Find the coordinates of the points of trisection of the line segment joining
[question] Question. Find the coordinates of the points of trisection of the line segment joining $(4,-1)$ and $(-2,-3)$. [/question] [solution] Solution: Points P and Q trisect the line segment joining the points A(4, – 1) and B(2, – 3), i.e., AP = PQ = QB. Here, P divides AB in the ratio 1 : 2 and Q divides AB in the ratio 2 : 1. $x$-coordinate of $P=\frac{1 \times(-2)+2 \times(4)}{1+2}=\frac{6}{3}=2$; $y-$ coordinate of $P=\frac{1 \times(-3)+2 \times(-1)}{1+2}=\frac{-5}{3}$ Thus, the coordina...
Read More →Find the co-ordinates of the point which divides the line joining
[question] Question. Find the co-ordinates of the point which divides the line joining of (–1, 7) and (4, –3) in the ratio 2 : 3. [/question] [solution] Solution: Let the required point be P(x, y). Here the end points are (–1, 7) and (4, –3) $\because \quad$ Ratio $=2: 3=\mathrm{m}_{1}: \mathrm{m}_{2}$ $\therefore \quad x=\frac{m_{1} x_{2}+m_{2} x_{1}}{m_{1}+m_{2}}=\frac{(2 \times 4)+3(-1)}{2+3}$ $=\frac{8-3}{5}=\frac{5}{5}=1$ And $y=\frac{m_{1} y_{2}+m_{2} y_{1}}{m_{1}+m_{2}}$ $=\frac{2 \times(...
Read More →Match the following
[question] Question. [/question] [solution] Solution: [/solution]...
Read More →Find a relation between x and y such that the point
[question] Question. Find a relation between x and y such that the point (x,y) is equidistant from the point (3, 6) and (– 3, 4). [/question] [solution] Solution: A(3,6) and B(–3, 4) are the given points. Point P (x, y) is equidistant from the points A and B. $\Rightarrow \mathrm{PA}=\mathrm{PB}$ $\Rightarrow \sqrt{(x-3)^{2}+(y-6)^{2}}=\sqrt{(x+3)^{2}+(y-4)^{2}}$ $\Rightarrow(x-3)^{2}+(y-6)^{2}=(x+3)^{2}+(y-4)^{2}$ $\Rightarrow\left(x^{2}-6 x+9\right)+\left(y^{2}-12 y+36\right)$ $=\left(x^{2}+6 ...
Read More →Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple
[question] Question. Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit. [/question] [solution] Solution: Since a hydrogen atom has only one electron, according to Bohr’s postulate, the angular momentum of that electron is given by: $m v r=n \frac{\mathrm{h}}{2 \pi} \ldots \ldots \ldots(1)$ Where, $n=1,2,3, \ldots$ According to de Broglie’s equation: $\lambda=\frac{\mathr...
Read More →If Q (0,1) is equidistant from P(5, – 3) and R(x, 6),
[question] Question. If Q (0,1) is equidistant from P(5, – 3) and R(x, 6), find the values of x. Also find the distances QR and PR. [/question] [solution] Solution: Here, $Q P=\sqrt{(5-0)^{2}+\mid(-3)-11^{2}}=\sqrt{5^{2}+(-4)^{2}}$ $=\sqrt{25+16}=\sqrt{41}$ $Q R=\sqrt{(x-0)^{2}+(6-1)^{2}}=\sqrt{x^{2}+5^{2}}=\sqrt{x^{2}+25}$ $\because \quad \mathrm{QP}=\mathrm{QR}$ $\therefore \quad \sqrt{41}=\sqrt{x^{2}+25}$ Squaring both sides, we have $x^{2}+25=41$ $\Rightarrow x^{2}+25-41=0$ $\Rightarrow x^{2...
Read More →New cells generate from
[question] Question. New cells generate from (a) bacterial fermentation (b) regeneration of old cells (c) pre-existing cells (d) abiotic materials [/question] [solution] Solution: Answer: (c) According to the biogenic theory, new cells can only arise from pre-existing cells. Only complete cells, in favourable conditions, can give rise to new cells. [/solution]...
Read More →How many electrons in an atom may have the following quantum numbers?
[question] Question. How many electrons in an atom may have the following quantum numbers? (a) $n=4$ $m_{x}=-\frac{1}{2}$ (b) $n=3, I=0$ [/question] [solution] Solution: (a) Total number of electrons in an atom for a value of $n=2 n^{2}$ $\therefore$ For $n=4$, Total number of electrons $=2(4)^{2}=32$ The given element has a fully filled orbital as $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10}$ Hence, all the electrons are paired. $\therefore$ Number of electrons (having $n=4$ and $\...
