Name the parts of an angiosperm flower in which development of male and female gametophyte take place.
Question: Name the parts of an angiosperm flower in which development of male and female gametophyte take place. Solution: The male gametophyte or the pollen grain develops inside the pollen chamber of the anther, whereas the female gametophyte (also known as the embryo sac) develops inside the nucellus of the ovule from the functional megaspore....
Read More →Without using the Pythagoras theorem,
Question: Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (1, 1) are the vertices of a right angled triangle. Solution: The vertices of the given triangle are A (4, 4), B (3, 5), and C (1, 1). It is known that the slope $(m)$ of a non-vertical line passing through the points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, x_{2} \neq x_{1}$. $\therefore$ Slope of $\mathrm{AB}\left(m_{1}\right)=\frac{5-4}{3-4...
Read More →Calculate and compare the energy released by
Question: Calculate and compare the energy released by (a) fusion of 1.0 kg of hydrogen deep within Sun and (b) the fission of 1.0 kg of 235U in a fission reactor. Solution: (a)Amount of hydrogen,m= 1 kg = 1000 g 1 mole, i.e., $1 \mathrm{~g}$ of hydrogen $\left({ }_{1}^{1} \mathrm{H}\right)$ contains $6.023 \times 10^{23}$ atoms. $\therefore 1000 \mathrm{~g}$ of ${ }_{1}^{1} \mathrm{H}$ contains $6.023 \times 10^{23} \times 1000$ atoms. Within the sun, four ${ }_{1}^{1} \mathrm{H}$ nuclei combin...
Read More →Find the slope of a line, which passes through the origin, and the mid-point of
Question: Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, 4) and B (8, 0). Solution: The coordinates of the mid-point of the line segment joining the points $P(0,-4)$ and $B(8,0)$ are $\left(\frac{0+8}{2}, \frac{-4+0}{2}\right)=(4,-2)$ It is known that the slope $(m)$ of a non-vertical line passing through the points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}},...
Read More →For what value of is the function defined by
Question: For what value ofis the function defined by $f(x)= \begin{cases}\lambda\left(x^{2}-2 x\right), \text { if } x \leq 0 \\ 4 x+1, \text { if } x0\end{cases}$ continuous at $x=0$ ? What about continuily at $x=1$ ? Solution: The given function $f$ is $f(x)= \begin{cases}\lambda\left(x^{2}-2 x\right), \text { if } x \leq 0 \\ 4 x+1, \text { if } x0\end{cases}$ Iffis continuous atx= 0, then $\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}} f(x)=f(0)$ $\Rightarrow \lim _{x \rightar...
Read More →Find a point on the x-axis,
Question: Find a point on thex-axis, which is equidistant from the points (7, 6) and (3, 4). Solution: Let (a, 0) be the point on thexaxis that is equidistant from the points (7, 6) and (3, 4). Accordingly, $\sqrt{(7-a)^{2}+(6-0)^{2}}=\sqrt{(3-a)^{2}+(4-0)^{2}}$ $\Rightarrow \sqrt{49+a^{2}-14 a+36}=\sqrt{9+a^{2}-6 a+16}$ $\Rightarrow \sqrt{a^{2}-14 a+85}=\sqrt{a^{2}-6 a+25}$ On squaring both sides, we obtain $a^{2}-14 a+85=a^{2}-6 a+25$ $\Rightarrow-14 a+6 a=25-85$ $\Rightarrow-8 a=-60$ $\Righta...
Read More →Obtain the maximum kinetic energy of β-particles,
Question: Obtain the maximum kinetic energy of-particles, and the radiation frequencies ofdecays in the decay scheme shown in Fig. 13.6. You are given that m(198Au) = 197.968233 u m(198Hg) =197.966760 u Solution: It can be observed from the given-decay diagram that1decays from the 1.088 MeV energy level to the 0 MeV energy level. Hence, the energy corresponding to1-decay is given as: E1= 1.088 0 = 1.088 MeV h1= 1.088 1.6 1019 106J Where, h= Plancks constant = 6.6 1034Js 1= Frequency of radiation...
Read More →Find the distance between and when: (i) PQ is parallel to the y-axis,
Question: Find the distance between $\mathrm{P}\left(x_{1}, y_{1}\right)$ and $\mathrm{Q}\left(x_{2}, y_{2}\right)$ when: (i) $\mathrm{PQ}$ is parallel to the $y$-axis, (ii) $\mathrm{PQ}$ is parallel to the $x$-axis. Solution: The given points are $\mathrm{P}\left(x_{1}, y_{1}\right)$ and $\mathrm{Q}\left(x_{2}, y_{2}\right)$. (i) When PQ is parallel to they-axis,x1=x2. In this case, distance between $\mathrm{P}$ and $\mathrm{Q}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$ $...
