Using various resources such as your school library or the internet and discussions with your teacher,
Question: Using various resources such as your school library or the internet and discussions with your teacher, trace the evolutionary stages of any one animal say horse. Solution: The evolution of horse started withEohippusduring Eocene period. It involved the following evolutionary stages. (i)Gradual increase in body size (ii)Elongation of head and neck region (iii)Increase in the length of limbs and feet (iv)Gradual reduction of lateral digits (v)Enlargement of third functional toe (vi)Stren...
Read More →Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
Question: Find the largest number which divides 615 and 963 leaving remainder 6 in each case. Solution: We need to find the largest number which divides 615 and 963 leaving remainder 6 in each case. The required number when divides 615 and 963 , leaves remainder 6 , this means $615-6=609$ and $963-6=957$ are completely divisible by the number. Therefore, The required number = H.C.F. of 609 and 957. By applying Euclids division lemma $957=609 \times 1+348$ $609=348 \times 1+261$ $348=216 \times 1...
Read More →What are the points on the y-axis whose distance from the line
Question: What are the points on they-axis whose distance from the line$\frac{x}{3}+\frac{y}{4}=1$ is 4 units. Solution: Let $(0, b)$ be the point on the $y$-axis whose distance from line $\frac{x}{3}+\frac{y}{4}=1$ is 4 units. The given line can be written as 4x+ 3y 12 = 0 (1) On comparing equation (1) to the general equation of lineAx+By+C= 0, we obtainA= 4,B= 3, andC= 12. It is known that the perpendicular distance $(d)$ of a line $A x+B y+C=0$ from a point $\left(x_{1}, y_{1}\right)$ is give...
Read More →Can we call human evolution as adaptive radiation?
Question: Can we call human evolution as adaptive radiation? Solution: No, human evolution cannot be called adaptive radiation. This is because adaptive radiation is an evolutionary process that produces new species from a single, rapidly diversifying lineage, which is not the case with human evolution. Human evolution is a gradual process that took place slowly in time. It represents an example of anagenesis....
Read More →Find :
Question: Find $\frac{d y}{d x}$ $x^{2}+x y+y^{2}=100$ Solution: The given relationship is $x^{2}+x y+y^{2}=100$ Differentiating this relationship with respect tox, we obtain $\frac{d}{d x}\left(x^{2}+x y+y^{2}\right)=\frac{d}{d x}(100)$ $\Rightarrow \frac{d}{d x}\left(x^{2}\right)+\frac{d}{d x}(x y)+\frac{d}{d x}\left(y^{2}\right)=0$ [Derivative of constant function is 0 ] $\Rightarrow 2 x+\left[y \cdot \frac{d}{d x}(x)+x \cdot \frac{d y}{d x}\right]+2 y \frac{d y}{d x}=0$ [Using product rule a...
Read More →Describe one example of adaptive radiation.
Question: Describe one example of adaptive radiation. Solution: Adaptive radiation is an evolutionary process that produces new species from a single, rapidly diversifying lineage. This process occurs due to natural selection. An example of adaptive radiation is Darwin finches, found in Galapagos Island. A large variety of finches is present in Galapagos Island that arose from a single species, which reached this land accidentally. As a result, many new species have evolved, diverged, and adapte...
Read More →An army contingent of 616 members is to march behind an army band of 32 members in a parade.
Question: An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Solution: We are given that an army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. We need to find the maximum number of columns in which they can march. Members in army = 616 Me...
Read More →Practise drawing various animals and plants.
Question: Practise drawing various animals and plants. Solution: Ask your teachers and parents to suggest the names of plants and animals and practice drawing them. You can also take help from your book to find the names of plants and animals....
Read More →If the HCF of 657 and 963 is expressible in the form
Question: If the HCF of 657 and 963 is expressible in the form 657x+ 963 15, findx. Solution: We need to find $x$ if the H.C.F of 657 and 963 is expressible in the form $657 x+963 y(-15)$. Given integers are 657 and 963. By applying Euclid's division lemma, we get $963=657 \times 1+306$. Since the remainder $\neq 0$, so apply division lemma on divisor 657 and remainder 306 $657=306 \times 2+45$ Since the remainder $\neq 0$, so apply division lemma on divisor 306 and remainder 45 $306=45 \times 6...
