Jay's Mathematics Classes

 Nutrition in Plants Multiple Choice Questions  1. Organisms that prepare food for themselves using simple naturally available raw materials are referred to as  (a) heterotrophs  (b) autotrophs  (c) parasites  (d) saprophytes 2. Which of the following statements is/are correct?  (i) All green plants can prepare their own food.  (ii) Most animals are autotrophs.  (iii) Carbon dioxide is not required for photosynthesis.  (iv) Oxygen is liberated during photosynthesis. Choose the correct answer from the options below:  (a) (i) and (iv) (b) (ii) only  (c) (ii) and  (iii) (d) (i) and (ii) 3. Which of the following raw material is available in the air for photosynthesis?  (a) Oxygen  (b) Carbon dioxide  (c) Nitrogen  (d) Hydrogen 4. When we observe the lower surface of a leaf through a magnifying lens we see numerous small openings. Which of the following is the term given to such openings?...

 NCERT Solutions For Class 6 Maths Chapter 2 Whole Numbers EXERCISE 2.1  1. Write the next three natural numbers after 10999. Solution 11,000 ; 11,001 ; 11,002 2. Write the three whole numbers occurring just before 10001. Solution 10,000 ; 9,999 ; 9,998  3. Which is the smallest whole number? Solution 0 4. How many whole numbers are there between 32 and 53 Solution  `53-32 = 21` `21-1 = 20` `therefore 20` whole numbers are there between 32 and 53 5. Write the successor of : (a) 2440701 (b) 100199 (c) 1099999 (d) 2345670 Solutions  (a) 2440701  Successor ➜  24,40,702 (b) 100199 Successor ➜  1,00,200 (c) 1099999 Successor ➜  11,000,00  (d) 2345670 Successor ➜  23,45,671 6. Write the predecessor of : (a) 94 (b) 10000 (c) 208090 (d) 7654321 Solutions (a) 94 Predecessor ➜ 93 (b) 10000 Predecessor ➜ 9999 (c) 208090 Predecessor ➜ (c) 2,08,089 (d) 7654321 Predecessor ➜ (c) 76,54,320

 Electric Charges at Rest Introduction  If we look into the history of the discovery and development of electricity, we find that it was in the sixteenth century that an interesting phenomenon was discovered. It was found that when amber was rubbed against a piece of flannel, it acquired the property of attracting light objects - like dry grass, tiny pieces of paper. This property was not shown by amber when it was not rubbed against the flannel. The rubbed piece of amber was referred to as having 'got electrified' or having acquired an electric charge. (The Greek name for amber is elektron and it was this name that was used for coining the term 'electric'.)

 📝 Respiration in Organisms Introduction  Respiration is the name of the general process in which organisms convert sugar into biochemical energy using oxygen.  `C_6H_12O_6 (aq) + 6O_2 (aq) rightarrow 6CO_2 (g) + 6H_2O (l)` + energy  The process occurs in all organisms including animals, plants, fungi and bacteria. During respiration, energy is released. The energy is then used in different processes,necessary to support life.  Respiration in Plants  In plants, the processes of respiration, as well as photosynthesis occur simultaneously during the day. However,  photosynthesis does not occur in the absence of light. At night, only respiration takes place in the plant. This means that during the night `O_2` is taken in and  `CO_2` is released by plants.  Cellular Respiration Cellular respiration is the process n which cells produces the energy they need to stay alive. During cellular respiration, cells use oxygen to break down the sugar (gluc...

📝 Fractions (Questions) Q. Convert each of the following into an improper fraction: (a) `5frac{5}{7}` (b) `9frac{3}{8}` (c) `6frac{3}{10}` (d) `3frac{5}{11}` (e) `10frac{9}{14}` (f) `12frac{7}{15}` (g) `8frac{8}{13}` (h) `51frac{2}{3}` Q. Convert each of the following into a  mixed fraction: (a) `17/5` (b) `62/7` (c) `101/8` (d) `95/13` (e) `81/11` (f) `87/16` (g) `103/12` (h) `117/20`

