Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: A man sells a bat for Rs 100 gaining Rs 20. His gain per cent is (a) 20% (b) 22% (c) 18% (d) 25% Solution: (d) 25% $\mathrm{SP}=\mathrm{Rs} 100$ $\mathrm{Gain}=\mathrm{Rs} 20$ $\mathrm{CP}=\mathrm{Rs}(100-20)$ = Rs 80 Gain percentage $=\left(\frac{\text { gain }}{\mathrm{CP}} \times 100\right) \%$ $=\left(\frac{20}{80} \times 100\right) \%$ $=25 \%$...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: On selling 100 pens, a man gains the selling price of 20 pens. The gain per cent is (a) 20% (b) 25% (c) $16 \frac{2}{2} \%$ (d) 15% Solution: (b) 25% Let Rs $x$ be the SP of 100 pen $s$. SP of 1 pen $=$ Rs $\frac{x}{100}$ Profit on 100 pen $s=$ selling price of 20 pens $=\frac{20}{100} \times x$ $=\frac{x}{5}$ Now, CP $=$ SP $-$ Profit $=x-\frac{\mathrm{x}}{5}$ $=\frac{4 \mathrm{x}}{5}$ $\therefore$ Profit percent on 100 pens $=\frac{\text { profit ...
Read More →What is the difference in colours
Question: What is the difference in colours of the sun observed during sunrise/sunset and noon ? Give explanation for each. Solution: At the time of sunrise or sunset, the position of the sun is very far away from us (Figure 16). The sunlight travels longer distance through the atmosphere of the earth before reaching our eyes. Scattering of blue light is more than the scattering of red light. As a result of this, more red light reaches our eyes than any other colour. Hence sunset and sunrise app...
Read More →Rajan bought a watch for Rs 1870 including VAT at 10%.
Question: Rajan bought a watch for Rs 1870 including VAT at 10%. Find the original price of the watch. Solution: Let the original price be Rs $x$. VAT $=10 \%$ of Rs $x$ $=\operatorname{Rs}\left(x \times \frac{10}{100}\right)$ $=\operatorname{Rs} \frac{x}{10}$ $\therefore$ Price including $\mathrm{VAT}=\mathrm{Rs}\left(\mathrm{x}+\frac{\mathrm{x}}{10}\right)$ $=$ Rs. $\frac{11 x}{10}$ $\therefore \frac{11 x}{10}=1870$ $\Rightarrow x=\left(1870 \times \frac{10}{11}\right)$ $\Rightarrow x=1700$ $\...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $(x \cos x)^{x}+(x \sin x)^{1 / x}$ Solution: Let $y=(x \cos x)^{x}+(x \sin x)^{\frac{1}{x}}$ $\Rightarrow y=a+b$ where $a=(x \cos x)^{x} ; b=(x \sin x)^{\frac{1}{x}}$ $\frac{d y}{d x}=\frac{d a}{d x}+\frac{d b}{d x}$ $\left\{\right.$ Using chain rule, $\frac{d(u+a)}{d x}=\frac{d u}{d x}+\frac{d a}{d x}$ where a and $u$ are any variables $\}$ $a=(x \cos x)^{x}$ Taking log both the sides: $\Rightarrow \log a=\log (x \cos x)^{x}...
Read More →Why is the colour of clear sky blue ?
Question: Why is the colour of clear sky blue ? Solution: When sunlight enters the earths atmosphere, the atoms or molecules of the gases present in the atmosphere scatter this light. Since wavelength of red colour is larger than the wavelengths of other colours in sunlight, so red colour is scattered least. Violet colour is scattered the most followed by blue, green, yellow, orange and red colours respectively. Our eye is more sensitive to the blue light than the violet light. Therefore, scatte...
Read More →Write the domain and the range of the function
Question: Write the domain and the range of the function, f(x) = |x|. Solution: (i) Domain $|x|$ is defined for all real values. Hence $-|x|$ is also defined for all real values. The domain is R. (ii) Range Range for $|x|$ is $[0, \infty)$ Therefore, range for $-|x|$ is $(-\infty, 0]$....
Read More →Write the domain and the range of the function
Question: Write the domain and the range of the function, f(x) = |x|. Solution: (i) Domain $|x|$ is defined for all real values. Hence $-|x|$ is also defined for all real values. The domain is R. (ii) Range Range for $|x|$ is $[0, \infty)$ Therefore, range for $-|x|$ is $(-\infty, 0]$....
