During dry weather,
Question: During dry weather, clothes made of synthetic fibre often stick to the skin. Which type of force is responsible for this phenomenon? Solution: The electrostatic force starts working between the cloth made of synthetic fibre and sticks to skin....
Read More →A girl is pushing a box towards East direction.
Question: A girl is pushing a box towards East direction. In which direction should her friend push the box SQ that it moves faster in the same direction? Solution: Her friend should push the box towards East direction, so that it will start moving more fast towards East because the magnitude of force increases....
Read More →Where do we apply
Question: Where do we apply a force while walking? Solution: We apply a force on ground while walking and ground applies reaction force on our foot due to which we are able to move forward....
Read More →A ball of dough Is rolled into
Question: A ball of dough Is rolled into a flat chapatti. Name the force exerted to change the shape of the dough. Solution: The shape of dough is changed due to the muscular force applied by the hand....
Read More →Which one of the following forces
Question: Which one of the following forces is a contact force? (a) Force of gravity (b) Force of friction (c) Magnetic force (d) Electrostatic force Solution: (b) Force of friction is a contact force. It always acts when the bodies are in contact....
Read More →The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.
Question: The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume. Solution: Let $r$ be the radius of the sphere. $r=10 \mathrm{~cm}$ $r+\Delta r=9.8 \mathrm{~cm}$ $\Rightarrow \Delta r=10.0-9.8=0.2 \mathrm{~cm}$ Volume of the sphere, $V=\frac{4}{3} \pi r^{3}$ $\Rightarrow \frac{d V}{d r}=\frac{4}{3} \pi \times 3 r^{2}=4 \pi r^{2}$ $\Rightarrow\left(\frac{d V}{d r}\right)_{r=10 \mathrm{~cm}}=4 \pi(10)^{2}=400 \pi \mathrm{cm}^{3} / \mathrm{cm}$ Change in th...
Read More →Two objects repel each other.
Question: Two objects repel each other. This repulsion could be due to the (a) frictional force only (b) electrostatic force only (c) magnetic force only (d) either a magnetic or an electrostatic force Solution: (d) The reason for repulsions may be either an electrostatic (in case of similar charges) or a magnetic (in case of similar pole_s) force....
Read More →Find the sum of 10 terms of the geometric series
Question: Find the sum of 10 terms of the geometric series $\sqrt{2}+\sqrt{6}+\sqrt{18}+\ldots$ Solution: We need to find the sum of 10 terms of GP. Sum of n terms of GP, with first term, a, common ratio, r, $S_{n}=\frac{a\left(r^{n}-1\right)}{r-1}$ So, the sum of given GP up to 10 terms, with $\mathrm{a}=\sqrt{2}$, $r=\sqrt{3}, n=10$ $S_{n}=\frac{a\left(r^{n}-1\right)}{r-1}=\frac{\sqrt{2}\left((\sqrt{3})^{10}-1\right)}{\sqrt{3}-1}$ The requires sum, $S_{n}=\frac{\sqrt{2\left((3)^{5}-1\right)}}{...
Read More →If y = sin x and x changes from π/2 to 22/14,
Question: If $y=\sin x$ and $x$ changes from $\pi / 2$ to $22 / 14$, what is the approximate change in $y$ ? Solution: Let: $x=\frac{\pi}{2}$ $x+\Delta x=\frac{22}{14}$ $\Rightarrow d x=\Delta x=\frac{22}{14}-\frac{\pi}{2}=0$ Now, $y=\sin x$ $\Rightarrow \frac{d y}{d x}=\cos x$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=\frac{x}{2}}=\cos \left(\frac{\pi}{2}\right)=0$ $\therefore \Delta y=\frac{d y}{d x} \Delta x=0 \times 0=0$ $\Rightarrow \triangle y=0$ Hence, there is no change in the value of...
