The size of the cells of an organism
Question: The size of the cells of an organism has no relation with the size of its body. Do you agree? Give reason for your answer. Solution: The size of the cells of an organism is not related with the size of its body. This can be understood with the example of an elephant and a rat. The cells in elephant are not bigger as compared to the cells of small animal like rat. Hence, proving that cells are not related to the size of organism. However, the size of a cell is related to the function it...
Read More →Why do plant cells have an additional
Question: Why do plant cells have an additional layer surrounding the cell membrane? What is the layer known as? Solution: The additional layer surrounding the cell membrane of plant cells is called cell wall. Since, the plants cannot show physical movement and escape themselves from extreme climatic conditions, therefore a cell wall is needed for protection. The cell wall protects the plant cells from temperature variation, high wind speed, atmospheric moisture, etc. It also gives shape and sup...
Read More →Cells consist of many organelles,
Question: Cells consist of many organelles, yet we do not call any of these organelles as structural and functional unit of living organisms. Explain. Solution: The cell organelles like mitochondria, Golgi complex, ribosomes, nucleus, etc., have specific functions and carry out specific functions in a cell but they cannot be called as the structural and functional units of living organisms. This is because they can function only when present inside a living cell. They cannot act as independent u...
Read More →If the solve the problem
Question: If $y=x^{4}-10$ and if $x$ changes from 2 to $1.99$, the change in $y$ is (a) $0.32$ (b) $0.032$ (c) $5.68$ (d) $5.968$ Solution: Let $x=2$ and $x+\Delta x=1.99$ $\therefore \Delta x=1.99-2=-0.01$ $y=x^{4}-10$ Differentiating both sides with respect to $x$, we get $\frac{d y}{d x}=4 x^{3}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=2}=4 \times(2)^{3}=4 \times 8=32$ $\therefore \Delta y=\left(\frac{d y}{d x}\right) \Delta x$ $\Rightarrow \Delta y=32 \times(-0.01)=-0.32$ Thus, the chang...
Read More →Fill in the blanks with the terms given in the box below:
Question: Fill in the blanks with the terms given in the box below: Nucleus, chromosomes, cell wall, cell membrane, protoplasm cytoplasm, ribosome, cell organelles The outermost layer of plant cells is the (a). beneath which is the (b).The term (c). refers to the jelly-like substance containing all the (d) The (e). contains thread-like structures called (f). Solution: (a) cell wall (b) cell membrane (c) cytoplasm (d) cell organelles (e) nucleus (f) chromosomes....
Read More →Find the sum of the series:
Question: Find the sum of the series: 5 + 7 + 13 + 31 + 85 + . To n terms Solution: In the given question we need to find the sum of the series. For that, first, we need to find the $\mathrm{n}^{\text {th }}$ term of the series so that we can use summation of the series with standard identities and get the required sum. The series given is $5+7+13+31+85+\ldots .+\mathrm{n}$ terms. This question can be solved by the method of difference. Note: Consider a sequence $a_{1}, a_{2}, a_{3} \ldots$ such...
Read More →Read the following statements
Question: Read the following statements and write the appropriate term against each statement. (i) I control the functions of a cell. Who am I? , (ii) I am like a policeman. I do not allow anything and everything to get in and out of the cell. Who am I? (iii) I transfer characters from parents to offsprings. Who am I? Solution: (i) Nucleus controls the functions of a cell. (ii) Cell membrane is like a policeman which does not allow everything and anything into and out of the cell. (iii) Genes pr...
Read More →Is the following statement correct?
Question: Is the following statement correct? If it is wrong, correct the statement. Unicellular organisms do not respire, only multicellular organisms respire Solution: The above mentioned statement is wrong. The unicellular organisms also respire, reproduce and carry all metabolic functions like multicellular organisms. The difference is that all the functions are performed by the single cell in a unicellular organism. Similar functions in multicellular organisms are performed by various organ...
Read More →What are the functions
Question: What are the functions of cell wall in plant cells? . Solution: Cell wall is an additional layer surrounding the plasma membrane in plant cells. Its functions are: (i) to give shape and support to the plant cell. (ii) to provide protection against variations in temperature, atmospheric moisture, etc. (iii) prevents water loss. (iv) controls the rate and direction of cell growth and regulates cell volume....
