Square of
Question: Square of $\left(\frac{-2}{3}\right)$ is (a) $-\frac{2}{3}$ (b) $\frac{2}{3}$ (c) $-\frac{4}{9}$ (d) $\frac{4}{9}$ Solution: (d) 4/9 To square a number is to raise it to the power of 2. Hence, the square of (2/3) is $\frac{(-2)^{2}}{3^{2}}=\frac{4}{9} \quad \cdots\left((a / b)^{n}=\left(a^{n}\right) /\left(b^{n}\right)\right)$...
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Question: If $A=\left[\begin{array}{ll}i 0 \\ 0 i\end{array}\right]$, write $A^{2}$ Solution: Given : $A=\left[\begin{array}{ll}i 0 \\ 0 i\end{array}\right]$ $A^{2}=A A$ $\Rightarrow A^{2}=\left[\begin{array}{ll}i 0 \\ 0 i\end{array}\right]\left[\begin{array}{ll}i 0 \\ 0 i\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{ll}i^{2}+0 0+0 \\ 0+0 0+i^{2}\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{cc}i^{2} 0 \\ 0 i^{2}\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{...
Read More →How do substance like carbon dioxide and water move in and out of the cell?
Question: How do substance like carbon dioxide and water move in and out of the cell? Solution: $\mathrm{CO}_{2}$ moves into and out of cells by diffusion while water does it through osmosis. Diffusion. It is movement of particles of various substances from the region of their higher concentration to the region of their lower concentration, 1. In a respiring cell, more $\mathrm{CO}_{2}$ is produced internally. As a result its internal concentration rises. As concentration of $\mathrm{CO}_{2}$ is...
Read More →Write the following numbers in the usual form:
Question: Write the following numbers in the usual form: (i) 4.83 107 (ii) 3.02 106 (iii) 4.5 104 (iv) 3 108 (v) 1.0001 109 (vi) 5.8 102 (vii) 3.61492 106 (viii) 3.25 107 Solution: (i) 4.83 x 107= 4.83 x 1,00,00,000 = 4,83,00,000 (ii) 3.02 x 106= 3.02/106= 3.02/10,00,000 = 0.00000302 (iii) 4.5 x 104= 4.5 x 10,000 = 45,000 (iv) 3 x 108= 3/108= 3/10,00,00,000 = 0.00000003 (v) 1.0001 x 109= 1.0001 x 1,00,00,00,000 = 1,00,01,00,000 (vi) 5.8 x 102= 5.8 x 100 = 580 (vii) 3.61492 x 106= 3.61492 x 10,00...
Read More →Without using trigonometric tables, evaluate:
Question: Without using trigonometric tables, evaluate: (i) $\frac{\sin 26^{\circ}}{\cos 64^{\circ}}$ (ii) $\frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}}$ (iii) $\frac{\tan 65^{\circ}}{\cot 25^{\circ}}$ (iv) $\frac{\cos 37^{\circ}}{\sin 53^{\circ}}$ (v) $\frac{\operatorname{cosec} 42^{\circ}}{\sec 48^{\circ}}$ (vi) $\frac{\cot 34^{\circ}}{\tan 56^{\circ}}$ Solution: (i) $\frac{\sin 26^{\circ}}{\cos 64^{\circ}}$ $\frac{\sin 26^{\circ}}{\cos 64^{\circ}}=\frac{\sin \left(90^{\circ}-64^{\c...
Read More →Solve the following equations
Question: If $A=\left[\begin{array}{ll}2 3 \\ 5 7\end{array}\right]$, find $A+A^{T}$ Solution: Given : $A=\left[\begin{array}{ll}2 3 \\ 5 7\end{array}\right]$ $A^{T}=\left[\begin{array}{ll}2 5 \\ 3 7\end{array}\right]$ Now, $A+A^{T}=\left[\begin{array}{ll}2 3 \\ 5 7\end{array}\right]+\left[\begin{array}{ll}2 5 \\ 3 7\end{array}\right]$ $\Rightarrow A+A^{T}=\left[\begin{array}{ll}2+2 3+5 \\ 5+3 7+7\end{array}\right]$ $\Rightarrow A+A^{T}=\left[\begin{array}{cc}4 8 \\ 8 14\end{array}\right]$...