 📝 Fractions Class 6 Proper Fraction ➤ A fraction whose numerator is less than its denominator is called a proper fraction.  Examples `2/3, 5/8, 11/17`, etc.  Improper Fraction ➤  A fraction  whose numerator is greater than or equal to its denominator is called an improper fraction. `5/4, 3/2, 25/7,10/10`, etc.  Mixed Fraction ➤  A combination of a whole number and a proper fraction is called a mixed fraction . Examples `2frac{1}{3}, 3frac{2}{5}, 4frac{5}{7}`, etc. Convert a mixed fraction into an improper fraction Mixed fraction = whole number + proper fraction (i) `2frac{3}{5} = 2 + 3/5 = frac{2 × 5 + 3}{5} = 13/5` (ii)  `3frac{4}{7} = 3 + 4/7 = frac{3 × 7 + 4}{7} = 25/7` Convert an improper fraction into a mixed fraction `29/8`  or 29 ÷ 8 Quotient = 3 and remainder = 5 `therefore 29/8 = 3 + 5/8 =  3 frac{5}{8}`

 📝 Ratio and Proportion Multiple Choice Questions  1. The ratio of 8 books to 20 books is (A) 2 : 5  (B) 5 : 2  (C) 4 : 5  (D) 5 : 4 2. The ratio of the number of sides of a square to the number of edges of a cube is (A) 1 : 2  (B) 3 : 2  (C) 4 : 1  (D) 1 : 3 3. A picture is 60cm wide and 1.8m long. The ratio of its width to its perimeter in lowest form is (A) 1 : 2  (B) 1 : 3  (C) 1 : 4  (D) 1 : 8  4. Neelam’s annual income is ₹ 288000. Her annual savings amount to ₹ 36000. The ratio of her savings to her expenditure is (A) 1 : 8  (B) 1 : 7  (C) 1 : 6  (D) 1 : 5 5. Mathematics textbook for Class VI has 320 pages. The chapter ‘symmetry’ runs from page 261 to page 272. The ratio of the number of pages of this chapter to the total number of pages of the book is (A) 11 : 320  (B) 3 : 40  (C) 3 : 80  (D) 272 : 320 6. In a box, the ratio of red marbles to blue marbles is 7:4. Which of the following cou...

📝 Motion and Time  Multiple Choice Questions  1. A bus travels 54 km in 90 minutes. The speed of the bus is (a) 0.6 m/s (b) 10 m/s (c) 5.4 m/s (d) 3.6 m/s 2. The correct symbol to represent the speed of an object is (a) 5 m/s (b) 5 mp (c) 5 m/`s^{-1}` (d) 5 s/m 3. Boojho walks to his school which is at a distance of 3 km from his home in 30 minutes. On reaching he finds that the school is closed and comes back by bicycle with his friend and reaches home in 20 minutes. His average speed in km/h is (a) 8.3 (b) 7.2 (c) 5 (d) 3.6 4. A student observes the positions of two vehicles at different instants of time as shown. Which of these statements explains the motion of the vehicles? (a) Car A is in motion as it changed its position with respect to the surroundings (b) Car B is in motion as it changed its position with respect to the surroundings (c) Car A is in motion as it did not change its position with respect to the surroundings (d) Car B is in motion as it did not chang...

 📝 Motion and Time   Motion An object is said to be in motion if its position, with respect to its immediate surroundings, changes with time.      Rest  An object is said to be at rest if its position, with respect to its immediate surroundings, does not change with time.  All Motion is Relative A given object may be regarded as 'being at rest' by one observer and as 'being in motion' by another observer. For example, two persons, sitting next to each other in a moving train, are at rest with respect to each other. However, they are both in motion with respect to a person standing outside on the platform.  Motion along a Straight Line The simplest type of motion is motion along a straight line (linear motion). For example, the motion of a train on a straight track, an apple falling from a tree, etc.  In all cases, the object nearly moving along a straight path. We call such motion rectilinear or simply linear motion.   Des...

