For any arbitrary motion in space, which of the following relations are true:
[question] Question. For any arbitrary motion in space, which of the following relations are true: (a) $\mathbf{v}_{\text {aventes }}=\left(\frac{1}{2}\right)\left(\mathbf{v}\left(t_{1}\right)+\mathbf{v}\left(t_{2}\right)\right)$ (b) $\mathbf{v}_{\text {avenee }}=\frac{\left[\mathbf{r}\left(t_{2}\right)-\mathbf{r}\left(t_{1}\right)\right]}{\left(t_{2}-t_{1}\right)}$ (c) $\mathbf{v}(t)=\mathbf{v}(0)+\mathbf{a} t$ (d) $\mathbf{r}(t)=\mathbf{r}(0)+\mathbf{v}(0) t+\left(\frac{1}{2}\right) \mathbf{a}...
Read More →In figure, DE
[question] Question. In figure, $D E \| O Q$ and $D F \| O R$. Show that $E F \| Q R$. [/question] [solution] Solution: In figure, $D E \| O Q$ and DF $\| O R$, then by Basic Proportionality Theorem, We have $\quad \frac{P E}{E Q}=\frac{P D}{D O}....(1) and $\quad \frac{P F}{F R}=\frac{P D}{D O}$\ldots(2)$ From $(1)$ and $(2), \quad \frac{P E}{E Q}=\frac{P F}{F R}$ Now, in $\triangle \mathrm{PQR}$, we have proved that $\Rightarrow \frac{P E}{E Q}=\frac{P F}{F R}$ $\mathrm{EF} \| \mathrm{QR}$ (By...
Read More →Prepare a list of some animals that are found parasitic on human beings.
[question] Question. Prepare a list of some animals that are found parasitic on human beings. [/question] [solution] Solution: [/solution]...
Read More →In figure, $\mathrm{DE} \| \mathrm{AC}$ and $\mathrm{DF} \| \mathrm{AE}$. Prove that $\frac{\mathrm{BF}}{\mathrm{FE}}=\frac{\mathrm{BE}}{\mathrm{EC}}$.
[question] Question. In figure, $D E \| A C$ and $D F \| A E$. Prove that $\frac{B F}{F E}=\frac{B E}{E C}$. [/question] [solution] Solution: In $\triangle \mathrm{ABE}$ $\mathrm{DF} \| \mathrm{AE}$ (Given) $\frac{B D}{D A}=\frac{B F}{F E} \ldots$ (i) (Basic Proportionality Theorem) In $\triangle \mathrm{ABC}$, $D E \| A C$(Given) $\frac{B D}{D A}=\frac{B E}{E C}$ (ii) (Basic Proportionality Theorem) From (i) and (ii), we get $\frac{B F}{F E}=\frac{B E}{E C} \quad$ Hence proved. [/solution]...
Read More →Match the following:
[question] Question. Match the following: [/question] [solution] Solution: [/solution]...
Read More →In figure, if $\mathrm{LM} \| \mathrm{CB}$ and $\mathrm{LN} \| \mathrm{CD}$, prove that $\frac{\mathrm{AM}}{\mathrm{AB}}=\frac{\mathrm{AN}}{\mathrm{AD}}$.
[question] Question. In figure, if $\mathrm{LM} \| \mathrm{CB}$ and $\mathrm{LN} \| \mathrm{CD}$, prove that $\frac{\mathrm{AM}}{\mathrm{AB}}=\frac{\mathrm{AN}}{\mathrm{AD}}$. [/question] [solution] Solution: In $\triangle \mathrm{ACB}$ (see figure), $\mathrm{LM} \| \mathrm{CB}$ (Given) $\Rightarrow \frac{A M}{M B}=\frac{A L}{L C}$ ...(1) (Basic Proportionality Theorem) In $\triangle \mathrm{ACD}$ (see figure), $\mathrm{LN} \| \mathrm{CD}$ (Given) $\Rightarrow \frac{A N}{N D}=\frac{A L}{L C}$ .....
Read More →$E$ and $F$ are points on the sides $P Q$ and $P R$ respectively of a $\triangle P Q R$.
[question] Question. $\mathrm{E}$ and $\mathrm{F}$ are points on the sides $\mathrm{PQ}$ and $\mathrm{PR}$ respectively of a $\Delta \mathrm{PQR}$. For each of the following cases, State whether EF $\| \mathrm{QR}$ : (i) $\mathrm{PE}=3.9 \mathrm{~cm}, \mathrm{EQ}=3 \mathrm{~cm}, \mathrm{PF}=3.6 \mathrm{~cm}$ and $\mathrm{FR}=2.4 \mathrm{~cm}$. (ii) $\mathrm{PE}=4 \mathrm{~cm}, \mathrm{QE}=4.5 \mathrm{~cm}, \mathrm{PF}=8 \mathrm{~cm}$ and $\mathrm{RF}=9 \mathrm{~cm}$. (iii) $\mathrm{PQ}=1.28 \mat...
