](https://deepamaths.com/research/applied-mathematics-graph-theory/): Applied Mathematics bridges abstract mathematical concepts with real-world applications in science, engineering, business, and computer science. - [maths project idea](https://deepamaths.com/research/maths-project-idea/): An easy visual representation of fractions using paper plates or colorful cardboard sheets to help students understand parts of a whole. - [published-papers-journals](https://deepamaths.com/research/published-papers-journals/): Expertise in simplifying complex mathematical concepts, algebra, calculus, and problem-solving techniques for school and college students. - [Join Community](https://deepamaths.com/engage-with-us/join-community/): Connect with fellow learners, share ideas, and grow your mathematical skills together! - [Workshops & Webinars](https://deepamaths.com/engage-with-us/workshops-webinars/): Join our interactive live sessions to master advanced concepts and sharpen your math skills! - [interative doupt clearning](https://deepamaths.com/engage-with-us/__trashed/): Stuck with a complex math problem? 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