Comprehensive ML Aggarwal Class 10 Solutions for Students

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ML Aggarwal's Class 10 solutions are an excellent resource for students to understand and practice mathematical concepts. The book covers a variety of topics, helping students prepare for exams efficiently. The step-by-step solutions are designed to build a strong foundation in Mathematics. In this guide, we will explore detailed questions and answers for the Class 10 syllabus, covering each topic comprehensively. By practicing these, students can improve their skills and be better prepared for their board exams.

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Mathematics Solutions:

Question
What is the Pythagoras theorem?

Answer
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It is expressed as a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, where $c$ is the hypotenuse.

Question
What is the formula to find the area of a circle?

Answer
The formula for the area of a circle is A=πr2A = \pi r^2A=πr2, where $r$ is the radius of the circle and $\pi$ is approximately 3.14159.

Question
How do you find the surface area of a sphere?

Answer
The surface area of a sphere is given by the formula A=4πr2A = 4\pi r^2A=4πr2, where $r$ is the radius of the sphere.

Question
What is the volume of a cylinder?

Answer
The volume of a cylinder is given by the formula V=πr2hV = \pi r^2 hV=πr2h, where $r$ is the radius and $h$ is the height of the cylinder.

Question
Explain the concept of simple interest.

Answer
Simple interest is calculated using the formula $I=P\times R\times T/100$, where $P$ is the principal amount, $R$ is the rate of interest, and $T$ is the time in years.

Question
What is the difference between a rational number and an irrational number?

Answer
A rational number can be expressed as a fraction, whereas an irrational number cannot be written as a simple fraction and has non-repeating, non-terminating decimal expansion.

Question
What is the quadratic formula?

Answer
The quadratic formula is used to find the roots of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0. It is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​.

Question
Define a polynomial and give an example.

Answer
A polynomial is an expression made up of terms in the form anxn+an−1xn−1+...+a1x+a0a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0an​xn+an−1​xn−1+...+a1​x+a0​, where $n$ is a non-negative integer. An example is 2x2+3x+52x^2 + 3x + 52x2+3x+5.

Question
What is the difference between mean, median, and mode?

Answer
The mean is the average of all numbers, the median is the middle value when numbers are arranged in order, and the mode is the most frequent number in a data set.

Question
Explain the concept of probability.

Answer
Probability is the measure of the likelihood of an event occurring. It is calculated using the formula P(E)=Number of favorable outcomesTotal number of outcomesP(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}P(E)=Total number of outcomesNumber of favorable outcomes​.

Question
How do you factorize the quadratic expression x2−5x+6x^2 - 5x + 6x2−5x+6?

Answer
The factorization of x2−5x+6x^2 - 5x + 6x2−5x+6 is $(x-2)(x-3)$.

Question
What is the formula for the area of a triangle?

Answer
The area of a triangle is given by the formula A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}A=21​×base×height.

Question
How do you solve simultaneous linear equations?

Answer
Simultaneous linear equations can be solved using the substitution method, elimination method, or matrix method.

Question
What is the difference between a combination and a permutation?

Answer
A combination is a selection of items without regard to the order, while a permutation is a selection of items where the order matters.

Question
What is an arithmetic progression?

Answer
An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. The formula for the nth term is an=a1+(n−1)×da_n = a_1 + (n-1) \times dan​=a1​+(n−1)×d, where $d$ is the common difference.

Question
What is the relation between angles in a cyclic quadrilateral?

Answer
In a cyclic quadrilateral, the sum of the opposite angles is always 180 degrees.

Question
Explain the concept of tangent to a circle.

Answer
A tangent to a circle is a straight line that touches the circle at exactly one point. This point is known as the point of tangency.

Question
How do you calculate the distance between two points?

Answer
The distance between two points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) is calculated using the distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​.

Question
What is the solution of the system of equations $3x+2y=12$ and $x-y=3$?

Answer
Solving the system of equations gives $x=5$ and $y=2$.

Question
What is a matrix and how is it represented?

Answer
A matrix is a rectangular array of numbers arranged in rows and columns. It is represented as [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}[ac​bd​], where $a,b,c,d$ are the elements.

Question
What is the formula for the volume of a cone?

Answer
The volume of a cone is given by the formula V=13πr2hV = \frac{1}{3} \pi r^2 hV=31​πr2h, where $r$ is the radius and $h$ is the height of the cone.

Question
How do you find the median of a set of numbers?

Answer
To find the median, arrange the numbers in ascending order, and then select the middle number. If the number of terms is even, the median is the average of the two middle numbers.

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