Simplify:
Question: Simplify: (i) $\left(4^{-1} \times 3^{-1}\right)^{2}$ (ii) $\left(5^{-1} \div 6^{-1}\right)^{3}$ (iii) $\left(2^{-1}+3^{-1}\right)^{-1}$ (iv) $\left(3^{-1} \times 4^{-1}\right)^{-1} \times 5^{-1}$ Solution: (i) $\left(4^{-1} \times 3^{-1}\right)^{2}=\left(\frac{1}{4} \times \frac{1}{3}\right)^{2} \quad \ldots\left(a^{-1}=1 / a\right)$ $=\left(\frac{1}{12}\right)^{2}$ $=\frac{1^{2}}{12^{2}}$ --- ((a/b)n= (an)/(bn) ) $=\frac{1}{24}$ (ii) $\left(5^{-1} \div 6^{-1}\right)^{3}=\left(\frac{1...
Read More →If A and B are symmetric matrices, then write the condition for which AB is also symmetric.
Question: IfAandBare symmetric matrices, then write the condition for whichABis also symmetric. Solution: Given:ABis symmetric. $\Rightarrow(A B)^{T}=A B$ $\Rightarrow B^{T} A^{T}=A B \quad\left[\because(A B)^{T}=B^{T} A^{T}\right]$ $\Rightarrow B A=A B \quad\left[\because A\right.$ and $B$ are symmetric matrices, so $A^{T}=A$ and $\left.B^{T}=B\right]$ Thus, $A B$ is also symmetric, if $A B=B A$....
Read More →List the characteristics of cork.
Question: List the characteristics of cork. How is it formed? (CCE 2014) Mention its role. Solution: (a) Characteristics: 1. Outer Tissue: Cork is outer protective tissue of older stems and roots. 2. Dead cells: The mature cork cells become dead and filled with tannins, resins and air. 3. Compact Tissue: Intercellular spaces are absent. Cork is a compact tissue. 4. Suberin: Cork cells are impermeable due to deposition of suberin in their walls. 5. Multilayered: Cork consists of several layers of...
Read More →Solve this
Question: If $A=\left[a_{i j}\right]$ is a skew-symmetric matrix, then write the value of $\sum_{i} \sum_{j} a_{i j}$. Solution: Given : $A=\left[a_{i j}\right]$ is a skew symmetric matrix. $\Rightarrow a_{i j}=-a_{j i} \quad$ [For all values of $\left.i, j\right]$ $\Rightarrow a_{i i}=-a_{i i} \quad[$ For all values of $i]$ $\Rightarrow a_{i j}=0$ Now, $\sum_{i} \sum_{j} a_{i j}=a_{11}+a_{12}+a_{13}+\ldots+a_{21}+a_{22}+a_{23}+\ldots+a_{31}+a_{32}+a_{33}+\ldots$ $=0+a_{12}+a_{13}+\ldots-a_{12}+...
Read More →Give reasons for
Question: Give reasons for (a) Meristematic cells have a prominent nucleus and dense cytoplasm but they lack vacuole. (b) Intercellular spaces are absent in sclerencymatous tissue. (c) We get a crunchy and granular feeling when we chew pear fruit. (d) Branches of a tree move and bend freely in high wind velocity. (e) It is difficult to pull out the husk of coconut. Solution: (a) They are undergoing divisions and do not store food. (b) They have lignified walls and form bundles for mechanical fun...
Read More →Find the value of each of the following:
Question: Find the value of each of the following: (i) $\left(\frac{1}{2}\right)^{-1}+\left(\frac{1}{3}\right)^{-1}+\left(\frac{1}{4}\right)^{-1}$ (ii) $\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}$ (iii) (21 41) 22 (iv) (51 21) 61 Solution: (i) $\left(\frac{1}{2}\right)^{-1}+\left(\frac{1}{3}\right)^{-1}+\left(\frac{1}{4}\right)^{-1}=\frac{1}{1 / 2}+\frac{1}{1 / 3}+\frac{1}{1 / 4} \quad \rightarrow\left(a^{-1}=1 / a\right)$ =2+3+4 =12 (ii)$\left(\fra...
Read More →Draw well albelled diagrams of various
Question: Draw well albelled diagrams of various types of muscles found in human body. Solution:...
