A stone tied to the end of a string 80 cm long is whirled in a
[question] Question. A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone? [/question] [solution] solution: Length of the string, $I=80 \mathrm{~cm}=0.8 \mathrm{~m}$ Number of revolutions $=14$ Frequency, $v=\frac{\text { Number of revolutions }}{\text { Time taken }}=\frac{14}{25} \mathrm{~Hz}$ Angular frequency, $\omega=2 \pi \mathrm{V}$...
Read More →A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance.
[question] Question. A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes. [/question] [solution] Solution: Let the Ist prize be of Rs. a. Then the next prize will be of Rs. (a – 20) Then the next prize will be of Rs. {(a – 20) – 20}, i.e., Rs. (a – 40) Thus, the seven prizes are of Rs. a, Rs. $(a-20)$, Rs. $(a-40), \ldots($ an AP) Then $...
Read More →A welding fuel gas contains carbon and hydrogen only. Burning a small sample
[question] Question. A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives 3.38 g carbon dioxide, 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Calculate (i)empirical formula, (ii)molar mass of the gas, and (iii)molecular formula. [/question] [solution] Solution: (i) 1 mole $(44 \mathrm{~g})$ of $\mathrm{CO}_{2}$ contains $12 \mathrm{~g}$ of carbon. $\therefore 3.38 \mathrm{~...
Read More →A cricketer can throw a ball to a maximum horizontal distance of 100 m.
[question] Question. A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball? [/question] [solution] solution: Maximum horizontal distance, R = 100 m The cricketer will only be able to throw the ball to the maximum horizontal distance when the angle of projection is $45^{\circ}$, i.e., $\theta=45^{\circ}$. The horizontal range for a projection velocity $v$, is given by the relation: $R=\frac{u^{2} \sin 2 \theta}...
Read More →Find the sum of the odd numbers between 0 and 50.
[question] Question. Find the sum of the odd numbers between 0 and 50. [/question] [solution] Solution: 1, 3, 5, 7 ..., 49 a = 1, d = 2 $\ell=\mathrm{t}_{\mathrm{n}}=49$ $\Rightarrow a+(n-1) d=49$ $\Rightarrow 1+(n-1)(2)=49$ $\Rightarrow 1+2 n-2=49$ $\Rightarrow 2 n=50$ or $n=25$ The sum $=\frac{25}{2}\{a+\ell\}=\frac{25}{2}\{1+49)$ $=\frac{25}{2} \times 50=625$ [/solution]...
Read More →The ceiling of a long hall is 25 m high.
[question] Question. The ceiling of a long hall is $25 \mathrm{~m}$ high. What is the maximum horizontal distance that a ball thrown with a speed of $40 \mathrm{~m} \mathrm{~s}^{-1}$ can go without hitting the ceiling of the hall? [/question] [solution] solution: Speed of the ball, $u=40 \mathrm{~m} / \mathrm{s}$ Maximum height, $h=25 \mathrm{~m}$ In projectile motion, the maximum height reached by a body projected at an angle $\theta$, is given by the relation: $h=\frac{u^{2} \sin ^{2} \theta}{...
Read More →Find the sum of the first 15 multiples of 8.
[question] Question. Find the sum of the first 15 multiples of 8. [/question] [solution] Solution: The multiples of 8 are 8, 16, 24, 3... These are in an A.P., having first term as 8 and common difference as 8. Therefore, a = 8 d = 8 $S_{15}=?$ $S_{n}=\frac{n}{2}[2 a+(n-1) d]$ $=\frac{15}{2}[2(8)+(15-1) 8]$ $=\frac{15}{2}[16+14(8)]$ $=\frac{15}{2}(16+112)$ $=\frac{15(128)}{2}=15 \times 64$ $=960$ [/solution]...
Read More →Find the sum of the first 40 positive integers divisible by 6.
[question] Question. Find the sum of the first 40 positive integers divisible by 6. [/question] [solution] Solution: The positive integers that are divisible by 6 are 6, 12, 18, 24 .... It can be observed that these are making an A.P. whose first term is 6 and common difference is 6. a = 6 d = 6 $\mathrm{S}_{40}=?$ $S_{n}=\frac{n}{2}[2 a+(n-1) d]$ $\mathrm{S}_{40}=\frac{40}{2}[2(6)+(40-1) 6]$ = 20[12 + (39) (6)] = 20(12 + 234) = 20 × 246 = 4920 [/solution]...