Read More →Find the sum of the series
Question: Find the sum of the series $\left\{2^{2}+4^{2}+6^{2}+\ldots .+(2 n)^{2}\right\}$ Solution: We need to find the sum of the series $\left\{2^{2}+4^{2}+6^{2}+\ldots .+(2 n)^{2}\right\}$. So, we can find it by using summation of the $\mathrm{n}^{\text {th }}$ term of the given series. The $n^{\text {th }}$ term of the series is $(2 n)^{2}=4 n^{2}$ (Given data) $a_{n}=4 n^{2}$ Now, sum of the series $S_{n}=\sum_{k=1}^{n} a_{k}$ $S_{n}=\sum_{k=1}^{n} a_{k}=\sum_{k=1}^{n} 4 n^{2}=4 \sum_{k=1}...
Read More →It is believed that height of a child
Question: It is believed that height of a child depends upon the genes inherited from parents. However, it is often seen that tall parents may have short children and vice-versa. Are these factors other than genes that can cause these variations? Solution: Height of a child depends upon the genes inherited from parents. However, there are some other factors also that can affect height. These factors include balanced diet, hormones, exercise and diseases. Balanced diet is essential for the adoles...
Read More →Our government has legalised
Question: Our government has legalised the age for marriage in boys and girls. Give reasons asTt) why one should get married after a certain age? Solution: In our country, the legal age for marriage is 18 years for girls and 21 years for boys. This is because teenage mothers are not prepared mentally or physically for motherhood. Early marriage and motherhood causes health problems in both mother and the child. It also curtails employment opportunities for the young woman and may cause mental ag...
Read More →Salma had a very soft and smooth skin
Question: Salma had a very soft and smooth skin during her childhood. As she entered adolescence, she developed pimples on her face. The skin specialist advised her to wash her face at regular intervals. Can you explain the reasons for the appearance of pimples on her face and suggest ways to prevent them? Solution: During adolescence, the secretion of sweat glands (sweat) and sebaceous glands (oil) increases. The excess oil and sweat gets collected in the tiny pores of the skin blocking them. B...
Read More →Prove that
Question: If $\sum_{k=1}^{n} k=45$, find the value of $\sum_{k=1}^{n} k^{3} .$ Solution: It is given that, $\sum_{k=1}^{n} k=45$ Note: I. Sum of first n natural numbers, 1 + 2 +3+n, $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}$ II. Sum of cubes of first $n$ natural numbers, $1^{3}+2^{3}+3^{3}+\ldots . n^{3}$, $\sum_{k=1}^{n} k^{3}=\left(\frac{n(n+1)}{2}\right)^{2}$ From the above identities, $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}=45$ We need to find, $\sum_{k=1}^{n} k^{3}=\left(\frac{n(n+1)}{2}\right)^{2}=45^...
Read More →John and Radha were classmates since childhood.
Question: John and Radha were classmates since childhood. When Radha became eleven years old, she developed a little swelling in her neck. She visited the doctor who started medication for her. After a few years, John also developed a slight protrusion on his throat. He got worried and went to the doctor. But, the doctor assured him that it was a normal feature in boys while they are growing up. Can you think of any reasons for the difference in diagnoses? Solution: The swelling on the neck of R...
Read More →In human females, each time during maturation
Question: In human females, each time during maturation and release of egg, the inner wall of uterus thickens. Is this thickening permanent? Give reasons. Solution: No, this thickening of the uterine wall is not permanent. If the egg gets fertilised, it begins to divide to form an embryo. The embryo gets embedded in the uterine wall resulting in pregnancy. During pregnancy, no more eggs are released and the thickened lining is discharged only when the baby is born. However, if fertilisation does...
Read More →Name the hormone which would
Question: Name the hormone which would be released during the following situations. (a) A frightened person (b) Growth of a child to adult (c) Development of caterpillar to moth (d) Development of tadpole to frog Solution: (a) Adrenaline is secreted from adrenal gland during the stress conditions like fright or fear, anger, worry or embarrassment. The hormone prepares the body to function at maximum efficiency by increasing the heart beat and breathing rate, raising B.R, etc. (b) Growth hormone ...