Read More →Consider the D−T reaction (deuterium−tritium fusion)
Question: Consider the DT reaction (deuteriumtritium fusion) ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+\mathrm{n}$ (a)Calculate the energy released in MeV in this reaction from the data: $m\left({ }_{1}^{2} \mathrm{H}\right)=2.014102 \mathrm{u}$ $m\left({ }_{1}^{3} \mathrm{H}\right)=3.016049 \mathrm{u}$ (b)Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion be...
Read More →The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin.
Question: The base of an equilateral triangle with side 2alies along theyy-axis such that the mid point of the base is at the origin.Find vertices of the triangle. Solution: Let ABC be the given equilateral triangle with side 2a. Accordingly, AB = BC = CA = 2a Assume that base BC lies along they-axis such that the mid-point of BC is at the origin. i.e., BO = OC =a, where O is the origin. Now, it is clear that the coordinates of point C are (0,a), while the coordinates of point B are (0, a). It i...
Read More →Consider the D−T reaction(deuterium−tritium fusion)
Question: Consider the DT reaction (deuteriumtritium fusion) ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+\mathrm{n}$ (a)Calculate the energy released in MeV in this reaction from the data: $m\left({ }_{1}^{2} \mathrm{H}\right)=2.014102 \mathrm{u}$ $m\left({ }_{1}^{3} \mathrm{H}\right)=3.016049 \mathrm{u}$ (b)Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion be...
Read More →Find the relationship between a and b so that the function f defined by
Question: Find the relationship betweenaandbso that the functionfdefined by $f(x)= \begin{cases}a x+1, \text { if } x \leq 3 \\ b x+3, \text { if } x3\end{cases}$ is continuous atx= 3. Solution: The given function $f$ is $f(x)=\left\{\begin{array}{l}a x+1, \text { if } x \leq 3 \\ b x+3, \text { if } x3\end{array}\right.$ Iffis continuous atx= 3, then $\lim _{x \rightarrow 3^{-}} f(x)=\lim _{x \rightarrow 3^{+}} f(x)=f(3)$ .....(1) Also, $\lim _{x \rightarrow 3^{-}} f(x)=\lim _{x \rightarrow 3^{...
Read More →Why are offspring of oviparous animals at a greater risk as compared to offspring of viviparous animals?
Question: Why are offspring of oviparous animals at a greater risk as compared to offspring of viviparous animals? Solution: Oviparous animals lay eggs outside their body. As a result, the eggs of these animals are under continuous threat from various environmental factors. On the other hand, in viviparous animals, the development of the egg takes place inside the body of the female. Hence, the offspring of an egg-laying or oviparous animal is at greater risk as compared to the offspring of a vi...
Read More →Consider the D−T reaction (deuterium−tritium fusion)
Question: Consider the DT reaction (deuteriumtritium fusion) ${ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+\mathrm{n}$ (a)Calculate the energy released in MeV in this reaction from the data: $m\left({ }_{1}^{2} \mathrm{H}\right)=2.014102 \mathrm{u}$ $m\left({ }_{1}^{3} \mathrm{H}\right)=3.016049 \mathrm{u}$ (b)Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion be...
Read More →Examine a few flowers of any cucurbit plant and try to identify the staminate and pistillate flowers.
Question: Examine a few flowers of any cucurbit plant and try to identify the staminate and pistillate flowers. Do you know any other plant that bears unisexual flowers? Solution: Cucurbit plant bears unisexual flowers as these flowers have either the stamen or the pistil. The staminate flowers bear bright, yellow coloured petals along with stamens that represent the male reproductive structure. On the other hand, the pistillate flowers bear only the pistil that represents the female reproductiv...
Read More →What is a bisexual flower?
Question: What is a bisexual flower? Collect five bisexual flowers from your neighborhood and with the help of your teacher find out their common and scientific names. Solution: A flower that contains both the male and female reproductive structure (stamen and pistil) is called a bisexual flower. Examples of plants bearing bisexual flowers are: (1)Water lily (Nymphaea odorata) (2)Rose (Rosa multiflora) (3)Hibiscus (Hibiscus Rosa-sinensis) (4)Mustard (Brassica nigra) (5)Petunia (Petunia hybrida)...
