A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
Question: A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is(a) 12000 mm3(b) 800 mm3(c) 80000 mm3(d) 120 mm3 Solution: (c) $80000 \pi \mathrm{mm}^{3}$ Letxbe the radius of the sphere andybe its volume. $x=100, x+\Delta x=98$ $\Rightarrow \Delta x=-2$ $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi x^{2}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=100}=40000 \pi$ $\therefore \Delta y=d y=\frac{d y}{d x} d x=40000 \pi \times(-2)=-80000 \...
Read More →A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
Question: A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is(a) 12000 mm3(b) 800 mm3(c) 80000 mm3(d) 120 mm3 Solution: (c) $80000 \pi \mathrm{mm}^{3}$ Letxbe the radius of the sphere andybe its volume. $x=100, x+\Delta x=98$ $\Rightarrow \Delta x=-2$ $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi x^{2}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=100}=40000 \pi$ $\therefore \Delta y=d y=\frac{d y}{d x} d x=40000 \pi \times(-2)=-80000 \...
Read More →Identify the correct statement about cells.
Question: Identify the correct statement about cells. (a) All the cells have nucleus (b) Cells of an organ have similar structure (c) Cells of a tissue have similar structure (d) Shape of all types of cells is round Solution: (c) A tjssue is a group of similar cells that work together to perform a particular function. The other statements in correct form are: Only eukaryotic cells have well-defined nucleus. An organ is a collection of differentfissues. Shape of a cell depends on its function....
Read More →Which of the following statements
Question: Which of the following statements are true for eukaryotic cells? (i) They do not have a nuclear membrane. (ii) They have a well organised nucleus. (iii) They have a nuclear membrane. (iv) Blue-green algae are eukaryotic cells. (a) (ii) and (iv) (b) (ii) and (iii) (c) (i) and (ii) (d) (i) and (iv) Solution: (b) The cells having well defined nucleus containing nuclear material, enclosed by a nuclear membrane are called eukaryotic cells. e.g. Cheek cells. Blue-green algae are prokaryotic ...
Read More →Find the sum of the series:
Question: Find the sum of the series: $\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\ldots$ to n terms Solution: In the given question we need to find the sum of the series. For that, firs, 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 $\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\cdots$ to $\mathrm{n}$ terms ...
Read More →If loge 4 = 1.3868, then loge 4.01 =
Question: If loge4 = 1.3868, then loge4.01 = (a) $1.3968$ (b) $1.3898$ (c) $1.3893$ (d) none of these Solution: (c) $1.3893$ Consider the function $y=f(x)=\log _{e} x$. Let: $x=4$ $x+\Delta x=4.01$ $\Rightarrow \Delta x=0.01$ For $x=4$ $\begin{aligned} y =\log _{e} 4=1.3868 \\ y =\log _{e} x \end{aligned}$ $\Rightarrow \frac{d y}{d x}=\frac{1}{x}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=4}=\frac{1}{4}$ $\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=\frac{1}{4} \times 0.01=0.0025$ $\therefore ...
Read More →If loge 4 = 1.3868, then loge 4.01 =
Question: If loge4 = 1.3868, then loge4.01 = (a) $1.3968$ (b) $1.3898$ (c) $1.3893$ (d) none of these Solution: (c) $1.3893$ Consider the function $y=f(x)=\log _{e} x$. Let: $x=4$ $x+\Delta x=4.01$ $\Rightarrow \Delta x=0.01$ For $x=4$ $\begin{aligned} y =\log _{e} 4=1.3868 \\ y =\log _{e} x \end{aligned}$ $\Rightarrow \frac{d y}{d x}=\frac{1}{x}$ $\Rightarrow\left(\frac{d y}{d x}\right)_{x=4}=\frac{1}{4}$ $\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=\frac{1}{4} \times 0.01=0.0025$ $\therefore ...
Read More →Identify the correct statement.
Question: Identify the correct statement. (a) Tissue is a group of dissimilar cells (b) An organ consists of similar cells (c) Vacuoles are not found in plant cells (d) Prokaryotes do not have nucleus Solution: (d) Prokaryotes do not have a well defined nucleus. The irregularly-shaped region that contains their genetic material is called nucleoid. The other statements in correct form are: Tissue is a group of similar cells. An organ consists of different tissues. Large vacuoles are found in plan...