Read More →Express the following numbers in standard form:
Question: Express the following numbers in standard form: (i) 6020000000000000 (ii) 0.00000000000943 (iii) 0.00000000085 (iv) 846 107 (v) 3759 104 (vi) 0.00072984 (vii) 0.000437 104 (viii) 4 100000 Solution: To express a number in the standard form, move the decimal point such that there is only one digit to the left of the decimal point. (i) 6020000000000000 = 6.02 x 1015 (The decimal point is moved 15 places to the left.) (ii) 0.0000000000943 = 9.43 x 1012 (The decimal point is moved 12 places...
Read More →How is bacterial cell different from an Onion peel cell ?
Question: How is bacterial cell different from an Onion peel cell ? Solution: See differences between prokaryotic (bacterial cell) and eukaryotic (Onion peel cell) cells....
Read More →Name the organelles which show analogy written as under
Question: Name the organelles which show analogy written as under (a) Transporting channels of the cell (b) Power house of the cell (c) Packaging and despatching unit of the cell (d) Digestive bag of the cell (e) Storage sac of the cell (f) Kitchen of the cell (g) Control room of the cell Solution: (a) Endoplasmic reticulum (b) Mitochondria (c) Golgi apparatus (d) Lysosome (e) Vacuole (f) Chloroplast (g) Nucleus....
Read More →Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
Question: Given an example of two non-zero $2 \times 2$ matrices $A$ and $B$ such that $A B=O$. Solution: Let the two matrices be $A=\left[\begin{array}{ll}5 0 \\ 9 0\end{array}\right]$ and $B=\left[\begin{array}{cc}0 0 \\ 12 -21\end{array}\right]$, such that $A B=\left[\begin{array}{ll}5 0 \\ 9 0\end{array}\right]\left[\begin{array}{cc}0 0 \\ 12 -21\end{array}\right]$. $\Rightarrow A B=\left[\begin{array}{ll}0 0 \\ 0 0\end{array}\right]$...
Read More →Find the value of x for which 52x ÷ 5−3 = 55.
Question: Find the value ofxfor which 52x 53= 55. Solution: We have: $5^{2 x} \div 5^{-3}=5^{5}$ $5^{2 x+3}=5^{5} \quad \cdots a^{m} \div a^{n}=a^{m-n}$ $2 x+3=5$ $2 x=2$ $x=1$ Hence,xis 1....
Read More →Write the name of different plant parts in
Question: Write the name of different plant parts in which chloroplast, chromoplast and leucoplast are present. Solution: 1. Chromoplast: Flower (petals) and fruits 2. Chloroplast : Green leaves and green parts of young stems. 3. Leucoplast: Root and underground stem....
Read More →Solve the following equations
Question: If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, write $A A^{T}$ Solution: Given : $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$ $A^{T}=\left[\begin{array}{lll}1 2 3\end{array}\right]$ Now, $A A^{T}=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\left[\begin{array}{lll}1 2 3\end{array}\right]$ $\Rightarrow A A^{T}=\left[\begin{array}{lll}1 2 3 \\ 2 4 6 \\ 3 6 9\end{array}\right]$...
Read More →Match the items of $A$ and $B$.
Question: Match the items of $A$ and $B$. Solution: $a-i v, b-v, c-i i i, d-i, e-i i$...
Read More →Solve the following equations
Question: If $A=\left[\begin{array}{ll}4 3 \\ 1 2\end{array}\right]$ and $B=\left[\begin{array}{r}-4 \\ 3\end{array}\right]$, write $A B$. Solution: $A B=\left[\begin{array}{ll}4 3 \\ 1 2\end{array}\right]\left[\begin{array}{c}-4 \\ 3\end{array}\right]$ $\Rightarrow A B=\left[\begin{array}{c}-16+9 \\ -4+6\end{array}\right]$ $\Rightarrow A B=\left[\begin{array}{c}-7 \\ 2\end{array}\right]$...
Read More →Bacteria do not have chloroplast but some
Question: Bacteria do not have chloroplast but some bacteria are photoautotrophic in nature and perform photosynthesis. Which part of bacterial cell performs this? Solution: Photoautotrophic bacteria posses photosynthetic pigments inside small vesicles which may be attached to the plasma membrane....