📝 Acids, Bases, and Salts Class 7 Questions Multiple Choice Questions  1. The correct way of making a solution of acid in water is to (a) add water to acid. (b) add acid to water. (c) mix acid and water simultaneously. (d) add water to acid in a shallow container. Ans: (b) 2. Products of a neutralisation reaction are always (a) an acid and a base. (b) an acid and a salt. (c) salt and water. (d) a salt and a base. Ans: (c) 3. Turmeric is a natural indicator.  On adding its paste to acid and base separately, which colours would be observed (a) Yellow in both acid and base. (b) Yellow in acid and red in base. (c) Pink in acid and yellow in base. (d) Red in acid and blue in base. Ans: (b) 4. Phenolphthalein is a synthetic indicator and its colours in acidic and basic solutions, respectively are (a) red and blue. (b) blue and red. (c) pink and colourless. (d) colourless and pink Ans: (d) 5. When the soil is too basic, plants do not grow well in it. To improve its quality what must...

 📝Refraction of Light Refraction of Light.   When a ray of light, propagating (in a straight line) in one transparent medium, enters another transparent medium, it is observed to (usually) change its direction of propagation or bend its path. We call this phenomenon as refraction of light.  Cause of Refraction of Light.  The speed of light is different in different media. In a vacuum, light propagates at a speed of `3 × 10^8 ms^{-1}`, but when it enters any other transparent medium, its speed decreases. It is this change in speed of light, that causes a light ray to bend when it goes from one medium to another. Thus, refraction is basically due to a change in the speed of light when it goes from one medium to another.  Optical Density The speed of light, in a given medium, is taken as an indicator of its optical density. We can say that the more is the speed of light in a given medium, the less is its optical density and vice-versa. Optically denser medium ...

📝 Squares & Square Roots Q. Evaluate  1.  `\sqrt{121/256}` 2.  `\sqrt{625/729}` 3. `\sqrt{3\frac{13}{36}}` 4. `\sqrt{1183/2023}`

📝 Algebraic Expressions ( Questions) Q. Find each of the following products a)  `-4/7xyz (9/2 x^2yz - 3/4xyz^2)` b)  `1.5a (10a^2b - 100ab^2)` c)  `10a^2( 0.1a - 0.5b)` Q. Find the product `-3y(xy + y^2)` and find its value for `x = 4` and `y = 5` Q. Find the values of the following polynomials at `a = – 2` and `b = 3`: (a)  `a^2 + 2ab + b^2`  (b)  `a^2 – 2ab + b^2`  (c)  `a^3 + 3a^2b + 3ab^2 + b^3`  (d)  `a^3 – 3a^2b + 3ab^2 – b^3`  (e)  `\frac {a^2 + b^2}{3}` (f)  `\frac {a^ 2 - b^2}{3}` (g)  `a /b + b/ a`  (h)  `a^2 + b^2 – ab – b^2 – a^2` Simplify (1) `a^2b (a- b^2) + ab^2 (4ab - 2a^2) - a^3b (1- 2b)` (2)  `4st ( s- t) -6s^2 (t- t^2) - 3t^2 (2s^2 - s) + 2st (s - t)` (3) `3x^2 + 2(x+ 2) -3x(2x+1)` (4) `x( x+ 4) + 3x(2x^2 -1) + 4x^2 + 4`

📝 Exponents and Powers Multiple-choice questions Q) `[(–3)^2]^ 3` is equal to  (a) `(–3)^8`  (b) `(–3)^6` (c) `(–3)^5` (d) `(–3)^23` Q) For a non-zero rational number `x,  x^8 ÷ x^2` is equal to  (a) `x^4`  (b) `x^6`  (c) `x^10`  (d) `x^16` Q) `x` is a non-zero rational number. Product of the square of `x` with the cube of `x` is equal to the  (a) second power of  `x` (b) third power of `x`  (c) fifth power of `x` (d) sixth power of `x` Q) For any two non-zero rational numbers `x` and `y, x^5 ÷ y^5` is equal to (a) `(x÷y)^1`  (b) `(x÷y)^0` (c) `(x÷y)^5`  (d) `(x÷y)^10` Q) `(1^0 + 2^0 + 3^0)` is equal to (a) 0  (b) 1  (c) 3  (d) 6

