Solve the following
Question: $\left(\frac{-1}{5}\right)^{3} \div\left(\frac{-1}{5}\right)^{8}$ is equal to (a) $\left(-\frac{1}{5}\right)^{5}$ (b) $\left(-\frac{1}{5}\right)^{11}$ (c) $(-5)^{5}$ (c) $(-5)^{5}$ Solution: (c) $(-5)^{5}$ we have: $\left(\frac{-1}{5}\right)^{3} \div\left(\frac{-1}{5}\right)^{8}=\left(\frac{-1}{5}\right)^{3-8}$ $=\left(\frac{-1}{5}\right)^{-5}$ $=\frac{1}{(-1 / 5)^{5}}$ $=\frac{1}{\left((-1)^{5} / 5^{5}\right)}$ $=\frac{5^{5}}{(-1)^{5}}$ $=\left(\frac{5}{-1}\right)^{5}$ $=(-5)^{5}$...
Read More →Differentiate between rough and smooth
Question: Differentiate between rough and smooth endoplasmic recticulum. How is endoplasmic reticulum important for membrane biosynthesis? Solution: (b) Membrane Biosynthesis : Both the types of E.R. take part in membrane biosynthesis. Rough endoplasmic reticulum synthesises proteins which are passed over to Golgi apparatus for glycolisation. Smooth endoplasmic reticulum forms lipids over its surface. They are also transported to Golgi apparatus. Golgi apparatus builds membrane with the help of ...
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Question: If $A=\left[\begin{array}{rrr}-1 0 0 \\ 0 -1 0 \\ 0 0 -1\end{array}\right]$, find $A^{2}$ Solution: Here, $A^{2}=A A$ $\Rightarrow A^{2}=\left[\begin{array}{ccc}-1 0 0 \\ 0 -1 0 \\ 0 0 -1\end{array}\right]\left[\begin{array}{ccc}-1 0 0 \\ 0 -1 0 \\ 0 0 -1\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{lll}1+0+0 0+0+0 0+0+0 \\ 0+0+0 0+1+0 0+0+0 \\ 0+0+0 0+0+0 0+0+1\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{lll}1 0 0 \\ 0 1 0 \\ 0 0 1\end{array}\right]$...
Read More →Draw a well labelled diagram of eukaryotic nucleus.
Question: Draw a well labelled diagram of eukaryotic nucleus. How is it different from nucloid? Solution:...
Read More →Solve the following
Question: $\left(\frac{-1}{2}\right)^{5} \times\left(\frac{-1}{2}\right)^{3}$ is equal to (a) $\left(\frac{-1}{2}\right)^{8}$ (b) $-\left(\frac{1}{2}\right)^{8}$ (c) $\left(\frac{1}{4}\right)^{8}$ (d) $\left(-\frac{1}{2}\right)^{15}$ Solution: (a) $\left(\frac{-1}{2}\right)^{8}$ We have: $\left(\frac{-1}{2}\right)^{5} \times\left(\frac{-1}{2}\right)^{3}=\left(\frac{-1}{2}\right)^{5+3}$ $=\left(\frac{-1}{2}\right)^{8}$...
Read More →Draw a neat labelled diagram of an animal cell.
Question: Draw a neat labelled diagram of an animal cell. Solution:...
Read More →Solve the following Question
Question: If $A=\left[\begin{array}{ll}1 1 \\ 1 1\end{array}\right]$ satisfies $A^{4}=\lambda A$, then write the value of $\lambda$. Solution: $A^{2}=A \cdot A$ $\Rightarrow A^{2}=\left[\begin{array}{ll}1 1 \\ 1 1\end{array}\right]\left[\begin{array}{ll}1 1 \\ 1 1\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{ll}1+1 1+1 \\ 1+1 1+1\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{ll}2 2 \\ 2 2\end{array}\right]$ Now. $A^{4}=A^{2} A^{2}$ $\Rightarrow A^{4}=\left[\begin{array}{...
Read More →Solve the following
Question: $\left(\frac{2}{3}\right)^{-5}$ is equal to (a) $\left(\frac{-2}{3}\right)^{5}$ (b) $\left(\frac{3}{2}\right)^{5}$ (c) $\frac{2 x-5}{3}$ (d) $\frac{2}{3 \times 5}$ Solution: (b) $\left(\frac{3}{2}\right)^{5}$ Rearrange (2/3)5to get a positive exponent. $\left(\frac{2}{3}\right)^{-5}=\frac{1}{\left(\frac{2}{3}\right)^{5}} \quad\left(a^{-n}=\frac{1}{a^{n}}\right)$ $=\frac{1}{\frac{2^{5}}{3^{5}}} \quad\left\{\left(\frac{a}{b}\right)^{n}=\frac{a^{n}}{b^{n}}\right\}$ $=\frac{3^{5}}{2^{5}}$ ...
Read More →Illustrate only a plant cell as seen under electron microscope.