Read More →Why do we see a rainbow
Question: Why do we see a rainbow in the sky only after rainfall ? Solution: Rainbow is the example of dispersion of sunlight. In sky, prism like objects are needed for the dispersion of light. After rainfall, tiny water drops suspended in air act as prisms. Hence, we see a rainbow in the sky only after rainfall....
Read More →Find the single discount equivalent to two successive discounts of
Question: Find the single discount equivalent to two successive discounts of 20% and 10%. Solution: Let the marked price be Rs 100 . Then, first discount on it $=$ Rs 20 Price after the first discount $=\mathrm{Rs}(100-20)$ = Rs 80 Second discount on it $=10 \%$ of Rs 80 $=\operatorname{Rs}\left(80 \times \frac{10}{100}\right)$ $=\operatorname{Rs} 8$ Price after the second discount $=$ Rs. $(80-8)$ = Rs72 Net selling price $=$ Rs. 72 Single discount equivalent to given successive discounts $=(10...
Read More →Is the position of a star as seen
Question: Is the position of a star as seen by us its true position. Justify your answer. Solution: No. Light emitted by distant stars (act as point sources of light) passes through the atmosphere of the earth before reaching our eyes. The atmosphere of the earth is not uniform but consists of many layers of different densities. The layers close to the surface of the earth are optically denser. As we go higher and higher, the density of layers and refractive index decreases progressively. As the...
Read More →Write the domain and the range of the function, f(x) =
Question: Write the domain and the range of the function, f(x) = $\sqrt{x-1}$ Solution: The graph of f(x) is (i) Domain Domain for $\sqrt{x}$ is $[0, \infty)$. Hence, domain for $\sqrt{x-1}$ is $[1, \infty)$. (ii) Range As the range of function $f(x)=\sqrt{x}$ is given by the interval $[0,+\infty)$. The graph of the given function $f(x)=\sqrt{x}-1$ is the graph of $\sqrt{x}$ shifted 1 unit to the right. A shift to the right does not affect the range. Hence the range of $f(x)=\sqrt{x}-1$ is also ...
Read More →Draw a ray diagram showing the dispersion through
Question: Draw a ray diagram showing the dispersion through a prism when a narrow beam of white light is incident on one of its refracting surfaces. Also indicate the order of the colours of the spectrum obtained. Solution:...
Read More →A trader marks his goods at 30% above cost price and allows a discount of 10%.
Question: A trader marks his goods at 30% above cost price and allows a discount of 10%. What is his gain per cent? Solution: Let the CP be Rs 100 . Then, marked price $=$ Rs 130 Discount $=10 \%$ of MP $=(10 \%$ of Rs. 130$)$ $=$ Rs. $\left(130 \times \frac{10}{100}\right)$ $=$ Rs. 13 Now, SP $=(\mathrm{MP})-($ discount $)$ $\quad=$ Rs. $(130-13)$ $\quad=$ Rs. 117 $\therefore$ Gain percentage $=(117-100) \%$ = 17% $\therefore$ The gain percentage of the trader is $17 \%$....
Read More →How will you use two identical prisms
Question: How will you use two identical prisms so that a narrow beam of white light incident on one prism emerges out of the second prism as white light ? Draw the diagram. Solution: Perform an activity to show that the colours of white light splitted by a glass prism can be recombined to get white light by another glass prism.Apparatus required. Two glass prisms made of same kind of glass, a card board having a fine hole at its centre, a white screen.Procedure: Place a card board in front of a...
Read More →A person needs a lens of power -4.5 D
Question: A person needs a lens of power -4.5 D for correction of her vision. (a) What kind of defect is she suffering from ? (b) What is the focal length of the corrective lens ? (c) What is the nature of the corrective lens ? (CBSE Sample Paper 2017-18) Solution: (a) She is suffering from myopia (b) $f=\frac{1}{\mathrm{P}}=-\frac{1}{4.5}=-0.22 \mathrm{~m}=-22 \mathrm{~cm}$ (c) Concave lens....
Read More →Write the domain and the range of the function,
Question: Write the domain and the range of the function, $f(x)=\frac{a x+b}{b x-a}$ Solution: (i) domain $f(x)=\frac{a x+b}{b x-a}$ As f(x) is a polynomial function whose domain is R except for the points where the denominator becomes 0. Hence $x \neq b$ Domain is $\mathrm{R}-\{\underline{b}\}$ (ii) Range Let $\mathrm{y}=\frac{a x+b}{b x-a}$ $Y(b x-a)=a x+b$ byx $-a y=a x+b$ byx $-a x=a y+b$ $x(b y-a)=a y+b$ x =$\frac{a y+b}{b y-a}$ x is not defined when denominator is zero. by $-a \neq 0$ ya/b...