Read More →Describe the post-fertilization changes in a flower.
Question: Describe the post-fertilization changes in a flower. Solution: Fertilization is the process of the fusion of the male and the female gamete to form a diploid zygote. After fertilization, the zygote divides several times to form an embryo. The fertilized ovule forms a seed. The seed contains an embryo, enclosed in a protective covering, called the seed coat. As the seed grows further, other floral parts wither and fall off. This leads to the growth of the ovary, which enlarges and ripen...
Read More →Draw a quadrilateral in the Cartesian plane,
Question: Draw a quadrilateral in the Cartesian plane, whose vertices are (4, 5), (0, 7), (5, 5) and (4, 2). Also, find its area. Solution: Let ABCD be the given quadrilateral with vertices A (4, 5), B (0, 7), C (5, 5), and D (4, 2). Then, by plotting A, B, C, and D on the Cartesian plane and joining AB, BC, CD, and DA, the given quadrilateral can be drawn as To find the area of quadrilateral ABCD, we draw one diagonal, say AC. Accordingly, area (ABCD) = area (ΔABC) + area (ΔACD) $=\frac{1}{2}|-...
Read More →Discuss the continuity of the function f, where f is defined by
Question: Discuss the continuity of the functionf, wherefis defined by $f(x)=\left\{\begin{array}{l}-2, \text { if } x \leq-1 \\ 2 x, \text { if }-11\end{array}\right.$ Solution: The given function $f$ is $f(x)=\left\{\begin{array}{l}-2, \text { if } x \leq-1 \\ 2 x, \text { if }-11\end{array}\right.$ The given function is defined atall points of the real line. Letcbe a point on the real line. Case I: If $c-1$, then $f(c)=-2$ and $\lim _{x \rightarrow c} f(x)=\lim _{x \rightarrow c}(-2)=-2$ $\th...
Read More →Differentiate between gametogenesis from embryogenesis.
Question: Differentiate between gametogenesis from embryogenesis. Solution:...
Read More →Differentiate between a zoospore and a zygote.
Question: Differentiate between a zoospore and a zygote. Solution:...
Read More →Define external fertilization. Mention its disadvantages.
Question: Define external fertilization. Mention its disadvantages. Solution: External fertilization is the process in which the fusion of the male and the female gamete takes place outside the female body in an external medium, generally water. Fish, frog, starfish are some organisms that exhibit external fertilization. Disadvantages of external fertilization: In external fertilization, eggs have less chances of fertilization. This can lead to the wastage of a large number of eggs produced duri...
Read More →Consider the fission of
Question: Consider the fission of ${ }_{92}^{238} \mathrm{U}$ by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are ${ }_{58}^{140} \mathrm{Ce}$ and ${ }_{44}^{99} \mathrm{Ru}$. Calculate $\mathrm{Q}$ for this fission process. The relevant atomic and particle masses are $m\left({ }_{92}^{238} \mathrm{U}\right)=238.05079 \mathrm{u}$ $m\left({ }_{58}^{140} \mathrm{Ce}\right)=139.90543 \mathrm{u}$ $m\left({ }_{...
Read More →Identify each part in a flowering plant and write whether it is haploid (n) or diploid (2n).
Question: Identify each part in a flowering plant and write whether it is haploid (n) or diploid (2n). (a)Ovary (b)Anther (c)Egg (d)Pollen (e)Male gamete (f )Zygote Solution: (a)OvaryDiploid (2n) (b)AntherDiploid (2n) (c)EggHaploid (n) (d)PollenHaploid (n) (e)Male gameteHaploid (n) (f )ZygoteDiploid (2n)...
Read More →Discuss the continuity of the function f, where f is defined by
Question: Discuss the continuity of the functionf, wherefis defined by $f(x)= \begin{cases}2 x, \text { if } x0 \\ 0, \text { if } 0 \leq x \leq 1 \\ 4 x, \text { if } x1\end{cases}$ Solution: The given function is $f(x)= \begin{cases}2 x, \text { if } x0 \\ 0, \text { if } 0 \leq x \leq 1 \\ 4 x, \text { if } x1\end{cases}$ The given function is defined atall points of the real line. Letcbe a point on the real line. Case I: If $c0$, then $f(c)=2 c$ $\lim _{x \rightarrow c} f(x)=\lim _{x \righta...
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