Read More →While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
Question: While measuring the side of an equilateral triangle an error ofk% is made, the percentage error in its area is (a) $k \%$ (b) $2 k \%$ (C) $\frac{k}{2} \%$ (d) $3 k \%$ Solution: (b) 2k% Letxbe the side of the triangle andybe its area. $\frac{\Delta x}{x} \times 100=k$ Also, $y=\frac{\sqrt{3}}{4} x^{2}$ $\Rightarrow \frac{d y}{d x}=\frac{\sqrt{3}}{2} x$ $\Rightarrow \frac{\Delta y}{y}=\frac{\sqrt{3} x}{2 y} d x=\frac{2}{x} \times \frac{k x}{100}$ $\Rightarrow \frac{\Delta y}{y} \times ...
Read More →While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
Question: While measuring the side of an equilateral triangle an error ofk% is made, the percentage error in its area is (a) $k \%$ (b) $2 k \%$ (C) $\frac{k}{2} \%$ (d) $3 k \%$ Solution: (b) 2k% Letxbe the side of the triangle andybe its area. $\frac{\Delta x}{x} \times 100=k$ Also, $y=\frac{\sqrt{3}}{4} x^{2}$ $\Rightarrow \frac{d y}{d x}=\frac{\sqrt{3}}{2} x$ $\Rightarrow \frac{\Delta y}{y}=\frac{\sqrt{3} x}{2 y} d x=\frac{2}{x} \times \frac{k x}{100}$ $\Rightarrow \frac{\Delta y}{y} \times ...
Read More →Cheek cells do not have
Question: Cheek cells do not have (a) cell membrane (b) Golgi apparatus (c) nucleus (d) plastid Solution: (d) Cheek cells are animal cells. So, there will be no plastids. All other cell organelles such as nucleus, GA, ribosomes, etc are enclosed in the cell membrane of cell....
Read More →Under a microscope Paheli observes
Question: Under a microscope Paheli observes a cell that has a cell wall but no distinct nucleus. The cell that she observes is (a) a plant cell (b) a nerve cell (c) an animal cell (d) a bacterial cell Solution: (d) The cell observed by Paheli is a bacterial cell. It is a prokaryotic cell that has a cell wall (like plants) but no distinct nucleus. A plant cell has a cell wall and a well defined nucleus, whereas in an animal cell, the former is not present. A nerve cell is an animal cell that is ...
Read More →Which of the following feature
Question: Which of the following feature will help you in distinguishing a plant cell from an animal cell? (a) Cell wall (b) Cell membrane (c) Mitochondria (d) Nucleus Solution: (a) A cell wall is the distinguishing feature between a plant cell and animal cell. It is thick wall made up of cellulose around cell membrane that exclusively present only in plant . cell....
Read More →The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
Question: The height of a cylinder is equal to the radius. If an error of % is made in the height, then percentage error in its volume is (a) %(b) 2 %(c) 3 %(d) none of these Solution: (c) 3%Letxbe the radius, which is equal to the height of the cylinder. Letybe its volume. $\frac{\Delta x}{x} \times 100=\alpha$ Also, $y=\pi x^{2} x=\pi x^{3}$ $[$ Radius $=$ Height of the cylinder $]$ $\Rightarrow \frac{d y}{d x}=3 \pi x^{2}$ $\Rightarrow \frac{\Delta y}{y}=\frac{3 \pi x^{2}}{y} d x=\frac{3}{x} ...
Read More →Find the sum of the series:
Question: Find the sum of the series: $\frac{1}{(1 \times 6)}+\frac{1}{(6 \times 11)}+\frac{1}{(11 \times 16)}+\ldots . .+\frac{1}{(5 n-4)(5 n+1)}$ 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 $\left(1 \times 2^{2}\right)+\left(2 \times 3^{2}\right)+\left(3 \times 4^{2}\right)+\ldots$ ...
Read More →Which of the following
Question: Which of the following is not a cell? (a) Red Blood Cell (RBC) (b) Bacterium (c) Spermatozoa (d) Virus Solution: (d) Virus is not considered a cell. It is an exception to the cell theory and cannot survive on its own....