Question: Illustrate only a plant cell as seen under electron microscope. How is it different from animal cell? Solution:...
Read More →Which of the following numbers is not equal to
Question: Which of the following numbers is not equal to $\frac{-8}{27} ?$ (a) $\left(\frac{2}{3}\right)^{-3}$ (b) $-\left(\frac{2}{3}\right)^{3}$ (c) $\left(-\frac{2}{3}\right)^{3}$ (d) $\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right)$ Solution: (a) $\left(\frac{2}{3}\right)^{-3}$ We can write $\frac{-8}{27}$ as $\frac{-2 \times(-2) \times(-2)}{3 \times 3 \times 3}$. It can be written in the forms given below. $\frac{-2 \times(-2) \times(-2)}{3 \times 3...
Read More →Solve this
Question: If $A=\left[\begin{array}{rr}1 -1 \\ -1 1\end{array}\right]$, satisfies the matrix equation $A^{2}=k A$, write the value of $k$. Solution: $A^{2}=A A$ $\Rightarrow A^{2}=\left[\begin{array}{cc}1 -1 \\ -1 1\end{array}\right]\left[\begin{array}{cc}1 -1 \\ -1 1\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{cc}1+1 -1-1 \\ -1-1 1+1\end{array}\right]$ $\Rightarrow A^{2}=\left[\begin{array}{cc}2 -2 \\ -2 2\end{array}\right]$ Now, $A^{2}=k A$ $\Rightarrow\left[\begin{array}{cc}2 -2...
Read More →Draw a plant cell and label the parts which
Question: Draw a plant cell and label the parts which 1. Determine function and development of the cell. 2. Provides resistance to microbes and to withstand hypotonic external medium without injury. 3. Packages materials coming from the endoplasmic reticulum. 4. Is a fluid contained inside the nucleus. 5. Is site for many biochemical reactions necessary to sustain life. Solution: 1. Nucleus 2. Cell wall 3. Golgi apparatus 4. Nucleoplasm 5. Cytoplasm....
Read More →What are consequences of the following conditions?
Question: What are consequences of the following conditions? 1. A cell containing higher water concentration than the surrounding medium. 2. cell having low water concentration as compared to its surrounding medium. 3. A cell having equal water concentration to its surrounding medium. Solution: High water concentration occurs in hypotonic solution, low water concentration in hypertonic solution while equal water concentration occurs in isotonic solution. 1. A cell having higher water content or ...
Read More →Without using trigonometric tables, prove that:
Question: Without using trigonometric tables, prove that:(i) cos 81 sin 9 = 0(ii) tan 71 cot 19 = 0(iii) cosec 60 sec 30 = 0(iv) cot34 tan56 = 0(v) sin248 + sin242 = 1(vi) cos272 + cos218 = 1 Solution: (i) $\mathrm{LHS}=\cos 81^{0}-\sin 9^{0}$ $=\cos \left(90^{0}-9^{0}\right)-\sin 9^{0}$ $=\sin 9^{0}-\sin 9^{0}$ $=0$ $=\mathrm{RHS}$ (ii) LHS $=\tan 71^{\circ}-\cot 19^{\circ}$ $=\tan \left(90^{\circ}-19^{\circ}\right)-\cot 19^{0}$ $=\cot 19^{0}-\cot 19^{0}$ $=0$ (iii) To Prove: cosec60 sec30 = 0 ...
Read More →Solve the following Question
Question: If $\left[\begin{array}{ll}1 0 \\ y 5\end{array}\right]+2\left[\begin{array}{rr}x 0 \\ 1 -2\end{array}\right]=l$, where $l$ is $2 \times 2$ unit matrix. Find $x$ and $y$. Solution: Given : $\left[\begin{array}{ll}1 0 \\ y 5\end{array}\right]+2\left[\begin{array}{cc}x 0 \\ 1 -2\end{array}\right]=I$ $\Rightarrow\left[\begin{array}{cc}1 0 \\ y 5\end{array}\right]+\left[\begin{array}{cc}2 x 0 \\ 2 -4\end{array}\right]=\left[\begin{array}{ll}1 0 \\ 0 1\end{array}\right]$ $\Rightarrow\left[\...
Read More →How are chromatin, chromatid and chromosomes related to each other? (CCE 2012)
Question: How are chromatin, chromatid and chromosomes related to each other? (CCE 2012) Solution: Chromatin is intertwined mass of fine thread like structures made of DNA and protein. During cell division, chromatin condenses to form thicker rod like structures called chromosomes. Each chromosome consists of two similar halves called chromatids. Formation of chromosomes having two similar halves or chromatids is meant for equitable distribution of chromatin which is hereditary material....