Read More →Find the values of y for which the distance between the points P(2, –3)
[question] Question. Find the values of y for which the distance between the points P(2, –3) and Q(10, y) is 10 units [/question] [solution] Solution: Distance between P(2, – 3) and Q(10, y) = 10 units $\Rightarrow \sqrt{(10-2)^{2}+(y+3)^{2}}=10$ $\Rightarrow 64+(y+3)^{2}=100$ $\Rightarrow(y+3)^{2}=36$ $\Rightarrow y^{2}+6 y+9=36$ $y^{2}+6 y-27=0$ $\Rightarrow y^{2}+9 y-3 y-27=0$ $\Rightarrow y(y+9)-3(y+9)=0$ $\Rightarrow(\mathrm{y}+9)(\mathrm{y}-3)=0$ $\Rightarrow y+9=0$ or $y-3=0$ $\Rightarrow...
Read More →Find the point on the x-axis which is equidistant from
[question] Question. Find the point on the x-axis which is equidistant from (2, – 5) and (– 2, 9). [/question] [solution] Solution: We know that any point on x-axis has its ordinate = 0 Let the required point be P(x, 0). Let the given points be A(2, –5) and B(–2, 9) $\therefore \quad \mathrm{AP}=\sqrt{(x-2)^{2}+5^{2}}=\sqrt{x^{2}-4 x+4+25}$ $=\sqrt{x^{2}-4 x+29}$ $\mathrm{BP}=\sqrt{[\mathbf{x}-(-2)]^{2}+(-\mathbf{9})^{2}}=\sqrt{(\mathbf{x}+2)^{2}+(-\mathbf{9})^{2}}$ $=\sqrt{x^{2}+4 x+4+81}=\sqrt...
Read More →Mention the function of the following
[question] Question. Mention the function of the following (a) Ureters in frog (b) Malpighian tubules (c) Body wall in earthworm [/question] [solution] Solution: (a) Ureters in frogs: A ureter acts as a urinogenital duct, which carries sperms along with urine in male frogs. (b) Malphigian tubules: Malphigian tubules are excretory organs in cockroaches. (c) Body wall in earthworms: In earthworms, the body wall consists of muscle layers. It helps in movement and burrowing. [/solution]...
Read More →Draw a neat diagram of digestive system of frog.
[question] Question. Draw a neat diagram of digestive system of frog. [/question] [solution] Solution: [/solution]...
Read More →Mention briefly about the circulatory system of earthworm
[question] Question. Mention briefly about the circulatory system of earthworm [/question] [solution] Solution: Earthworms (Pheretima) have closed blood vascular systems, which consists of the heart, blood vessels, and capillaries. The heart pumps blood for circulating it in one direction. Blood is supplied by smaller blood cells to the gut nerve cord and the body wall. Blood glands are present in the $4^{\text {th }}, 5^{\text {th }}$, and $6^{\text {th }}$ segments, which produce blood cells a...
Read More →Match the terms in column I with those in column II:
[question] Question. Match the terms in column I with those in column II: [/question] [solution] Solution: [/solution]...
Read More →Name the quadrilateral formed,
[question] Question. Name the quadrilateral formed, if any, by the following points, and give reasons for your answer. (i) (–1, –2), (1, 0), (–1, 2), (– 3, 0) (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4) (iii) (4, 5), (7, 6), (4, 3), (1, 2) [/question] [solution] Solution: (i) A(–1, –2), B(1, 0), C(–1, 2), D(–3, 0) Determine distances : AB, BC, CD, DA, AC and BD. $\mathrm{AB}=\sqrt{(1+1)^{2}+(0+2)^{2}}=\sqrt{4+4}=\sqrt{8}=2 \sqrt{2}$ $\mathrm{BC}=\sqrt{(-1-1)^{2}+(2-0)^{2}}=\sqrt{4+4}=\sqrt{8}=2 \sqr...
Read More →Explain, giving reasons, which of the following sets of quantum numbers are not possible.
[question] Question. Explain, giving reasons, which of the following sets of quantum numbers are not possible. (a) $n=0 I=0 m_{\imath}=0$ $m_{s}=+\frac{1}{2}$ (b) $n=1 I=0 m_{\imath}=0$ $m_{x}=-\frac{1}{2}$ (c) $n=1 I=1 m_{l}=0$ $m_{x}=+\frac{1}{2}$ (d) $n=2 l=1 m i=0$ $m_{x}=+\frac{1}{2}$ (e) $n=3 I=3 m_{l}=-3$ $m_{x}=+\frac{1}{2}$ (f) $n=3 I=1 m_{l}=0$ $m_{x}=+\frac{1}{2}$ [/question] [solution] Solution: (a) The given set of quantum numbers is not possible because the value of the principal q...
Read More →Mark the odd one in each series:
[question] Question. Mark the odd one in each series: (a) Areolar tissue; blood; neuron; tendon (b) RBC; WBC; platelets; cartilage (c) Exocrine; endocrine; salivary gland; ligament (d) Maxilla; mandible; labrum; antennae (e) Protonema; mesothorax; metathorax; coxa [/question] [solution] Solution: (a) Areolar tissue, blood, and tendons are examples of connective tissues. Neuron is an example of neural tissue. (b) RBCs, WBCs, and platelets are the three most important components of blood. Cartilag...