Read More →List 10 modern-day animals and using the internet resources link it to a corresponding ancient fossil. Name both.
Question: List 10 modern-day animals and using the internet resources link it to a corresponding ancient fossil. Name both. Solution: The modern day animals and their ancient fossils are listed in the following table....
Read More →Find the equations of the lines,
Question: Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and 6, respectively. Solution: Let the intercepts cut by the given lines on the axes beaandb. It is given that a+b= 1 (1) ab= 6 (2) On solving equations (1) and (2), we obtain a= 3 andb= 2 ora= 2 andb= 3 It is known that the equation of the line whose intercepts on the axes areaandbis $\frac{x}{a}+\frac{y}{b}=1$ or $b x+a y-a b=0$ Case I:a= 3 andb= 2 In this case, the equation of the line ...
Read More →Find :
Question: Find $\frac{d y}{d x}$ $x y+y^{2}=\tan x+y$ Solution: The given relationship is $x y+y^{2}=\tan x+y$ $\frac{d}{d x}\left(x y+y^{2}\right)=\frac{d}{d x}(\tan x+y)$ $\Rightarrow \frac{d}{d x}(x y)+\frac{d}{d x}\left(y^{2}\right)=\frac{d}{d x}(\tan x)+\frac{d y}{d x}$ $\Rightarrow\left[y \cdot \frac{d}{d x}(x)+x \cdot \frac{d y}{d x}\right]+2 y \frac{d y}{d x}=\sec ^{2} x+\frac{d y}{d x}$[Using product rule and chain rule] Differentiating this relationship with respect to $x$, we obtain $...
Read More →Find the values of θand p, if the equation
Question: Find the values of $\theta$ and $p$, if the equation $x \cos \theta+y \sin \theta=p$ is the normal form of the line $\sqrt{3} x+y+2=0$. Solution: The equation of the given line is $\sqrt{3} x+y+2=0$. This equation can be reduced as $\sqrt{3} x+y+2=0$ $\Rightarrow-\sqrt{3} x-y=2$ On dividing both sides by $\sqrt{(-\sqrt{3})^{2}+(-1)^{2}}=2$, we obtain $-\frac{\sqrt{3}}{2} x-\frac{1}{2} y=\frac{2}{2}$ $\Rightarrow\left(-\frac{\sqrt{3}}{2}\right) x+\left(-\frac{1}{2}\right) y=1$ $\ldots(1...
Read More →Find out through internet and popular science articles whether animals other than man have self-consciousness.
Question: Find out through internet and popular science articles whether animals other than man have self-consciousness. Solution: There are many animals other than humans, which have self consciousness. An example of an animal being self conscious is dolphins. They are highly intelligent. They have a sense of self and they also recognize others among themselves and others. They communicate with each other by whistles, tail-slapping, and other body movements. Not only dolphins, there are certain...
Read More →Try to trace the various components of human evolution
Question: Try to trace the various components of human evolution (hint: brain size and function, skeletal structure, dietary preference, etc.) Solution: The various components of human evolution are as follows. (i) Brain capacity (ii) Posture (iii) Food / dietary preference and other important features...
Read More →If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5,
Question: If the HCF of 408 and 1032 is expressible in the form 1032m 408 5, findm. Solution: We need to find $m$ if the H.C.F of 408 and 1032 is expressible in the form $1032 m-408 \times 5$. Given integers are 408 and 1032 where $4081032$. By applying Euclid's division lemma, we get $1032=408 \times 2+216$. Since the remainder $\neq 0$, so apply division lemma on divisor 408 and remainder 216 $408=216 \times 1+192$ Since the remainder $\neq 0$, so apply division lemma on divisor 216 and remain...
Read More →Find the values of k for which the lineis
Question: Find the values of $k$ for which the line $(k-3) x-\left(4-k^{2}\right) y+k^{2}-7 k+6=0$ is (a) Parallel to the $x$-axis, (b) Parallel to the $y$-axis, (c) Passing through the origin. Solution: The given equation of line is $(k-3) x-\left(4-k^{2}\right) y+k^{2}-7 k+6=0 \ldots(1)$ (a) If the given line is parallel to thex-axis, then Slope of the given line = Slope of thex-axis The given line can be written as $\left(4-k^{2}\right) y=(k-3) x+k^{2}-7 k+6=0$ $y=\frac{(k-3)}{\left(4-k^{2}\r...
