Class 11 maths ncert solutions for all chapters to help students understand key concepts, solve exercises, and prepare for exams efficiently. Access now for detailed answers.
Class 11 Maths NCERT solutions offer comprehensive explanations and step-by-step guides for each topic, making complex concepts easier to grasp. These solutions are perfect for exam preparation, helping students build a strong foundation in algebra, geometry, calculus, and more. With expert-backed recommendations, mastering Class 11 Maths becomes achievable.
Class 11 Maths NCERT Solutions: Sample Questions and Answers
Sample Question 1: Find the value of the following determinant:
det(2357)\text{det} \left( \begin{matrix} 2 & 3 \\ 5 & 7 \end{matrix} \right)
Answer:
The determinant of a 2x2 matrix is given by ad−bcad - bc, where the matrix is:
(abcd)\left( \begin{matrix} a & b \\ c & d \end{matrix} \right)
For the given matrix:
(2357)\left( \begin{matrix} 2 & 3 \\ 5 & 7 \end{matrix} \right)
The determinant is (2×7)−(3×5)=14−15=−1(2 \times 7) - (3 \times 5) = 14 - 15 = -1.
Sample Question 2: Find the distance between the points (2, 3) and (5, 7). Answer:
The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:
d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Substituting the values:
d=(5−2)2+(7−3)2=9+16=25=5d = \sqrt{(5 - 2)^2 + (7 - 3)^2} = \sqrt{9 + 16} = \sqrt{25} = 5
So, the distance is 5 units.
Sample Question 3: Solve for x: x2−5x+6=0x^2 - 5x + 6 = 0. Answer:
This is a quadratic equation. Factorizing the equation:
x2−5x+6=(x−2)(x−3)=0x^2 - 5x + 6 = (x - 2)(x - 3) = 0
Setting each factor equal to 0:
x−2=0orx−3=0x - 2 = 0 \quad \text{or} \quad x - 3 = 0
Thus, x=2x = 2 or x=3x = 3.
Sample Question 4: Find the slope of the line passing through the points (1, 2) and (3, 6). Answer:
The slope of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:
slope=y2−y1x2−x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
Substituting the given points:
slope=6−23−1=42=2\text{slope} = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2
So, the slope is 2.
Sample Question 5: What is the area of a triangle with vertices at (0, 0), (4, 0), and (0, 3)? Answer:
The area of a triangle with vertices (x1,y1)(x_1, y_1), (x2,y2)(x_2, y_2), and (x3,y3)(x_3, y_3) is given by:
Area=12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣\text{Area} = \frac{1}{2} | x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) |
Substituting the values:
Area=12∣0(0−3)+4(3−0)+0(0−0)∣=12∣0+12+0∣=122=6\text{Area} = \frac{1}{2} | 0(0 - 3) + 4(3 - 0) + 0(0 - 0) | = \frac{1}{2} | 0 + 12 + 0 | = \frac{12}{2} = 6
So, the area is 6 square units.
Class 11 Chemistry NCERT Solutions: Sample Questions and Answers
Next, let's explore some sample questions from Class 11 Chemistry. These questions focus on important concepts in the subject, offering both theoretical and practical approaches.
Sample Question 1: What is the molecular mass of methane (CH₄)? Answer:
The molecular mass of methane (CH₄) is the sum of the atomic masses of its constituent atoms:
Thus, the molecular mass of CH₄ is:
12+(4×1)=12+4=1612 + (4 \times 1) = 12 + 4 = 16
So, the molecular mass of methane is 16 g/mol.
Sample Question 2: What is an exothermic reaction? Give an example. Answer:
An exothermic reaction is a chemical reaction that releases energy in the form of heat or light. One common example is the combustion of methane:
CH4+2O2→CO2+2H2O+heatCH₄ + 2O₂ \rightarrow CO₂ + 2H₂O + \text{heat}
In this reaction, heat is released as a product.
Sample Question 3: What is the difference between an ionic bond and a covalent bond? Answer:
An ionic bond is formed when one atom donates an electron to another atom, resulting in the formation of oppositely charged ions that are held together by electrostatic attraction. For example, in NaCl (sodium chloride), sodium donates an electron to chlorine.
A covalent bond, on the other hand, is formed when two atoms share electrons. For example, in H₂O (water), hydrogen and oxygen atoms share electrons to form a stable molecule.
Sample Question 4: Define the term 'molarity'. Answer:
Molarity (M) is defined as the number of moles of solute present in one liter of solution. It is given by the formula:
Molarity=Moles of soluteVolume of solution in liters\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}
Sample Question 5: What is the pH of pure water? Answer:
The pH of pure water is 7. This is because pure water is neutral, meaning the concentration of hydrogen ions (H⁺) is equal to the concentration of hydroxide ions (OH⁻), both being 1×10−71 \times 10^{-7} mol/L.
Class 11 Physics NCERT Solutions: Sample Questions and Answers
Finally, let's look at some sample questions and answers from Class 11 Physics, designed to help you grasp key concepts in mechanics, electricity, and more.
Sample Question 1: What is Newton's First Law of Motion? Answer:
Newton's First Law of Motion states that an object at rest will remain at rest, and an object in motion will continue to move with a constant velocity in a straight line, unless acted upon by an external force. This is also known as the law of inertia.
Sample Question 2: What is the SI unit of force? Answer:
The SI unit of force is the Newton (N), which is defined as the force required to accelerate a one-kilogram mass by one meter per second squared.
Sample Question 3: What is the law of conservation of energy? Answer:
The law of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another. The total energy of an isolated system remains constant.
Sample Question 4: Explain the concept of acceleration. Answer:
Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of acceleration is meters per second squared (m/s²).
Sample Question 5: What is the relationship between work and energy? Answer:
Work is said to be done when a force causes displacement of an object. The amount of work done is equal to the change in the energy of the object. The SI unit of work is the joule (J), and it is numerically equal to the energy transferred.
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