Read More →Solve this
Question: If $\sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{k}=210$, find the value of $\sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{k}^{2}$. Solution: It is given that, $\sum_{k=1}^{n} k=210$ Note: I. Sum of first n natural numbers, 1 + 2 +3+n, $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}$ II. Sum of squares of first $n$ natural numbers, $1^{2}+2^{2}+3^{2}+\ldots n^{2}$, $\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$ From the above identities, $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}=210$ $n^{2}+n=420$ $n^{2}+n-420=0$ ...
Read More →Read the statements given below
Question: Read the statements given below and fill up the blanks with the correct words listed in the box. deep, ductless, nutrients, thyroxine (i) The meal that includes all. is a balanced diet. (ii) Insufficient production of.. in the tadpoles leads to their incomplete development. (iii) Endocrine glands are also called.. glands. (iv) After attaining puberty, boys develop a .voice Solution: (i) nutrients (ii) thyroxine (iii) ductless (iv) deep...
Read More →A few of Paheli’s classmates eat potato
Question: A few of Pahelis classmates eat potato chips and- burgers regularly during the recess in school. Are these healthy eating habits? Give reasons. Solution: No, these are not healthy eating habits because burgers and potato chipshave very little nutritional value. Although, these are very tasty but can never replace regular meals that forms balanced diet and is essential for the adolescents for their normal growth and development....
Read More →We should avoid taking medicines/drugs
Question: We should avoid taking medicines/drugs unless prescribed by a doctor. Give reasons. Solution: We should avoid taking medicines/drugs unless prescribed by a doctor because: (i) Several medicines have adverse side effects and have specific dosage levels which if not followed may harm the body. (ii) Drugs can be addictive too and can ruin our health and happiness....
Read More →Mention any two features of each
Question: Mention any two features of each that are seen in boys and girls which distinguish them from %ach other at puberty. Solution: Two features seen in boys at puberty are: (i) Growth of facial hairs (moustache and beard). (ii) Voice becomes hoarse (Adams apple seen as bulge). Two features seen in girls at puberty are: (i) Development of breasts.(ii) Region below the waist becomes wider (broader hips)....
Read More →Lila always eats only dal and rice in every meal.
Question: Lila always eats only dal and rice in every meal. She often falls ill and has become prone to diseases. Can you suggest changes in her diet which can make her healthy and free from disease? Solution: Lilas diet is not a balanced diet because her meal does not contain the adequate nutritional requirement. She takes only proteins and carbohydrates in every meal. She also requires vitamins and minerals in her meal to protect from various diseases. Thus, I would suggest her to include frui...
Read More →Name the female hormone produced
Question: Name the female hormone produced by ovaries that helps in development of mammary glands. Solution: Oestrogen Is the female hormone produced by ovaries that help in development of breasts/mammary glands. It also produces female secondary sexual characteristics and causes the growth and development of female sex organs. Short Answer Type Questions...
Read More →Find the sum
Question: Find the sum $6^{3}+7^{3}+8^{3}+9^{3}+10^{3}$ Solution: It is required to find the sum $6^{3}+7^{3}+8^{3}+9^{3}+10^{3}$. $6^{3}+7^{3}+8^{3}+9^{3}+10^{3}=$ Sum of cubes of natural numbers starting from 1 to 10 - Sum of cubes of natural numbers starting from 1 to 5 . Note: Sum of cubes of first $n$ natural numbers, $1^{3}+2^{3}+3^{3}+\ldots \ldots n^{3}$, $\sum_{k=1}^{n} k^{3}=\left(\frac{n(n+1)}{2}\right)^{2}$ From the above identities, Sum of cubes of natural numbers starting from 1 to...
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