Read More →Find
Question: Find $\frac{d y}{d x}$ $a x+b y^{2}=\cos y$ Solution: The given relationship is $a x+b y^{2}=\cos y$ Differentiating this relationship with respect tox, we obtain $\frac{d}{d x}(a x)+\frac{d}{d x}\left(b y^{2}\right)=\frac{d}{d x}(\cos y)$ $\Rightarrow a+b \frac{d}{d x}\left(y^{2}\right)=\frac{d}{d x}(\cos y)$ ...(1) Using chain rule, we obtain $\frac{d}{d x}\left(y^{2}\right)=2 y \frac{d y}{d x}$ and $\frac{d}{d x}(\cos y)=-\sin y \frac{d y}{d x}$ ...(2) From (1) and (2),we obtain $a+...
Read More →Attempt giving a clear definition of the term species
Question: Attempt giving a clear definition of the term species Solution: Species can be defined as a group of organisms, which have the capability to interbreed in order to produce fertile offspring....
Read More →Express the HCF of 468 and 222 as 468x + 222y where x, y
Question: Express the HCF of 468 and 222 as 468x+ 222ywherex, yare integers in two different ways. Solution: We need to express the H.C.F. of 468 and 222 as $468 x+222 y$ Wherex, yare integers in two different ways. Given integers are 468 and 222 , where $468222$ By applying Euclid's division lemma, we get $468=222 \times 2+24$. Since the remainder $\neq 0$, so apply division lemma on divisor 222 and remainder 24 $222=24 \times 9+6$ Since the remainder $\neq 0$, so apply division lemma on diviso...
Read More →Find out from newspapers and popular science articles any new fossil discoveries or controversies about evolution.
Question: Find out from newspapers and popular science articles any new fossil discoveries or controversies about evolution. Solution: Fossils of dinosaurs have revealed the evolution of reptiles in Jurassic period. As a result of this, evolution of other animals such as birds and mammals has also been discovered. However, two unusual fossils recently unearthed in China have ignited a controversy over the evolution of birds.Confuciusornisis one such genus of primitive birds that were crow sized ...
Read More →If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b,
Question: Ifpis the length of perpendicular from the origin to the line whose intercepts on the axes areaandb,then show that $\frac{1}{p^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}$. Solution: It is known that the equation of a line whose intercepts on the axes areaandbis $\frac{x}{a}+\frac{y}{b}=1$ or $b x+a y=a b$ or $b x+a y-a b=0$ $\ldots(1)$ The perpendicular distance $(d)$ of a line $A x+B y+C=0$ from a point $\left(x_{1}, y_{1}\right)$ is given by $d=\frac{\left|A x_{1}+B y_{1}+C\right|}{\sqrt{A...
Read More →Explain antibiotic resistance observed in bacteria in light of Darwinian selection theory.
Question: Explain antibiotic resistance observed in bacteria in light of Darwinian selection theory. Solution: Darwinian selection theory states that individuals with favourable variations are better adapted than individuals with less favourable variation. It means that nature selects the individuals with useful variation as these individuals are better evolved to survive in the existing environment. An example of such selection is antibiotic resistance in bacteria. When bacterial population was...
Read More →Use Euclid's division algorithm to find the HCF of
Question: Use Euclid's division algorithm to find the HCF of (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 (iv) 184, 230 and 276 (v) 136, 170 and 255 Solution: (i) Given integers are 225 and 135. Clearly 225 135. So we will apply Euclids division lemma to 225 and 135, we get, $867=(225)(3)+192$ Since the remainder $90 \neq 0$. So we apply the division lemma to the divisor 135 and remainder 90 . We get, $135=(90)(1)+45$ Now we apply the division lemma to the new divisor 90 and remainder 45...
Read More →Use Euclid's division algorithm to find the HCF of
Question: Use Euclid's division algorithm to find the HCF of (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 (iv) 184, 230 and 276 (v) 136, 170 and 255 Solution: (i) Given integers are 225 and 135. Clearly 225 135. So we will apply Euclids division lemma to 225 and 135, we get, $867=(225)(3)+192$ Since the remainder $90 \neq 0$. So we apply the division lemma to the divisor 135 and remainder 90 . We get, $135=(90)(1)+45$ Now we apply the division lemma to the new divisor 90 and remainder 45...
Read More →