Read More →Segmentation in the body is first observed in which of the following:
[question] Question. Segmentation in the body is first observed in which of the following: (a) Platyhelminthes (b) Aschelminthes (c) Annelida (d) Arthropoda [/question] [solution] Solution: The body segmentation first appeared in the phylum, Annelida (annulus meaning little ring). [/solution]...
Read More →Calculate the number of electrons which will together weigh one gram
[question] Question. (i)Calculate the number of electrons which will together weigh one gram. (ii)Calculate the mass and charge of one mole of electrons [/question] [solution] Solution: (i) Mass of one electron $=9.10939 \times 10^{-31} \mathrm{~kg}$ $\therefore$ Number of electrons that weigh $9.10939 \times 10^{-31} \mathrm{~kg}=1$ $\therefore$ Number of electrons that will weigh $1 \mathrm{~g}\left(1 \times 10^{-3} \mathrm{~kg}\right)$ $=\frac{1}{9.10939 \times 10^{-31} \mathrm{~kg}} \times\l...
Read More →In figure,
[question] Question. In figure, (i) and (ii), $\mathrm{DE} \| \mathrm{BC}$. Find $\mathrm{EC}$ in (i) and $\mathrm{AD}$ in (ii). [/question] [solution] Solution: (i) In figure, (i) DE $\| \mathrm{BC}$ (Given) $\Rightarrow \frac{A D}{D B}=\frac{A E}{E C}$ (By Basic Proportionality Theorem) $\Rightarrow \frac{1.5}{3}=\frac{1}{E C}$ $\{\because \mathrm{AD}=1.5 \mathrm{~cm}, \mathrm{DB}=3 \mathrm{~cm}$ and $\mathrm{AE}=1 \mathrm{~cm}\}$ $\Rightarrow \mathrm{EC}=\frac{3}{1.5}=2 \mathrm{~cm}$ (ii) In ...
Read More →State whether the following quadrilaterals are similar or not :
[question] Question. State whether the following quadrilaterals are similar or not : [/question] [solution] Solution: The two quadrilateral in figure are not similar because their corresponding angles are not equal. [/solution]...
Read More →Give two different examples of pair of
[question] Question. Give two different examples of pair of (i) Similar figures. (ii) Non-similar figures. [/question] [solution] Solution: (i) 1. Pair of equilateral triangles are similar figures. 2. Pair of squares are similar figures. (ii) 1. One equilateral triangle and one isosceles triangle are non-similar. 2. Square and rectangle are non-similar. [/solution]...
Read More →Chlorine is prepared in the laboratory by treating manganese dioxide
[question] Question. Chlorine is prepared in the laboratory by treating manganese dioxide $\left(\mathrm{MnO}_{2}\right)$ with aqueous hydrochloric acid according to the reaction $4 \mathrm{HCl}_{(a q)}+\mathrm{MnO}_{2(s)} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}_{(l)}+\mathrm{MnCl}_{2(a q)}+\mathrm{Cl}_{2(g)}$ How many grams of HCl react with 5.0 g of manganese dioxide? [/question] [solution] Solution: $1 \mathrm{~mol}[55+2 \times 16=87 \mathrm{~g}] \mathrm{MnO}_{2}$ reacts completely with $4 \m...
Read More →Could the number of eggs or young ones produced by an oviparous and viviparous mother be equal? Why?
[question] Question. Could the number of eggs or young ones produced by an oviparous and viviparous mother be equal? Why? [/question] [solution] Solution: The numbers of eggs produced by an oviparous mother will be more than the young ones produced by a viviparous mother. This is because in oviparous animals, the development of young ones takes place outside the mother’s body. Their eggs are more prone to environmental conditions and predators. Therefore, to overcome the loss, more eggs are prod...
Read More →Fill in the blanks using the correct word given in brackets :
[question] Question. Fill in the blanks using the correct word given in brackets : (i) All circles are ______. (congruent, similar) (ii) All squares are _______. (similar, congruent) (iii) All _______ triangles are similar.(isosceles, equilateral) (iv) Two polygons of the same number of sides are similar, if(a) their corresponding angles are _______ and (b) their corresponding sides are _______. (equal, proportional) [/question] [solution] Solution: (i) All circles are similar. (ii) All squares ...
Read More →What are the modifications that are observed in birds that help them fly?