Read More →Which of the following is not reciprocal of
Question: Which of the following is not reciprocal of $\left(\frac{2}{3}\right)^{4} ?$ (a) $\left(\frac{3}{2}\right)^{4}$ (b) $\left(\frac{2}{3}\right)^{-4}$ (c) $\left(\frac{3}{2}\right)^{-4}$ (d) $\frac{3^{4}}{2^{4}}$ Solution: (c) $\left(\frac{3}{2}\right)^{-4}$ The reciprocal of $\left(\frac{2}{3}\right)^{4}$ is $\left(\frac{3}{2}\right)^{4}$. Therefore, option (a) is the correct answer. Option (b) is just re-expressing the number with a negative exponent. Option (d) is obtained by working o...
Read More →Why do plant cells possess large sized vacuole? (CCE 2011)
Question: Why do plant cells possess large sized vacuole? (CCE 2011) Solution: Vacuole of plant cells has to be large because it takes part in 1. Storage : It stores salts, sugar, amino acids, organic acids and some proteins. 2. Cellular Wastes : They are dumped in the vacuole. 3. Lysosomal Enzymes: They occur in the vacuole of plant cells. 4. Turgidity: The vacuole contains cell sap which provides turgidity to the cells. 5. Absorption of Water: Plant cell vacuole contains an osmotic concentrati...
Read More →Which kind of plastid is more common in
Question: Which kind of plastid is more common in (a) Root of the plant (b) Leaves of the plant (c) Flowers and fruits? Solution: (a) Roots : Leucoplasts (b) Leaves: Chloroplasts (c) Flowers and Fruits : Chromoplasts....
Read More →Solve this
Question: If $A=\left[\begin{array}{cc}\cos x -\sin x \\ \sin x \cos x\end{array}\right]$, find $A A^{\top}$ Solution: Given : $A=\left[\begin{array}{cc}\cos x -\sin x \\ \sin x \cos x\end{array}\right]$ $\Rightarrow A^{T}=\left[\begin{array}{cc}\cos x \sin x \\ -\sin x \cos x\end{array}\right]$ $A A^{T}=\left[\begin{array}{cc}\cos x -\sin x \\ \sin x \cos x\end{array}\right]\left[\begin{array}{cc}\cos x \sin x \\ -\sin x \cos x\end{array}\right]$ $\Rightarrow A A^{T}=\left[\begin{array}{cc}\cos...
Read More →Which of the following is not equal to
Question: Which of the following is not equal to $\left(\frac{-3}{5}\right)^{4} ?$ (a) $\frac{(-3)^{4}}{5^{4}}$ (b) $\frac{3^{4}}{(-5)^{4}}$ (c) $-\frac{3^{4}}{5^{4}}$ (d) $\frac{-3}{5} \times \frac{-3}{5} \times \frac{-3}{5} \times \frac{-3}{5}$ Solution: (c) $-\frac{3^{4}}{5^{4}}$ $\left(\frac{-3}{5}\right)^{4}=\frac{(-3)^{4}}{5^{4}}=\frac{3^{4}}{(-5)^{4}}=\frac{-3}{5} \times \frac{-3}{5} \times \frac{-3}{5} \times \frac{-3}{5}$ It is not equal to $-\frac{3^{4}}{5^{4}}$....
Read More →Name two organelles in the plant cell
Question: Name two organelles in the plant cell that contain their own genetic materials and ribosomes. Solution: 1. Plastids 2. Mitochondria....
Read More →solve the problem
Question: If $A=\left[\begin{array}{cc}\cos x \sin x \\ -\sin x \cos x\end{array}\right]$, find $x$ satisfying $0x\frac{\pi}{2}$ when $A+A^{T}=1$ Solution: Given : $A=\left[\begin{array}{cc}\cos x \sin x \\ -\sin x \cos x\end{array}\right]$ $A^{T}=\left[\begin{array}{cc}\cos x -\sin x \\ \sin x \cos x\end{array}\right]$ Now, $A+A^{T}=I$ $\Rightarrow\left[\begin{array}{cc}\cos x \sin x \\ -\sin x \cos x\end{array}\right]+\left[\begin{array}{cc}\cos x -\sin x \\ \sin x \cos x\end{array}\right]=\le...
Read More →Cube of
Question: Cube of $\frac{-1}{2}$ is (a) $\frac{1}{8}$ (b) $\frac{1}{16}$ (c) $-\frac{1}{8}$ (d) $\frac{-1}{16}$ Solution: (c) -1/8 The cube of a number is the number raised to the power of 3. Hence the cube of 1/2 is $\frac{(-1)^{3}}{2^{3}} \quad \cdots\left((a / b)^{n}=\left(a^{n}\right) /\left(b^{n}\right)\right.$ $-\frac{1}{8}$...
Read More →How does Amoeba obtain its food?
Question: How does Amoeba obtain its food? Solution: Plasma membrane of Amoeba is flexible. With its help, Amoeba engulfs food particle. The engulfed food particle passes into the body of Amoeba as a phagosome. Phagosome combines with lysosome to produce digestive or food vacuole. Digestion occurs in food vacuole. The digested food passes into surrounding cytoplasm. The undigested matter is thrown out of the cell in exocytosis....
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