Read More →Find the sum of the series:
Question: Find the sum of the series: $\frac{1}{(1 \times 6)}+\frac{1}{(6 \times 11)}+\frac{1}{(11 \times 16)}+\ldots . .+\frac{1}{(5 n-4)(5 n+1)}$ 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 $\left(1 \times 2^{2}\right)+\left(2 \times 3^{2}\right)+\left(3 \times 4^{2}\right)+\ldots$ ...
Read More →The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
Question: The height of a cylinder is equal to the radius. If an error of % is made in the height, then percentage error in its volume is (a) %(b) 2 %(c) 3 %(d) none of these Solution: (c) 3%Letxbe the radius, which is equal to the height of the cylinder. Letybe its volume. $\frac{\Delta x}{x} \times 100=\alpha$ Also, $y=\pi x^{2} x=\pi x^{3}$ $[$ Radius $=$ Height of the cylinder $]$ $\Rightarrow \frac{d y}{d x}=3 \pi x^{2}$ $\Rightarrow \frac{\Delta y}{y}=\frac{3 \pi x^{2}}{y} d x=\frac{3}{x} ...
Read More →If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
Question: If an error ofk% is made in measuring the radius of a sphere, then percentage error in its volume is (a) $k \%$ (b) $3 k \%$ (c) $2 k \%$ (d) $k / 3 \%$ Solution: (b) 3k%Letxbe the radius of the sphere andybe its volume.Then, $\frac{\Delta x}{x} \times 100=k$ Also, $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi x^{2}$ $\Rightarrow \frac{\Delta y}{y}=\frac{4 \pi x^{2}}{y} d x=\frac{4 \pi x^{2}}{\frac{4}{3} \pi x^{3}} \times \frac{k x}{100}$ $\Rightarrow \frac{\Delta y}{y} ...
Read More →If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
Question: If an error ofk% is made in measuring the radius of a sphere, then percentage error in its volume is (a) $k \%$ (b) $3 k \%$ (c) $2 k \%$ (d) $k / 3 \%$ Solution: (b) 3k%Letxbe the radius of the sphere andybe its volume.Then, $\frac{\Delta x}{x} \times 100=k$ Also, $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi x^{2}$ $\Rightarrow \frac{\Delta y}{y}=\frac{4 \pi x^{2}}{y} d x=\frac{4 \pi x^{2}}{\frac{4}{3} \pi x^{3}} \times \frac{k x}{100}$ $\Rightarrow \frac{\Delta y}{y} ...
Read More →Identify the statement which is true for cells.
Question: Identify the statement which is true for cells. (a) Cells can be easily seen with naked eyes. (b) Insects egg is not a cell. (c) A single cell can perform all the functions in a unicellular organism. (d) The size and shape of cells is uniform in multicellular organisms. Solution: (c) A unicellular organism consists of a single cell that is capable of performing all the functions. The other statements in true form are: Cells cannot be seen easily with naked eyes. Insects egg is a single...
Read More →The thre&Mike structures
Question: The threMike structures present in the nucleus are (a) nucleolus (b) chromosomes (c) genes (d) ribosomes Solution: (b) Chromosomes are the thread-like structures present in the nucleus. They contain genes that function to transfer the characteristics from the parents to the offsprings....
Read More →Of the following parts of a cell
Question: Of the following parts of a cell name the part that is common to plant cell, animal cell and a bacterial cell. (a) Chloroplast (b) Cell wall (c) Cell membrane (d) Nucleus Solution: (c) Cell membrane is the common part of every cell. It encloses the protoplasm, protects the cell, gives the cell its shape and control the entry and exit of substances....
Read More →Paheli accidentally placed her hand
Question: Paheli accidentally placed her hand over a flame and immediately pulled it back. She felt the sensation of heat and reacted due to the action of (a) blood cells (b) skin surface (c) nerve cells (d) nucleus of cells Solution: (c) Nerve cells have a special shape-long and branched (with projections) to receive and transmit message between the brain and other body parts. Thus they help to feel sensations and in responding to them....
Read More →The unit of measurement used
Question: The unit of measurement used for expressing dimension (size) of cells is (a) centimeter r (b) millimeter (c) micrometer (d) meter Solution: (a) The cell membrane controls the entry (movement into the cell) and exit (movement out of the cell) of materials. It also protects and gives shape to the cell....
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