Read More →The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
Question: The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is (a) $\frac{1}{14}$ (b) $0.01$ (C) $\frac{1}{7}$ (d) none of these Solution: (a) $\frac{1}{14}$ Let $x$ be the radius of the circle and $y$ be its circumference. $x=28 \mathrm{~cm}$ $\Delta x=0.01 \mathrm{~cm}$ $x=2 \pi r$ $y=\pi r^{2}=\pi \times \frac{x^{2}}{4 \pi^{2}}=\frac{x^{2}}{4 \pi}$ $\Rightarrow \frac{d y}{d x}=\frac{x}{2 \pi}$ $\Rightarrow \frac{\Delta y}{y}=\frac{x}...
Read More →Amoeba and Paramecium belong
Question: Amoeba and Paramecium belong to which category of organisms? Solution: Amoeba and Paramecium are unicellular prokaryotic organisms, i.e. they are made up of a single cell and their nucleus is not well defined. No cell organelle is present....
Read More →The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
Question: The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is (a) $\frac{1}{14}$ (b) $0.01$ (C) $\frac{1}{7}$ (d) none of these Solution: (a) $\frac{1}{14}$ Let $x$ be the radius of the circle and $y$ be its circumference. $x=28 \mathrm{~cm}$ $\Delta x=0.01 \mathrm{~cm}$ $x=2 \pi r$ $y=\pi r^{2}=\pi \times \frac{x^{2}}{4 \pi^{2}}=\frac{x^{2}}{4 \pi}$ $\Rightarrow \frac{d y}{d x}=\frac{x}{2 \pi}$ $\Rightarrow \frac{\Delta y}{y}=\frac{x}...
Read More →In a cell, where are the genes
Question: In a cell, where are the genes located? Solution: Genes are located on thread-like structures called chromosomes. These are present inside the nucleus. These are units of inheritance in living organisms, that control transfer of hereditary characteristics from parents to offsprings....
Read More →We do not sense any pain
Question: We do not sense any pain when we clip our nails or cut our hair. Why? Solution: Nails and hair are made up of dead cells. They do not have nerve cells, hence one does not feel pain, when they are clipped or cut....
Read More →The instrument used to observe cells is
Question: The instrument used to observe cells is Solution: Microscope...
Read More →In leaves name the cell organelle
Question: In leaves name the cell organelle and pigment that is responsible for green colour. Solution: The cell organelle is chloroplast and chlorophyll is the pigment responsible for green colour of leaves. It is because of this pigment that sunlight (energy) is captured by plant and photosynthesis takes place....
Read More →The approximate value
Question: The approximate value of $(33)^{1 / 5}$ is (a) 2.0125(b) 2.1(c) 2.01(d) none of these Solution: (a) 2.0125 Consider the function $y=f(x)=x^{\frac{1}{5}}$. Let : $x=32$ $x+\Delta x=33$ $\Rightarrow \Delta x=1$ $y=(x)^{\frac{1}{5}}$ For $x=32$, $y=2$ $\mathrm{AlsO}, \frac{d y}{d x}=\frac{1}{5(x)^{\frac{4}{5}}}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=32}=\frac{1}{80}$ $\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=\frac{1}{80} \times 1=0.0125$ $\therefore(33)^{\frac{1}{5}}=y+\Delta y=...
Read More →The approximate value
Question: The approximate value of $(33)^{1 / 5}$ is (a) 2.0125(b) 2.1(c) 2.01(d) none of these Solution: (a) 2.0125 Consider the function $y=f(x)=x^{\frac{1}{5}}$. Let : $x=32$ $x+\Delta x=33$ $\Rightarrow \Delta x=1$ $y=(x)^{\frac{1}{5}}$ For $x=32$, $y=2$ $\mathrm{AlsO}, \frac{d y}{d x}=\frac{1}{5(x)^{\frac{4}{5}}}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=32}=\frac{1}{80}$ $\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=\frac{1}{80} \times 1=0.0125$ $\therefore(33)^{\frac{1}{5}}=y+\Delta y=...