Read More →A dealer gets Rs 30 less if instead of selling a chair at a gain of 12% he sells it at a gain of 8%.
Question: A dealer gets Rs 30 less if instead of selling a chair at a gain of 12% he sells it at a gain of 8%. Find the cost price of the chair. Solution: Let the $\mathrm{CP}$ be $\mathrm{Rs} x$. Then, we have: $(12 \%$ of $\mathrm{x})-(8 \%$ of $\mathrm{x})=30$ $\Rightarrow\left(\mathrm{x} \times \frac{12}{100}\right)-\left(\mathrm{x} \times \frac{8}{100}\right)=30$ $\Rightarrow\left(\frac{12 \mathrm{x}}{100}-\frac{8 x}{100}\right)=30$ $\Rightarrow \frac{4 x}{100}=30$ $\Rightarrow x=\left(30 \...
Read More →How are we able to see nearby
Question: How are we able to see nearby and also the distant objects clearly? (CBSE 2012) Solution: Human eye is able to see nearby and also the distant objects clearly using its power of accommodation....
Read More →A student sitting at the back of the classroom
Question: A student sitting at the back of the classroom cannot read clearly the letters written on the black board. What advice will a doctor give to her ? Draw ray diagram for the correction of this defect. Solution: Doctor will advice the student to wear spectacles havi ng concave lens of suitable focal length or power as she is suffering from myopia. For diagram,...
Read More →If the cost price of 12 pens is equal to the selling price of 16 pens,
Question: If the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent. Solution: Let the $\mathrm{CP}$ of each pen be Rs $x$. CP of 16 pens $=$ Rs $16 x$ SP of 16 pens $=$ CP of 12 pens $=$ Rs $12 x$ i.e., $\mathrm{CP}\mathrm{SP}$ Now, loss $=\mathrm{CP}-\mathrm{SP}$ $=(16 x-12 x)$ $=R s .4 x$ $\therefore$ Loss percentage $=\frac{\text { loss }}{\mathrm{CP}} \times 100$ $=\frac{4 x}{16 x} \times 100$ $=25 \%$...
Read More →Draw ray diagrams each showing
Question: Draw ray diagrams each showing (i) myopic eye and (ii) hypermetropic eye. Solution:...
Read More →Which of the following statement is correct ?
Question: Which of the following statement is correct ? (a)A person with myopia can see distant objects clearly. (b)A person with hypermetropia can see nearby objects clearly. (c)A person with myopia can see nearly objects clearly. (d)A person with hypermetropia cannot see distant objects clearly. Solution: (c). Explanation :Hypermetropia : A person suffering from this defect can see far off objects clearly but cannot see nearby objects clearly. Myopia : A person suffering from this defect can s...
Read More →By selling a flower pot for Rs 322, a man gains 15%.
Question: By selling a flower pot for Rs 322, a man gains 15%. At what price should he sell it to gain 20%? Solution: $\mathrm{SP}=\mathrm{Rs} 322$ Gain percentage $=15 \%$ $\therefore \mathrm{CP}=\left\{\frac{100}{(100+\text { gain } \%)} \times \mathrm{SP}\right\}$ $=$ Rs. $\left\{\frac{100}{(100+15)} \times 322\right\}$ $=$ Rs. $\left(\frac{100}{115} \times 322\right)$ $=$ Rs. 280 Now, desired SP $=\left\{\frac{(100+\text { gain } \%)}{100} \times \mathrm{CP}\right\}$ $=$ Rs. $\left\{\frac{(1...
Read More →Solve this
Question: If $f\left(x+\frac{1}{x}\right)=\left(x^{2}+\frac{1}{x^{2}}\right)$ for all $x \in R-\{0\}$ then write an expression for $f(x)$. Solution: Given, $f\left(x+\frac{1}{x}\right)=\left(x^{2}+\frac{1}{x^{2}}\right)$ Let $y=x+\frac{1}{x}$ $x y=x^{2}+1$ $x^{2}-x y+1=0$ $\mathrm{X}=\frac{-(-y) \pm \sqrt{(-y)^{2}-4(1)(1)}}{2}$ $\mathrm{X}=\frac{\frac{y \pm \sqrt{y^{2}-4}}{2}}{2}$ $\mathrm{f}(\mathrm{y})=y^{2}-2$...
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