Read More →Distinguish between
[question] Question. Distinguish between (a) Simple epithelium and compound epithelium. (b) Cardiac muscle and striated muscle (c) Dense regular and dense irregular connective tissues (d) Adipose and blood tissue (e) Simple gland and compound gland [/question] [solution] Solution: (a) [/solution]...
Read More →Using $s, p, d$ notations, describe the orbital with the following quantum numbers.
[question] Question. Using s, p, d notations, describe the orbital with the following quantum numbers. (a) $n=1, I=0 ;$ (b) $n=3 ; I=1$ (c) $n=4 ; I=2 ;$ (d) $n=4 ; I=3$ [/question] [solution] Solution: (a) $n=1, I=0$ (Given) The orbital is $1 s$. (b) For $n=3$ and $I=1$ The orbital is $3 p$. (c) For $n=4$ and $I=2$ The orbital is $4 d$. (d) For $n=4$ and $I=3$ The orbital is $4 f$. [/solution]...
Read More →Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
[question] Question. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle. [/question] [solution] Solution: Let the points be A(5, –2), B(6, 4) and C(7, –2). $\therefore \quad \mathrm{AB}=\sqrt{(\mathbf{6}-\mathbf{5})^{2}+\mathbf{4}-(\mathbf{- 2})^{2}}$ $=\sqrt{(1)^{2}+(B)^{2}}=\sqrt{1+36}=\sqrt{37}$ $B C=\sqrt{(7-6)^{2}+(-2-4)^{2}}$ $=\sqrt{(1)^{2}+(-6)^{2}}=\sqrt{1+36}=\sqrt{37}$ $A C=\sqrt{(7-5)^{2}+(-2-(-2))^{2}}$ $=\sqrt{(+2)^{2}+(0)^{2}}=\sqrt{4+0}=2$ We ha...
Read More →An atomic orbital has $n=3$. What are the possible values of $/$ and $m_{l}$ ?
[question] Question. (i) An atomic orbital has $n=3$. What are the possible values of $/$ and $m_{l}$ ? (ii) List the quantum numbers ( $m$ i and $I$ ) of electrons for $3 d$ orbital. (iii) Which of the following orbitals are possible? $1 p, 2 s, 2 p$ and $3 f$ [/question] [solution] Solution: (i) $n=3$ (Given) For a given value of $n, I$ can have values from 0 to $(n-1)$. $\therefore$ For $n=3$ $I=0,1,2$ For a given value of $I, m_{1}$ can have $(2 I+1)$ values. For $I=0, m=0 I=1, m=-1,0,1 I=2,...
Read More →A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand
[question] Question. A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of $6 \mathrm{~m} \mathrm{~s}^{-2}$ (b) climbs down with an acceleration of $4 \mathrm{~m} \mathrm{~s}^{-2}$ (c) climbs up with a uniform speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ (d) falls down the rope nearly freely under gravity? (lgnore the mass of the rope). [/question] [solutio...
Read More →Determine if the points (1,5), (2,3) and (– 2, – 11) are collinear.
[question] Question. Determine if the points (1,5), (2,3) and (– 2, – 11) are collinear. [/question] [solution] Solution: The given points are : A(1, 5), B(2, 3) and C(–2, –11). Let us calculate the distance : AB, BC and CA by using distance formula. $A B=\sqrt{(2-1)^{2}+(3-5)^{2}}=\sqrt{(1)^{2}+(-2)^{2}}$ $=\sqrt{1+4}=\sqrt{5}$ units $B C=\sqrt{(-2-2)^{2}+(-11-3)^{2}}=\sqrt{(-4)^{2}+(-14)^{2}}$ $=\sqrt{16+196}=\sqrt{212}=2 \sqrt{53}$ units $\mathrm{CA}=\sqrt{(-2-1)^{2}+(-11-5)^{2}}$ $=\sqrt{(-3...
Read More →Describe various types of epithelial tissues with the help of labelled diagrams.
[question] Question. Describe various types of epithelial tissues with the help of labelled diagrams. [/question] [solution] Solution: Epithelial tissue lines the surface of a body and forms a protective covering. Epithelium cells are packed tightly together with little intercellular matrix. Epithelial tissue in the body is of two types. (a) Simple epithelium: It consists of a single layer of cells where cells are in direct contact with the basement membrane. It is further sub-divided into the f...
Read More →Find the distance between the points (0,0) and (36,15).
[question] Question. Find the distance between the points (0,0) and (36,15). [/question] [solution] Solution: Part-I Let the points be A(0, 0) and B(36, 15) $\therefore \quad \mathrm{AB}=\sqrt{(36-0)^{2}+(15-0)^{2}}$ $=\sqrt{(36)^{2}+(15)^{2}}=\sqrt{1296+225}$ $=\sqrt{\mathbf{1 5 2 1}}=\sqrt{\mathbf{3 9}^{\mathbf{2}}}=39$ Part-II We have A(0, 0) and B(36, 15) as the positions of two towns Here $x_{1}=0, x_{2}=36$ and $y_{1}=0, y_{2}=15$ $\therefore \quad \mathrm{AB}=\sqrt{(\mathbf{3 6}-\mathbf{0...
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