Read More →If A = [aij] is a skew-symmetric matrix,
Question: If $A=\left[a_{i j}\right]$ is a skew-symmetric matrix, then write the value of $\sum_{i} \sum_{j} a_{i j}$. Solution: Given: $A=\left[a_{i j}\right]$ is a skew symmetric matrix. $\Rightarrow a_{i j}=-a_{j i} \quad$ [For all values of $\left.i, j\right]$ $\Rightarrow a_{i i}=-a_{i i} \quad[$ For all values of $i]$ $\Rightarrow a_{i j}=0$ Now, $\sum_{i} \sum_{j} a_{i j}=a_{11}+a_{12}+a_{13}+\ldots+a_{21}+a_{22}+a_{23}+\ldots+a_{31}+a_{32}+a_{33}+\ldots$ $=0+a_{12}+a_{13}+\ldots-a_{12}+0...
Read More →Without using trigonometric tables, prove that:
Question: Without using trigonometric tables, prove that:(i) sin53 cos37 + cos53 sin37 = 1(ii) cos54 cos36 sin54 sin36 = 0(iii) sec70 sin20 + cos20 cosec70 = 2 (iv) $\tan 15^{\circ} \tan 60^{\circ} \tan 75^{\circ}=\sqrt{3}$ (v) tan48 tan23 tan42 tan67 tan 45 = 1(vi) (sin72 + cos18)(sin72 cos18) = 0(vii) cosec 39 cos 51 + tan 21 cot 69 sec221 = 0 Solution: (i) LHS $=\sin 53^{0} \cos 37^{0}+\cos 53^{0} \sin 37^{0}$ $=\sin \left(90^{\circ}-37^{0}\right) \cos 37^{0}+\cos \left(90^{0}-37^{0}\right) \...
Read More →Solve the following equations
Question: If $A=\left[a_{i j}\right]$ is a skew-symmetric matrix, then write the value of $\sum_{i} a_{i j}$. Solution: Given : $A=\left[a_{i j}\right]$ is a skew - symmetric matrix. $\Rightarrow a_{i j}=-a_{i j} \quad$ [For all values of $\left.i, j\right]$ $\Rightarrow a_{i i}=-a_{i i} \quad$ [For all values of $i$ ] $\Rightarrow a_{i j}+a_{i i}=0$ $\Rightarrow 2 a_{i i}=0$ $\Rightarrow a_{i i}=0$ [For all values of $i$ ] $\sum_{i} a_{i i}=0+0+\ldots+0 \quad[$ itimes $]$ $=0$ Thus, $\sum_{i} a...
Read More →Describe the structure and function of different types of epithelial tissues.
Question: Describe the structure and function of different types of epithelial tissues. Draw well labelled diagrams. Solution: 1. Protection: Surface epithelium lying over the skin protects the body from drying up, microbes, chemicals and injury. A similar function of protection is carried out by epithelium lining mouth, nasal tract and alimentary canal. 2. Absorption: Some epithelia have become specialised for absorption, e.g., intestinal mucosa. 3. Epithelium lining the different parts of urin...
Read More →Fiind the value of each of the following:
Question: Fiind the value of each of the following: (i) 31+ 41 (ii) (30+ 41) 22 (iii) (31+ 41+ 51)0 (iv) $\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}$ Solution: (i) We know from the property of powers that for every natural numbera,a1= 1/a. Then: $3^{-1}+4^{-1}=\frac{1}{3}+\frac{1}{4} \quad \ldots\left(a^{-1}=1 / a\right)$ $=\frac{4+3}{12}$ $=\frac{7}{12}$ (ii) We know from the property of powers that for every natural numbera,a1= 1/a. Moreover,a0is 1 for ever...
Read More →Differentiate between sclerenchyma and parenchyma tissue. Draw diagram as well.
Question: Differentiate between sclerenchyma and parenchyma tissue. Draw diagram as well. Solution:...
Read More →For any square matrix write whether
Question: For any square matrix write whether $A A^{\top}$ is symmetric or skew-symmetric. Solution: Here, $\left(A A^{T}\right)^{T}=\left(A^{T}\right)^{T} A^{T} \quad\left[\because(A B)^{T}=B^{T} A^{T}\right]$ $\Rightarrow\left(A A^{T}\right)^{T}=A A^{T} \quad\left[\because\left(A^{T}\right)^{T}=A\right]$ Thus, $A A^{\top}$ is a symmetric matrix....
Read More →Fill in the blanks :
Question: Fill in the blanks : .. are forms of complex tissue. .. have guard cells. Cells of cork contain a chemical called .. Husk of coconut is made of . tissue. and .. are both conducting tissues. .. gives flexibility in plants. Xylem transports .. and . from soil. Phloem transports from .. to other parts of the plant. Solution: 1. Xylem and phloem 2. Stomata 3. Suberin 4. sclerenchyma 5. Xylem, phloem, 6. Collenchyma 7. water, minerals 8. food, leaves....