Read More →If the sum of the first $\mathrm{n}$ terms of an $\mathrm{AP}$ is $4 \mathrm{n}-\mathrm{n}^{2}$,
[question] Question. If the sum of the first $n$ terms of an $A P$ is $4 n-n^{2}$, what is the first term (that is $S_{1}$ ) ? What is the sum of first two terms? What is the second term? Similarly, find the $3 \mathrm{rd}$, the 10 th and the nth terms. [/question] [solution] Solution: $\mathrm{S}_{\mathrm{n}}=4 \mathrm{n}-\mathrm{n}^{2}$ Putting $n=1$, we get $S_{1}=4-1=3$ i.e., $\mathrm{t}_{1}=3$ $\mathrm{S}_{2}=4(2)-(2)^{2}=8-4=4$, i.e., $\mathrm{S}_{2}=4$ $\Rightarrow \mathrm{t}_{1}+\mathrm{...
Read More →Rain is falling vertically with a speed of
[question] Question. Rain is falling vertically with a speed of $30 \mathrm{~m} \mathrm{~s}^{-1}$. A woman rides a bicycle with a speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$ in the north to south direction. What is the direction in which she should hold her umbrella? [/question] [solution] solution: The described situation is shown in the given figure. Here, $v_{c}=$ Velocity of the cyclist $v_{\mathrm{r}}=$ Velocity of falling rain In order to protect herself from the rain, the woman must hold h...
Read More →Show that $a_{1}, a_{2}, \ldots a_{n}, \ldots$ form an $A P$ where $a_{n}$ is defined as below :
[question] Question. Show that $a_{1}, a_{2}, \ldots a_{n}, \ldots$ form an $A P$ where $a_{n}$ is defined as below : (i) $a_{n}=3+4 n$ (ii) $a_{n}=9-5 n$ Also find the sum of the first 15 terms in each case. [/question] [solution] Solution: (i) $a_{n}=3+4 n$ Putting $\mathrm{n}=1,2,3,4, \ldots$ in $(1)$, we get $a_{1}=3+4=7, a_{2}=3+8=11$ $a_{3}=3+12=15, a_{4}=3+16=19, \ldots$ Thus, the sequence (list of numbers) is 7, 11, 15, 19, ..... Here, $\quad a_{2}-a_{1}=11-7=4$ $a_{3}-a_{2}=15-11=4$ $a_...
Read More →What are the reasons that you can think of for the arthropods
[question] Question. What are the reasons that you can think of for the arthropods to constitute the largest group of the animal kingdom? [/question] [solution] Solution: The phylum, Arthropoda, consists of more than two-thirds of the animal species on earth. The reasons for the success of arthropods are as follows. i. Jointed legs that allow more mobility on land ii. Hard exoskeleton made of chitin that protects the body iii. The hard exoskeleton also reduces water loss from the body of arthrop...
Read More →Calculate the number of atoms in each of the following
[question] Question. Calculate the number of atoms in each of the following (i)52 moles of Ar (ii)52 u of He (iii)52 g of He. [question] [solution] Solution: (i) 1 mole of $A r=6.022 \times 10^{23}$ atoms of $A r$ $\therefore 52 \mathrm{~mol}$ of $\mathrm{Ar}=52 \times 6.022 \times 10^{23}$ atoms of $\mathrm{Ar}$ $=3.131 \times 10^{25}$ atoms of $A r$ (ii) 1 atom of $\mathrm{He}=4 \mathrm{u}$ of $\mathrm{He}$ Or, 4 u of He = 1 atom of He $1 \mathrm{u}$ of $\mathrm{He}=\frac{1}{4}$ atom of $\math...
Read More →What are the peculiar features that you find in parasitic platyhelminthes?
[question] Question. What are the peculiar features that you find in parasitic platyhelminthes? [/question] [solution] Solution: Taenia (Tapeworm) and Fasciola (liver fluke) are examples of parasitic platyhelminthes. Peculiar features in parasitic platyhelminthes are as follows. 1. They have dorsiventrally flattened body and bear hooks and suckers to get attached inside the body of the host. 2. Their body is covered with thick tegument, which protects them from the action of digestive juices of ...
Read More →Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces
[question] Question Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces: (i) 5…A (ii) 8…A (iii) 0…A (iv) 4…A (v) 2…A (vi) 10…A [/question] [solution] Solution (i) 5 ∈ A (ii) 8 ∉ A (iii) 0 ∉ A (iv) 4 ∈ A (v) 2 ∈ A (vi) 10 ∉ A [/solution]...
Read More →Distinguish between intracellular and extracellular digestion?
[question] Question. Distinguish between intracellular and extracellular digestion? [question] [solution] Solution: [solution]...