Read More →Find the sum of the series:
Question: Find the sum of the series: 1 + 5 + 12 + 22 + 35 +... to n terms Solution: In the given question we need to find the sum of the series. For that, first, we need to find the $\mathrm{n}^{\text {th }}$ term of the series so that we can use summation of the series with standard identities and get the required sum. The series given is $1+5+12+22+35 \ldots$ to $n$ terms. This question can be solved by the method of difference. Note: Consider a sequence $a_{1}, a_{2}, a_{3} \ldots$ such that...
Read More →If the solve the problem
Question: If $y=x^{n}$, then the ratio of relative errors in $y$ and $x$ is (a) $1: 1$ (b) $2: 1$ (c) $1: n$ (d) $n: 1$ Solution: (d) $n: 1$ Let $\frac{\Delta x}{x}$ be the relative error in $x$ and $\frac{\Delta y}{y}$ be the error in $y$. Now, $y=x^{n}$ $\Rightarrow \frac{d y}{d x}=n x^{n-1}$ $\Rightarrow \frac{\Delta y}{y}=\frac{n x^{n-1}}{y} d x$ $\Rightarrow \frac{\Delta y}{y}=\frac{n x^{n-1}}{x^{n}} d x=n \frac{\Delta x}{x}$ $\Rightarrow \frac{\Delta y}{y}: \frac{\Delta x}{x}=n: 1$...
Read More →The pressure P and volume V of a gas are connected by
Question: The pressurePand volumeVof a gas are connected by the relationPV1/4= constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is (a) $\frac{1}{2} \%$ (b) $\frac{1}{4} \%$ (c) $\frac{1}{8} \%$ (d) none of these Solution: (C) $\frac{1}{8} \%$ We have $\frac{\Delta V}{V}=\frac{-1}{2} \%$ $P V^{\frac{1}{4}}=$ constant $=k \quad$ (say) Taking $\log$ on both sides, we get $\log \left(P V^{\frac{1}{4}}\right)=\log k$ Differentiating both sides w.r...
Read More →The pressure P and volume V of a gas are connected by
Question: The pressurePand volumeVof a gas are connected by the relationPV1/4= constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is (a) $\frac{1}{2} \%$ (b) $\frac{1}{4} \%$ (c) $\frac{1}{8} \%$ (d) none of these Solution: (C) $\frac{1}{8} \%$ We have $\frac{\Delta V}{V}=\frac{-1}{2} \%$ $P V^{\frac{1}{4}}=$ constant $=k \quad$ (say) Taking $\log$ on both sides, we get $\log \left(P V^{\frac{1}{4}}\right)=\log k$ Differentiating both sides w.r...
Read More →If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume is
Question: If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is %, then the error in its volume is (a) %(b) 2 %(c) 3 %(d) none of these Solution: (c) 3% Let the radius of the cone bex,the height be 2xand the volume bey. $\frac{\Delta x}{x}=\lambda \%$ $\Rightarrow y=\frac{1}{3} \pi x^{2} \times 2 x=\frac{2}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=2 \pi x^{2}$ $\Rightarrow \frac{\Delta y}{y}=\frac{2 \pi x^{2}}{y} d x=\frac{3}{x} \times \lambda x$ $\Rightar...
Read More →If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume is
Question: If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is %, then the error in its volume is (a) %(b) 2 %(c) 3 %(d) none of these Solution: (c) 3% Let the radius of the cone bex,the height be 2xand the volume bey. $\frac{\Delta x}{x}=\lambda \%$ $\Rightarrow y=\frac{1}{3} \pi x^{2} \times 2 x=\frac{2}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=2 \pi x^{2}$ $\Rightarrow \frac{\Delta y}{y}=\frac{2 \pi x^{2}}{y} d x=\frac{3}{x} \times \lambda x$ $\Rightar...
Read More →Find the sum of the series:
Question: Find the sum of the series: 3 + 15 + 35 + 63 +...to n terms Solution: In the given question we need to find the sum of the series. For that, first, we need to find the $n^{\text {th }}$ term of the series so that we can use summation of the series with standard identities and get the required sum. The series given is $3,15,35,63 \ldots$ to $n$ terms. The series can be written as, $\left[2^{2}-1,4^{2}-1,6^{2}-1 \ldots(2 n)^{2}-1\right]$. So, $\mathrm{n}^{\text {th }}$ term of the series...
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