Read More →Solve this
Question: If $A=\left[\begin{array}{lll}2 1 4 \\ 4 1 5\end{array}\right]$ and $B=\left[\begin{array}{rr}3 -1 \\ 2 2 \\ 1 3\end{array}\right]$. Write the orders of $A B$ and $B A$. Solution: The order of matrix $A$ is $2 \times 3$ and the order of matrix $B$ is $3 \times 2$. Since the number of columns in $A$ is equal to the number of rows in $B, A B$ exists and it is of order $2 \times 2$. Also, since the number of columns in $B$ is equal to the number of rows in $A, B A$ exists and it is of ord...
Read More →If cells of Onion peel and RBC are separately kept in hypotonic solution
Question: If cells of Onion peel and RBC are separately kept in hypotonic solution what among the following will take place ? Explain the reason for your answer, (a) Both the cells will swell (b) RBC will burst easily while cells of Onion peel will resist the bursting to some extent (c) $\mathrm{a}$ and $\mathrm{b}$ both are correct (d) RBC and Onion peel cells will behave similarly. Solution: (b) RBC will burst as there is no mechanism to restrict entry of water into them. Onion peel cells do n...
Read More →If you are provided with some vegetables to cook,
Question: If you are provided with some vegetables to cook, you genenrally add salt into vegetables during cooking process. After adding salt, vegetables release water. What mechanism is responsible for this? (CCE 2014) Solution: On adding salt, vegetables release water due to exosmosis. Exosmosis occurs whenever the external medium is hypertonic as compared to the osmotic concentration inside living cells....
Read More →Solve the following
Question: (i) If $x=\left(\frac{3}{2}\right)^{2} \times\left(\frac{2}{3}\right)^{-4}$, find the value of $x^{-2}$. (ii) If $x=\left(\frac{4}{5}\right)^{-2} \div\left(\frac{1}{4}\right)^{2}$, find the value of $x^{-1}$. Solution: (i) First, we have to findx. $x=\left(\frac{3}{2}\right)^{2} \times\left(\frac{2}{3}\right)^{-4} \quad \ldots\left(a^{-1}=1 / a\right)$ $=\left(\frac{3}{2}\right)^{2} \times\left(\frac{3}{2}\right)^{4}$ $=\left(\frac{3}{2}\right)^{6}$ Hence,x2is: $x^{-2}=\left(\left(\fra...
Read More →Solve the following
Question: (i) If $x=\left(\frac{3}{2}\right)^{2} \times\left(\frac{2}{3}\right)^{-4}$, find the value of $x^{-2}$. (ii) If $x=\left(\frac{4}{5}\right)^{-2} \div\left(\frac{1}{4}\right)^{2}$, find the value of $x^{-1}$. Solution: (i) First, we have to findx. $x=\left(\frac{3}{2}\right)^{2} \times\left(\frac{2}{3}\right)^{-4} \quad \ldots\left(a^{-1}=1 / a\right)$ $=\left(\frac{3}{2}\right)^{2} \times\left(\frac{3}{2}\right)^{4}$ $=\left(\frac{3}{2}\right)^{6}$ Hence,x2is: $x^{-2}=\left(\left(\fra...
Read More →We eat food composed of all the nutrients like carbohydrates,
Question: We eat food composed of all the nutrients like carbohydrates, proteins, fats, vitamins, minerals and water. After digestion, they are absorbed in the form of glucose, amino acids, fatty acids, glycerol, etc. What mechanisms are involved in the absorption of digested food and water? Solution: Digested Food: 1. Glucose, amino acids and some ions - Active transport. 2. Fatty acids, Glycerol - Diffusion (Passive transport). Water: Osmosis....
Read More →Name any cell organelle which is non-membranous.
Question: Name any cell organelle which is non-membranous. Solution: Ribosome....
Read More →A person takes concentrated solution of salt.
Question: A person takes concentrated solution of salt. After some time he starts vomiting. What is the phenomenon responsible for such a situation? Explain. Solution: Concentrated salt solution causes irritation and excessive dehydration in the wall of alimentary canal due to exosmosis. There is uncomfortable stretching which causes reverse movements and hence vomiting....
Read More →Why is endocytosis found in animals only? (CCE 2012)
Question: Why is endocytosis found in animals only? (CCE 2012) Solution: Endocytosis is engulfment of food and other substances from external medium by plasma membrane. This is possible only when plasma membrane is in direct contact with external medium. It occurs only in animal cells. In plant cells, a cell wall is present over the plasma membrane. Therefore, their plasma membrane cannot perform endocytosis....
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