📝 Materials: Metals and Non-Metals  Pure substance  ➤ Materials made up of same kind of particles are known as  pure substances. Elements and compounds are pure substances.  Element ➤ An element is made up of atoms of the same kind.  Elements differ from each other in their physical and chemical properties, as different elements consist of atoms of different kind.  Classification of Elements There are 118 elements known at present. It is difficult to study and describe all the properties of these elements separately. Hence, the element showing similar properties are grouped together.   👉 Metals can be distinguished from non-metals on the basis of their physical and chemical properties.  Appearance and Hardness of Materials  Chemical Properties of Metals and Non-metals 👉 Metals react with Oxygen  Metal + Oxygen `\rightarrow` Metal Oxide  Examples `Mg + O_2 \rightarrow MgO` `Na + O_2 \rightarrow Na_2O` The phenomenon of rusti...

📝 Electricity and Circuits  Electric Cell Electricity to the bulb in a torch is provided by the electric cell . You might have noticed that it has a small metal cap on one side and a metal disc on the other side.  Did you notice a positive (+) sign and a negative (–) sign marked on the electric cell? The metal cap is the positive terminal of the electric cell. The metal disc is the negative terminal. All electric cells have two terminals ; a positive terminal and a negative terminal . An electric cell produces electricity from the chemicals stored inside it. When the chemicals in the electric cell are used up, the electric cell stops producing electricity. Torch Bulb (a) Torch bulb and (b) its inside view A torch bulb has an outer case of glass that is fixed on a metallic base. The thin wire that gives off light is called the filament of the bulb. The filament is fixed to two thicker wires, which also provide support to it. One of these thick wires is connected...

 Decimals  Find: (i) 2.5 × 0.3 (ii) 0.1 × 51.7 (iii) 0.2 × 316.8 (iv) 1.3 × 3.1 (v) 0.5 × 0.05 (vi) 11.2 × 0.15 (vii) 1.07 × 0.02 (viii) 10.05 × 1.05 (ix) 101.01 × 0.01 (x) 100.01 × 1.1

 Integers ( Questions)  Q) Compute each of the following   a) 30 + (–25) + (–10) b) (–20) + (–5) c) 70 + (–20) + (–30) d) –50 + (–60) + 50 e) 1 + (–2) + (– 3) + (– 4) f) 0 + (– 5) + (– 2) g) 0 – (–6) – (+6) h) 0 – 2 – (–2) i) 49 – (–40) – (–3) + 69

 Nutrition in Animals Animals get their food from plants, either directly by eating plants or indirectly by eating animals that eat plants. Animal nutrition includes nutrient requirement , mode of intake of food and its utilisation in the body Digestion:   The breakdown of complex components of food into simpler substances is called digestion.  The components of food such as carbohydrates are complex substances. These complex substances cannot be utilised as such. So they are broken down into simpler substances. DIGESTION IN HUMANS We take in food through the mouth, digest, and utilise it. The unused parts of the food are defecated. What happens to the food  inside the body? The food passes  through a continuous canal ( alimentary canal )  which begins at the buccal cavity and  ends at the anus. The canal can be  divided into various compartments:  (1) the buccal cavity, (2) f ood pipe or  oesophagus, (3) stomach, (4) small...

 Nutrition in Plants ➤ Carbohydrates, proteins, fats, vitamins, and minerals are components of food. Nutrients: The components of food are called nutrients and are necessary for our body. MODE OF NUTRITION IN PLANTS Plants are the only organisms that can prepare food for themselves by using water, carbon dioxide, and minerals. The raw materials are present in their surroundings. ➤  The nutrients enable living organisms to build their bodies, to grow, repair damaged parts of their bodies, and provide the energy to carry out life processes. ➤    Nutrition is the mode of taking food by an organism and its  utilisation by the body. Two modes of nutrition  Autotrophic  Heterotrophic  1.  The mode of nutrition in which organisms make food themselves from simple substances is called autotrophic (auto = self; trophos = nourishment) nutrition. Therefore, plants are called autotrophs. 2. The mode of nutrition in which organisms do not make food th...