Read More →If the sum of 7 terms of an AP is 49 and that of 17 terms is 289,
[question] Question. If the sum of 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of n terms. [/question] [solution] Solution: $\mathrm{S}_{7}=49$ $\Rightarrow \frac{7}{2}\{2 \mathrm{a}+6 \mathrm{~d}\}=49 \Rightarrow \mathrm{a}+3 \mathrm{~d}=7 \ldots(1)$ $\mathrm{S}_{17}=289$ $\Rightarrow \frac{17}{2}\{2 a+16 d\}=289 \Rightarrow a+8 d=17 \ldots(2)$ Subtracting (1) from (2), we get $5 \mathrm{~d}=17-7=10$ $\Rightarrow d=2$ From (1), a + 3 × 2 = 7 $\Rightarrow \mathrm{a}=1$ $\mat...
Read More →Use the data given in the following table to calculate the molar mass of naturally occurring argon isotopes
[question] Question. Use the data given in the following table to calculate the molar mass of naturally occurring argon isotopes [/question] [solution] Solution: Molar mass of argon $=39.947 \mathrm{gmol}^{-1}$ [/solution]...
Read More →How useful is the study of the nature of body
[question] Question. How useful is the study of the nature of body cavity and coelom in the classification of animals? [/question] [solution] Solution: Coelom is a fluid filled space between the body wall and digestive tract. The presence or absence of body cavity or coelom plays a very important role in the classification of animals. Animals that possess a fluid filled cavity between body wall and digestive tract are known as coelomates. Annelids, mollusks, arthropods, echinodermates, and chord...
Read More →Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively
[question] Question. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively [/question] [solution] Solution: $\mathrm{t}_{2}=14, \mathrm{t}_{3}=18$ $\mathrm{d}=\mathrm{t}_{3}-\mathrm{t}_{2}=18-14=4$, i.e., $\mathrm{d}=4$ Now $\quad \mathrm{t}_{2}=14 \quad \Rightarrow \mathrm{a}+\mathrm{d}=14$ $\Rightarrow a+4=14 \quad \Rightarrow a=10$ $\mathrm{S}_{51}=\frac{51}{2}\{2 \mathrm{a}+50 \mathrm{~d}\}=\frac{51}{2}\{2 \times 10+50 \times 4\}$ $=\frac{51}{2} \tim...
Read More →Find the sum of first 22 terms of an AP in which d = 7
[question] Question. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149. [/question] [solution] Solution: $d=7$ $a_{22}=149$ \mathrm{S}_{22}=? $a_{22}=a+(22-1) d$ 149 = a + 21 × 7 149 = a + 147 a = 2 $S_{n}=\frac{n}{2}\left(a+a_{n}\right)=\frac{22}{2}(2+149)=11(151)=1661$ [/solution]...
Read More →The first and the last term of an AP are 17 and 350 respectively
[question] Question. The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum? [/question] [solution] Solution: Given that, $a=17$ $\ell=350$ d = 9 Let there be n terms in the A.P. $\ell=a+(n-1) d$ 350 = 17 + (n – 1)9 333 = (n – 1)9 (n – 1) = 37 n = 38 $\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+\ell)$ $\Rightarrow S_{n}=\frac{38}{2}(17+350)=19(367)=6973$ Thus, this A.P. contains 38 terms and the ...
Read More →Given $\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}=0$, which of the following statements are correct:
[question] Question. Given $\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}=0$, which of the following statements are correct: (a) $\mathbf{a}, \mathbf{b}, \mathbf{c}$, and $\mathrm{d}$ must each be a null vector, (b) The magnitude of $(\mathbf{a}+\mathbf{c})$ equals the magnitude of $(\mathbf{b}+\mathbf{d})$, (c) The magnitude of a can never be greater than the sum of the magnitudes of $\mathbf{b}, \mathbf{c}$, and $\mathbf{d}$, (d) $\mathbf{b}+\mathbf{c}$ must lie in the plane of $\mathbf{a}$ and ...
Read More →If you are given a specimen,
[question] Question. If you are given a specimen, what are the steps that you would follow to classify it? [/question] [solution] Solution: There is a certain common fundamental feature that helps in classification of living organisms. The features that can be used in classification are as follows. On the basis of above features, we can easily classify a specimen into its respective category. [/solution]...
Read More →How many significant figures should be present in the answer of the following calculations
[question] Question. How many significant figures should be present in the answer of the following calculations? (i) $\frac{0.02856 \times 298.15 \times 0.112}{0.5785}$ (ii) $5 \times 5.364$ (iii) $0.0125+0.7864+0.0215$ [/question] [solution] Solution: (i) $\frac{0.02856 \times 298.15 \times 0.112}{0.5785}$ Least precise number of calculation = 0.112 Number of significant figures in the answer = Number of significant figures in the least precise number = 3 (ii) $5 \times 5.364$ Least precise num...
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