[question] Question. What are the modifications that are observed in birds that help them fly? [/question] [solution] Solution: Birds have undergone many structural adaptations to suit their aerial life. Some of these adaptations are as follows. (i) Streamlined body for rapid and smooth movement (ii) Covering of feathers for insulation (iii) Forelimbs modified into wings and hind limbs used for walking, perching, and swimming (iv) Presence of pneumatic bones to reduce weight (v) Presence of addi...
Read More →How important is the presence of air bladder in Pisces?
[question] Question. How important is the presence of air bladder in Pisces? [/question] [solution] Solution: Gas bladder or air bladder is a gas filled sac present in fishes. It helps in maintaining buoyancy. Thus, it helps fishes to ascend or descend and stay in the water current. [/solution]...
Read More →“All vertebrates are chordates but all chordates are not vertebrates”. Justify the statement.
[question] Question. “All vertebrates are chordates but all chordates are not vertebrates”. Justify the statement. [/question] [solution] Solution: The characteristic features of the phylum, Chordata, include the presence of a notochord and paired pharyngeal gill slits. In sub-phylum Vertebrata, the notochord present in embryos gets replaced by a cartilaginous or bony vertebral column in adults. Thus, it can be said that all vertebrates are chordates but all chordates are not vertebrates. [/solu...
Read More →Water vascular system is the characteristic of which group of the following:
[question] Question. Water vascular system is the characteristic of which group of the following: (a) Porifera (b) Ctenophora (c) Echinodermata (d) Chordata [/question] [solution] Solution: Water vascular system is a characteristic feature of the phylum, Echinodermata. It consists of an array of radiating channels, tube feet, and madreporite. The water vascular system helps in locomotion, food capturing, and respiration. [/solution]...
Read More →Calcium carbonate reacts with aqueous HCl to give
[question] Question. Calcium carbonate reacts with aqueous $\mathrm{HCl}$ to give $\mathrm{CaCl}_{2}$ and $\mathrm{CO}_{2}$ according to the reaction, $\mathrm{CaCO}_{3}(s)+2 \mathrm{HCl}_{(a q)} \rightarrow \mathrm{CaCl}_{2(a q)}+\mathrm{CO}_{2(g)}+\mathrm{H}_{2} \mathrm{O}(l)$ What mass of $\mathrm{CaCO}_{3}$ is required to react completely with $25 \mathrm{~mL}$ of $0.75 \mathrm{M} \mathrm{HCl}$ ? [/question] [solution] Solution: 0.75 M of HCl ≡ 0.75 mol of HCl are present in 1 L of water $\e...
Read More →The position of a particle is given by
[question] Question. The position of a particle is given by $\mathbf{r}=3.0 t \hat{\mathbf{i}}-2.0 t^{2} \hat{\mathbf{j}}+4.0 \hat{\mathbf{k}} \mathrm{m}$ Where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres. (a) Find the $\mathbf{v}$ and $\mathbf{a}$ of the particle? (b) What is the magnitude and direction of velocity of the particle at $t=2.0 \mathrm{~s}$ ? [/question] [solution] solution: (a) $\vec{v}(t)=(3.0 \hat{\mathbf{i}}-4.0 t \hat{\mathbf{j}}) ; \ve...
Read More →200 logs are stacked in the following manner :
[question] Question. 200 logs are stacked in the following manner : 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see figure). In how many rows are the 200 logs placed and how many logs are in the top row? [/question] [solution] Solution: It can be observed that the numbers of logs in rows are in an A.P. $20,19,18 \ldots$ For this A.P., a = 20 $\mathrm{d}=\mathrm{a}_{2}-\mathrm{a}_{1}=19-20=-1$ Let a total of 200 logs be placed in n rows. $S_{n}=200$ $S_{n}=\...
Read More →What is the difference between direct and indirect development?
[question] Question. What is the difference between direct and indirect development? [/question] [solution] Solution: [/solution]...
Read More →Read each statement below carefully and state,
[question] Question. Read each statement below carefully and state, with reasons, if it is true or false: (a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre (b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point (c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector [/question] [solution] solution: (a) False The ...
Read More →An aircraft executes a horizontal loop of radius 1.00 km with
[question] Question. An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity. [/question] [solution] solution: Radius of the loop, $r=1 \mathrm{~km}=1000 \mathrm{~m}$ Speed of the aircraft, $v=900 \mathrm{~km} / \mathrm{h}=900 \times \frac{5}{18}=250 \mathrm{~m} / \mathrm{s}$ Centripetal acceleration, $a_{\mathrm{c}}=\frac{v^{2}}{r}$ $=\frac{(250)^{2}}{1000}=62.5 \mathrm{~m} / \mathrm{s}^{...
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