Read More →Express each of the following as a rational number of the form
Question: Express each of the following as a rational number of the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. (i) $2^{-3}$ (ii) $(-4)^{-2}$ (iii) $\frac{1}{3^{-2}}$ (iv) $\left(\frac{1}{2}\right)^{-5}$ (v) $\left(\frac{2}{3}\right)^{-2}$ Solution: We know that $\mathrm{a}^{-\mathrm{n}}=\frac{1}{\mathrm{a}^{\mathrm{n}}}$. Therefore, (i) $2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}$ (ii) $(-4)^{-2}=\frac{1}{(-4)^{2}}=\frac{1}{16}$ (iii) $\frac{1}{3^{-2}}=3^{2}=9$ (iv) $\left(\frac{...
Read More →Why is epidermis important for the plants?
Question: Why is epidermis important for the plants? Solution: 1. Strength: Collenchyma is a living mechanical tissue which provides both mechanical strength as well as flexibility. Because of collenchyma, plant organs can bend without breaking. 2. Growth: Collenchyma allows growth and elongation of organs. 3. Storage: Being living tissue, collenchyma stores food. 4. Photosynthesis: Collenchyma cells may contain chloroplasts and take part in photosynthesis....
Read More →Fill in the blanks :
Question: Fill in the blanks : (a) Cork cells possess on .. their walls that makes them impervious to gases and water. (b) . have tubular cells with perforated walls and are living in nature. (c) Bone possesses a hard matrix composed of .. and Solution: a -suberin, b-sieve tubes, c-calcium, phosphorus....
Read More →Which structure protects the plant
Question: Which structure protects the plant body against the invasion of parasites? Solution: Epidermis is the outer protective layer of plant body which does not allow the parasites to gain entry into the internal tissues due to 1. Absence of intercellular spaces 2. Thick outer walls 3. Deposition of cutin and wax in the cuticle covering the epidermis 4. Silica and other deposidons....
Read More →For a non zero rational number a,
Question: For a non zero rational numbera, (a3)2is equal to (a)a9 (b)a6 (c)a9 (d)a1 Solution: (b)a6 We have: $\left(a^{3}\right)^{-2}=a^{3 \times(-2)} \quad \ldots\left(\left(a^{m}\right)^{n}=a^{m \times n}\right)$ $a^{-6 \mid}$...
Read More →For any square matrix write whether
Question: For any square matrix write whether $A A^{\top}$ is symmetric or skew-symmetric. Solution: Here, $\left(A A^{T}\right)^{T}=\left(A^{T}\right)^{T} A^{T} \quad\left[\because(A B)^{T}=B^{T} A^{T}\right]$ $\Rightarrow\left(A A^{T}\right)^{T}=A A^{T} \quad\left[\because\left(A^{T}\right)^{T}=A\right]$ Thus, $A A^{\top}$ is a symmetric matrix....
Read More →Water Hyacinth floats on water
Question: Water Hyacinth floats on water surface. Explain. (CCE 2012) Solution: Water Hyacinth has spongy petioles which enclose a lot of air in its aerenchyma. Air makes the plant lighter than water so that it is able to float on surface of water....
Read More →For a non-zero rational number a,
Question: For a non-zero rational numbera,a7a12is equal to (a)a5 (b)a19 (c)a5 (d)a19 Solution: (c)a5 $a^{m} \div a^{n}=a^{m-n}$ Hence, $a^{7} \div a^{12}=a^{7-12}=a^{-5}$...
Read More →Fill in the blanks :
Question: Fill in the blanks : Lining of blood vessels is made up of . Lining of small intestine is made up of .. . Lining of kidney tubules is made up of . . Epithelial cells with cilia are found in of our body. Solution: 1. squamous epithelium 2. columuar epithelium 3. cuboidal epithelium 4. respiratory tract....
Read More →If A = [aij] is a square matrix such that
Question: If $A=\left[a_{i j}\right]$ is a square matrix such that $a_{i j}=r^{2}-j^{2}$, then write whether $A$ is symmetric or skew-symmetric. Solution: Here, $a_{i j}=i^{2}-j^{2}, 1 \leq i \leq 2$ and $1 \leq j \leq 2$ $\therefore a_{11}=1^{2}-1^{2}=1-1=0, a_{12}=1^{2}-2^{2}=1-4=-3$ $a_{21}=2^{2}-1^{2}=4-1=3$ and $a_{22}=2^{2}-2^{2}=4-4=0$ $\therefore A=\left[\begin{array}{ll}a_{11} a_{12} \\ a_{21} a_{22}\end{array}\right]=\left[\begin{array}{cc}0 -3 \\ 3 0\end{array}\right]$ $A^{T}=\left[\b...
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